Talk:Eratosthenes/Archive 1

Archive 1

Archive 2

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If you want to mention the various names of the Ptolemy III, please do so on his page, not here.

Okay

I also removed He also assumed these two cities were on the same meridian. His method for computing the Earth's size does not depend on the two cities being on the same meridian. It always works as long as you know the distance of the two cities. The information on the Astronomy online page is incorrect. AxelBoldt

I am not so shure about this. It seems quite accurate. But we shall check this out again. First I have to freshen my memories about all those old measures: stadia, Egyptian ell, Arabic ell, and so forth ... --XJamRastafire 22:54 Sep 19, 2002 (UTC)

He also assumed these two cities were on the same meridian. is a correct statement. He assumed that Earth is a perfect sphere, and he was looking for the circumference of the great circle of this sphere. Meridians are great circles so he thought that Alexandria and Syene were on the same meridian. So he thought that their distance was an arc of a meridian and that he could have found the whole meridian measure with this proportion: -->center_angol_of_the_arc_Alexandria-Syene:Alexandria-Syene_distance=360°:2πr<--- Eratosthenes's little measurements faults were caused (also) by the fact that Alexandria and Syene aren't on the same meridian. dedotombo

---

The measurement of the inclination of the ecliptic with an angle error 7'.

The above confuses me Lir 16:08 Nov 3, 2002 (UTC)

I'll check this soon as possible. You can also put this statement temporarly out from Eratosthenes article. It is hard to see the exact values from these ancient scientists. Also I have Eartosthenes' value for Earth circumference to be 39,690 km, and you put in the article 42,000 km. What is correct? Hard to tell, also. --XJam 16:18 Nov 3, 2002 (UTC)

I find it really hard to tell when somebody responds if they respond on their own page. I dont understand what an angle error 7' means.

We know that the inclination of the ecliptic is 23° 26' 27.77" so his error was 23° 26'+7'=33' or 23° 26'-7'=19'. This statement is okay for me. Please let me know, what you do not understand still. I have to check what was his actual error. +7' or -7'.

I would guess that issue regarding Eartosthenes' value has to do with the conversion from 250,000 stades to kilometers.

Rktect 8/7/05

Ertosthenes results, that make the degree 700 stadia,

imply the circumference of the earth is 252,000 stadia and

would be off by 1 part in 6 if the stadia he were using

were Greek or Roman stadia of 185 m.

If his results were acurate his stadia would have measured 158.57 m.

As it happens this works out to 302 Egyptian royal cubits.

The Egyptians had a very well documented standard of measure called

the khet which was 100 royal cubits in length and

was the side of an 3ht or field called a st3t

In Greek and Roman times the Egyptian fields were generally farmed

in clusters of three with one left fallow,

one plowed and sowed in grain and another planted in hay

for the plow animal.

This means the Egyptians clusters of fields would have been

surveyed by a standard of 300 royal cubits that Eratosthenes

could have found useful in his work.

The calculation is based on the assumption that the Earth is spherical

and that the Sun is so far away that its rays can be taken as parallel.

Summer solstice:

It appears possible that he might have obtained that knowledge

at the library or by observation of an earlier standard.

Also take a look at astronomy and astrophysics I think it should mainly be a disambiguation page. Other's seem to think otherwise. Before I edited it they had large amounts of text which I moved to positional astronomy, history of astronomy, radio astronomy etc. but they want to move it all back-I think thats a bad idea. Lir 16:26 Nov 3, 2002 (UTC)

This is a good idea for shure. I don't know why should be everything on that page.

from activemind.com conversion is: 1 stade = 607 ft or 185 meters (mile = 5280 feet so 1 stade = .11 mile) which would give Eartosthene's value to be 46,000 km Lir 16:27 Nov 3, 2002 (UTC)

Aristotle refers to the calculation of "mathematicians" who had investigated the subject (without naming them) that the earth was 400,000 stades in circumference. This distinction may belong to Eudoxus of Cnidus (ca. 370 B.C.) who also estimated its measurement at 400,000 stades. A calculation of 300,000 stades is credited to Dicæarchus (died 296 B.C.), a student of Aristotle

Thus 5,000 stades x 50 equals 250,000 stades, the circumference of the earth. But as a mathematical ploy, in order to achieve a number divisible by 60 or 360, so as to correlate stades with his subdivisions or degrees, he emended this to 252,000 stades [ a stade, stadion, stadia ), originally the distance covered by a plough before turning, was 600 feet of whatever standard was used]. A conversion to modern units of measure finds Eratosthenes' calculation to be somewhere between 45,007 km (27,967 miles) to 39,690 km (24,663 miles), as compared to actual equatorial circumference of 40,075 km (24,902 miles). Lir 16:30 Nov 3, 2002 (UTC)

Yes I know this. There were three stades in usage at that time as I know. The smallest was 157 m, the largest was 211 m. Many times we take medium value of 172 m. We can also find another value of 184.2 m. We also believe that Eratosthenes' value was 15 % too big. (You wrote 5 %). --XJamRastafire 16:47 Nov 3, 2002 (UTC)

Rktect: 8/7/05

The information mentioned above about stades needs some revision

All stades are subdivisions of a degree, usually like this

1 degree

10 Egyptian schoenus, itrw, atur 1/10 degree = 21,000 royal cubits

20 Persian parasang, 1/20 degree, 30 furlongs

stade, 1/600, 1/500, 1/700 degree

sos, 1/600 stadion,1/600 stadium,1/600 furlong 1/600

foot, pes, pous, remen, short cubit, long cubit

There were the following stades in use at the time

Sumerian 600 sos of 180 m 600 x 180 = 108 km

Egyptian 10 itrw of 700 3ht of 157 m or 3 st3t of 100 royal cubits

Egyptian itrw, atur also = 60 minutes of march = 350 royal cubits

the itrw is one hour of travel on the river

the atur is one hour of travel on land 700 x 157m = 109.9 km

Persian 700 minutes of march = 700 x 158 m =110.6 km = 10 farsang

Eratosthenes 700 minutes of march

Marinus 500 stadia of 222 m = 500 x 222 = 111 km

Ptolomy 500 stadia of 222 m = 500 x 222 = 111 km

Greek 600 stadions of 600 pous = 600 x 185 m = 111 km

Roman 600 stadiums of 625 pes = 600 x 185 m = 111 km

English 600 furlong before 1593 = 600 x 185 m = 111 km

The smallest was 157 m, the largest was 211 m. 

The largest was 222 m = 600 Egyptian remen of 370 mm = 14.56"

Many times we take medium value of 172 m.

It makes absolutely no sense to take a median value

On the distance of 5000 stadia:

7 degrees would be 4200 Greek or Roman stadia so where does the

caravan measure Eratosthenes reports come from?

Where does his standard of stadia measure come from?

How was the length was actually measured. The Nile

itself (along which the passage must have been made) makes a couple of quite significat curves north of Thebes, for instance. How were these compensated for? Also, how were the measurement done? If it was paced -- that would add a significant uncertainty.

Rktect 8/7/05 The length was measured with knotted cords

Each knotted cord was stretched by a gang of rope stretchers

Common lengths would be

the Egyptian hayt or cord of 100 royal cubits = the side of 1 st3t

The Greek plethron of 100 pous

In Sumer the cord might be the side of an iku of 100 kus of 600 mm = 60 m

In Akkad the éše of 10 nundan rods = 120 cubits of 500 mm = 60 m

Another thing: Would you not think a scholar like E. used a well founded value of the stadion? I'm sure the different stadion in different cities was a problem known at the time? As an Egyptian scholar, perhaps E. used the 3 / 5 Egyptian royal cubit definition of the Greek foot, by which we get 188.3 m with an uncertainty of maybe 1 % based on the variation of the cubit standards.

-- Egil 08:32 Feb 14, 2003 (UTC)

rktect 8/7/05

The only good explanation is that he is working in Egyptian units

that dated back to before the Persians arrived in Egypt and before

the time of Alexander let alone Alexandria and Eratosthenes.

The Egyptian value for the itrw or river journey was 21,000 royal cubits

This equated to one hour of travel along the river but also

to 70 units of 3 khet which was defined as 100 Royal cubits.

If his "calculations" were more correct

Eratosthenes stadia would have been 10 itrw of 21,000 royal cubits

The itrw and atur which is equivalent but an hour of march

are measures that have existed in Egypt since the pyramid age.

I had translated this page into chinese ,i think it is okay.But now i have a question:there is a sentense Aswan is in fact slightly north of the tropic

so where is assumption?Is it possible the actor forgot to write the sentense "assuming aswan local on the tropic of the cancer"--heryu 11:13, 8 Dec 2004 (UTC)

"Chaldaean origins"

I removed the "Chaldaean origins" for this native of Cyrene. But a couple of sentences about the Library as the Hellenistic repository for Babylonian astronomy might improve the context of this article, which does need to be cleaned up, though I hesitate to apply one of those stickers... --21:22, 28 July 2005 (UTC)

Content removed from article

Rktect 8/13/05

How about content proposed to be removed from article if cites are not furnished within one week and a pressumption of innocence until proved guilty?

It appears to be original research to a great extent, and besides, it is not formatted properly for a Wikipedia article:

Rktect 8/7/05

What about it appears to be original research?

If you are knowledgable about the topic you should be familiar

with the argument made in metrum and elsewhere that the

stated methodology and measurements do not agree

Which parts would you like to see in the article proper?

The results:

His results, that make the degree 700 stadia,

imply the circumference of the earth is 252,000 stadia and

would be off by 1 part in 6 if the stadia he were using

were Greek or Roman stadia of 185 m.

If his results were acurate his stadia would have measured 158.57 m.

As it happens this works out to 302 Egyptian royal cubits.

The Egyptians had a very well documented standard of measure called

the khet which was 100 royal cubits in length and

was the side of an 3ht or field called a st3t

In Greek and Roman times the Egyptian fields were generally farmed

in clusters of three with one left fallow,

one plowed and sowed in grain and another planted in hay

for the plow animal.

This means the Egyptians clusters of fields would have been

surveyed by a standard of 300 royal cubits that Eratosthenes

could have found useful in his work.

The calculation is based on the assumption that the Earth is spherical and that the Sun is so far away that its rays can be taken as parallel.

Summer solstice:

It appears possible that he might have obtained that knowledge

at the library or by observation of an earlier standard.

On the distance of 5000 stadia:

7 degrees would be 4200 Greek or Roman stadia so where does the

caravan measure Eratosthenes reports come from?

Where does his standard of stadia measure come from?

The only good explanation is that he is working in Egyptian units

that dated back to before the Persians arrived in Egypt and before

the time of Alexander let alone Alexandria and Eratosthenes.

The Egyptian value for the itrw or river journey was 21,000 royal cubits

This equated to one hour of travel along the river but also

to 70 units of 3 khet which was defined as 100 Royal cubits.

If his "calculations" were more correct

Eratosthenes stadia would have been 10 itrw of 21,000 royal cubits

The itrw and atur which is equivalent but an hour of march

are measures that have existed in Egypt since the pyramid age.

Perhaps some if this material can be used in the article proper. -- 80.203.249.114 14:11, 1 August 2005 (UTC)

Reasoning behind revert

I reverted because of large changes to the facts presented, many of which I couldn't verify, ...

Rktect 8/13/05 Did you look?

...and some of which I found that all sources avainable to me agreed were wrong. One specific is the length of the "itrw", which Rktect asserted was 21,000 cubits. Every reference I can find states that it was 20,000 cubits.

While you might find 20,000 Royal cubits in Gardiner with a ?, a better and more encyclopedic methodology might have gotten you further.

"At the beginning of the nineteenth century it was determined that the Egyptian royal cubit is 525 mm. and hence it was concluded that Eratosthenes calculated by stadia of 300 Egyptian royal cubits." [metrum]

Now that is online so certainly available to you but you either didn't find it (bad methodology) or chose not to report it (worse methodology)

I can recognize that as (3) 3ht or fields (Gardiner) of st3t (Gardiner and Gillings)of 100 royal cubits. Why 3 fields? because of crop rotation one field was left fallow and one was used for fodder for the plow animal.

I began writing a series of articles Egyptian fields, khet, st3t, 3ht, cross referenced so you can get there more than one way, to discuss this in case someone wanted to know where the information comes from but you marked it for deletion because you in your wisdom decided that must be original research and after all you would know because you had checked.

"But several authors of the Roman period mention a degree of 700 stadia. This degree value should not be confused with that of Eratosthenes and is based on a stadion of 300 royal cubits of the Pharaonic period; these two points have been made by Letronne. I have reported that the correct Egyptian royal cubit was 525 mm"

Ibid.

Now it also helps to know that Egyptian standards are essentially septenary. so 20,000 royal cubits doesn't fit their system but 300 x 21,000 does.

Additionally, I found much that smacks of original research, such as:

"The exact size of the stadion he used can only be ..."

Rktect 8/13/05 Run the numbers for yourself Ken. There are only a limited set of possibilities to chose from and the commonly accepted choices don't add up. That isn't original research, the discussion goes back centuries.

Aside from that it wouldn't hurt if when you don't know something you might just ask for a cite before reverting or deleting pages.

[Karnak]

"By stadion the Greeks meant either the distance covered in a minute of march or the distance covered in a double minute of march; generally they called stadion the double minute of march corresponding to the division of the day into 12 double hours, but the stadion of 300 feet or one minute of march was also used."

[Metrum]

"The French scholars thought that the calculation performed by Eratosthenes represents an independent figure, but this does not prove to be correct. Kleomedes reports that Eratosthenes calculated the latitude of Alexandria in Egypt and that of Syene at the First Cataract, and found that this distance, which is the entire length of Egypt, would be 1/50 of the circumference of the earth. Eratosthenes would have calculated the distance between Alexandria and Syene as 5000 stadia, so that the circumference is 250,000 stadia.

At the beginning of the nineteenth century it was determined that the Egyptian royal cubit is 525 mm. and hence it was concluded that Eratosthenes calculated by stadia of 300 Egyptian royal cubits. Newton too had tried quite successfully to ascertain the length of the Egyptian royal cubit from the dimensions of the Great Pyramid, in order to interpret Eratosthenes’ datum."

Ancient metrological tables state that the Philetairic or Ptolemaic royal cubit (which is the Babylonian-Egyptian royal cubit according to Boeckh’s terminology) is 9/5 of the Roman foot, so that the figure of Eratosthenes comes to be the usual figure of 75 Roman miles to the degree.

But several authors of the Roman period mention a degree of 700 stadia. This degree value should not be confused with that of Eratosthenes and is based on a stadion of 300 royal cubits of the Pharaonic period; these two points have been made by Letronne. I have reported that the correct Egyptian royal cubit was 525 mm."

"The reconstruction of the system of ancient lineal units allows to confirm the conclusion of French scholars of the eighteenth and early nineteenth centuries that the ancients had achieved a most accurate calculation of the circumference of the earth and that this calculation had been performed earlier than Greek times. The French scholars concluded that all the estimations reported by authors of the Hellenistic and Greek period repeat, according to different stadia, the statement of Aristotle that the mathematikoi had calculated the circumference of the earth as 400,000 stadia. Since the different stadia relate to each other by simple fractions, these scholars concluded that the ancient linear units were all modules of a single basic unit." The result is that a lie is perpetuated because even though it has been questioned many times, some people just prefer to go with whatever the encyclopedia says.

That isn't a good scientific method.

Rktect is currently engaged in mediation whose root was large changes, questionable facts, possible original research, and poorly formatted edits which made reading difficult at best. As an initial "gesture of good faith" he and the other party had agreed (I thought) to a truce on the "weights and measures" front, as a gesture of good faith. I think this is becoming a problem; I suspect that he is not negotiating entirely in good faith as it is usually defined here.

Ken ^{talk|contribs} 04:37, August 13, 2005 (UTC)

Rktect 8/13/05 Mediation was supposed to result in user Egil and those he has contacted to ask to assist him, leaving things at status quo until they could be discussed.

If you and Gene quit reverting pages and systematically marking for deletion the pages and sentences where I am putting the definitions and cites and references for the units involved it would be easier to have the discussion.

I also find you characterization of the issues of the mediation somewhat biased the principal issues were people making changes unilaterally without discussion and enlisting others to make changes to give the appearance of propriety while still violating the spirit of the accord.

If user Egil were negotiating in good faith then those things would not be ongoing and it would be possible to move forward. It certainly makes no sense for one side to be constrained while the other takes advantage of a cessation of hostilities to do irreversible damage.

I'm very concerned that you would characterise a list of books cited as sources as "large changes, questionable facts, possible original research" and that you continue to delete references.

As regards formatting, Wikipedia presents several options for formating which there appear to be a wide range of differing opinions regarding. Some people apparently like to see long bulleted lists, others think bullets should be reserved for emphasis and prefer tables, still others add graphic content which looks pretty but wastes bandwidth, others prefer to include an indented outline. The main page for example uses an indented style for two features and a bulleted style for two features. Culture has two columns and a bulleted sidebar, Geography has two columns and an indented style. If you think there is consensus with no disagreement then why do such a wide variety of styles exist?

Your first reference is by Dieter Lelgemann, who as far as I can see, is also a believer of the Megalithic Yard (see for instance [1]).

[[2]]

IMHO its possible not to accept everything a source says, maintain a good scientific scepticism and still learn some things. In this case I find his paper on Eratosthenes well informed and his paper on the foot which includes a comparison to many well established standards as well as Thom's Megalithic remen not so far over the edge as to raise any doubts about his credentials.

Like Thom and to a degree Stechhini, he makes his claims based on doing number magic on a lot of measurements. It is bad science, as I have pointed out before.

Nothing I can find in either article leads to that conclusion. He says his findings are the results of taking field measures. If that is what you think equates to magic and bad science then you need a refresher course in logic.

Your second reference makes me none the wiser. You cannot just assume that an accurate measurement of the linear distance between the cities were available in Alexandria library, without any evidence on how that measurement was obtained.

I'm not assuming anything. I can look at Herodotus who comes along a bit earlier than Eratosthenes and find the data right there in Book 2. How do you explain that? I can find it in the campaign records of the 18th dynasty and in the Wilbour and Rhind papyri. If your real question is how that measurement was obtained, the fact is the Egyptians surveyors are famous for having measured everyting with knotted cords. Amarna, a new city built in the 18th dynasty exactly midway between Alexandria and Syene has boundary stele giving the distance between the town limits.

Finally, your sources gives no regard to the other factors in the error budget of the entire calculation. Let me remind you of 4 very important factors:

• • Measuring the actual distance between the two cities as the crow flies (the road between them is along the Nile, which is not a straight line)

Any elementary course in surveying will tell you how to use baseline offsets and triangulation.

• • Aswan is NOT on the tropic of cancer as E. assumed

• • Aswan and Alexandria are NOT on the same meridian as E. assumed (they are in fact about 3 degrees separated, a very significant factor)

• • E. did not measure the angle at Alexandria entirely correctly

Did Eratosthenes measure the angle? or, did he just read about what someone else had done in the library

So doing the numbers game on just one of these factors, the definition of a stadion, to make the numbers fit for one of these factors is plain ridicule. -- Egil 17:22, 22 August 2005 (UTC)

Your lack of really basic knowledge about standards of measure is revealing. Go to the library and look it up in Gardiner who is a pretty much unimpeachable source for Egyptian measures. 1 khet is 100 royal cubits and the side of a field. 1 itrw is a multiple of a khet. Gardiner estimates its in the range of 20,000 royal cubits but since all the Egyptian measurement systems are septenary 21,000 royal cubits is a better number. 21,000/700 stadia is a unit of 300 royal cubits. Refering to Salley L.D. Katary "Land Tenure in the Rameside Period" Kegan Paul International ISBN0710302983, Its evident that since "all the land in Egypt is measured either in aroura of 2/3 acre or mh t3 land cubits of 1/2 acre", all the land is measured.Rktect 17:07, August 23, 2005 (UTC)

Sorry for the delay, but I fell off my chair, laughing. Do you really believe in the maze of absurdities you are producing? You produce enough material for an entire congress, as they said in Fawlty Towers.

Let me just add a few comments that hasn't been mentioned before:

• The Egyptian system is not septenary. There is only one occurence of the factor 7: the number of palms in a royal cubit.

• • • All of Egyptian mathematics including its measures is septenary.

"The Egyptian measurement system was septenary in nature, that is, based on

the number 7 and its multiples. Septenary units proved to be convenient in practical reckoning. They also used a nondecimal system based on the number 11. By combining calculations by the factor of 7 and calculations by the factor 11, one could solve practically, a host of geometric problems involving irrational numbers J2, /3, and TT. For example, the circumference of a circle was computed as 22/7 of its diameter equalling 3+1/7 = 3.142857, a very good approximation of n-. Thus the number 7, they observed, was the key to the dimensions of Egypt itself and the link between the shape and structure of Egypt and the order in the universe."

[septenary]

The Egyptians worked their calculations using unit fractions. Gillings "Mathematics in the Time of the Pharoahs" p 99 discusses line 12 of the 4th group of the Egyptian Mathematical Leather Roll.

"The number 7, Line 12 of the 4th Group is perhaps the most interesting of all the 26 entry's of the EMLR." "The number 7 was constantly before the Egyptian scribe for in his multiplication based upon the method of continued doubling (and halving in division), the sequence 1 + 2 + 4 = 7 appeared frequently. Furthermore the Egyptian table of length was 4 digits or fingers = 1 palm, 7 palms = 1 royal cubit, hence 28 digits = 1 royal cubit, at once from this the scribe has 1 digit = '28 cubit, 2 digits = '14 cubit, 4 digits = '7 cubit, 7 digits = '4 cubit. so that 4 + 2 + 1 = 7. in digits then '7 + '14 + '28 = '4 in cubits. Establishing this important relationship between unit fractions might very well have been a useful and regular teaching point in the scribal schools.

"1. The scribe in RMP 34 shows that 4 x (1 '2 '4) = 7 he then writes '7 of (1 '2'4) = '4

whence '7 '14 '28 = '4

"2. Since from ordinary multiplication with integers 1 + 2 + 4 = 7, dividing throughout by 7 (using the recto table, where 2/7 = '4 '28 and hence 4/7 = '2 '14) gives '7('4 '28)('2 '14) = 1

rearanging this is ('2 '4)( '7 '14 '28) = 1 noting that '2 '4 '4 = 1 subtract '2 '4 from each side whence '7 '14 '28 = '4

"3. Using a reference number, (here obviously 28)the reasoning is '7 =4, '14 = 2, '28 =1 then adding '7 '14 '28 is 7 which applied to 28 is '4

" 4. The EMLR group slightly extended is '4 '12 = '3, '5 '20 = '4, '6 '30 = '5, '7 '42 = '6

Doubling the last equality gives '7 '14 ('42 '84) = '6 '12 hence '7 '14 '28 = '4 for both '42 '84= '28 and '6 '12 = '4 are members of the second group in which the second term is always the double of the first."

To make a long story short this allowed the Egyptian scribe to use unit fractions to work with geometric and arithmetic progressions, the fibonicci series, find the area of a semicylinder and a hemisphere, and form equations of the 1st and 2nd degree.

• Gardnier refers to a measure of 20,000 royal cubits, but since 21,000 better fits your purpose, you claim it is a better number because it is divisible by seven! Excuse me, but exactly what are you smoking?

" Both 20,000 rc and 21,000 rc could be supported by cites to scholarly opinion."

Generally primary sources are prefered to secondary sources.

The Primary source is Herodotus who is the one telling us the Greek schoenus is a measure of Egyptian origin equal to 60 furlongs. The English furlong is used to translate the original Greek term for a stadion of 600 pous of 304.8 mm or 185m . 60 x 185 m = 11100 m. The royal cubit is 525 mm so there are 21,000 rc or 210 rods of cord in the Greek Schoenus.

Gardiner says the itrw is a schoenus. This makes it a lot easier to support 10 rods of cord = 21,000 rc, than the 20,000 rc "estimate" in the Egyptian itrw. A second point in support of this would be the Egyptian preference for septenary numbers in their mathematics.

• Gardiner "Egyptian Grammar" § 266 p 199 is often cited. " In citing Gardiner it should be taken into account that while the Grammer is a definitive work in the field it was written in 1927 and is in its 3rd edition, most of its cites are c 1869-1907 and some things have been studied in more detail in the interim and its primary focus is grammar rather than mensuration.

Gardiner "Egyptian Grammar§ 266 p 199 says" The chief multiple of the cubit was the ht rod of 100 cubits, also called ht n nwh rod of cord." "I made a wide road, (lit. made wide a road)for my offerings considting of 21 rods of cord, ie 2,100 cubits. " swsh n i w3t n wdhw i m ht n nhw 21 " " 3ht n ht 10 r ht 2 a field of 10 rods"

We have 2,100 cubits and decimal multiples of rods of cord.

" Gardiner § 266 p 199 continues " A much larger linear measure was the itrw, river measure, (see AZ 41,58) the Greek schoenus, now estimated on good grounds at 20,000 cubits = 10.5 km" (Borschardt, Lehmann Haupt c 1907)

Some secondary sources cite this as "the itrw, river measure, 20,000 cubits = 10.5 km".

You can go there if you want to, but my thinking is if you do, that demonstrates some serious problems with your methodology. You will have found it necessary to neglect the primary source altogether and because you havn't looked at the primary version of the secondary source you will be neglecting some substantive portions of that.

" Gardiner § 266 p 199 continues. "However in one place a smaller itrw occurs in conjunction with the ht rod and with two fractions of this which we shall find below as measures of area." "The distance between stela and stela on the hill east of Akhenaten itrw n itrw 6 ht rmn hsb mh 4 makes 6 itrw 1 3/4 rods and 4 cubits. For itrw n makes see § 422, 3."

Another way to read it is that this itrw is one of 6 ht(cord of 100)rmn and that this cord of rmn uses the rmn (diagonal of the square) of 4 mh. Gardiner § 266 p 200 discussion of area " st3t, the Greek Aroura, this was a measure of 1 square khet or 100 cubits squared. A measure of ten arouras is written lit thousand, more fully h3 t3. an abreviated writing is 3ht h3 2, st3t 2 twenty two arouras of field)"

• Instead of assuming that the Greek scholar Eratosthenes would use some Greek stadion, you invent an Egyptian stadion of 300 royal cubits, from thin air, because it fits your purpose.

• Generally whenever the Greeks and Romans use a stadia measure it is a division of a degree, either 185m, 222m, or 157.5m. The number of pous in the stadia, the number of stadia in the degree and the length of the pous multiply out to 111 km. That is a testable hypothesis.

  Greek stadion = 600 pous = 185 m

  600 stadions = 1 degree = 111 kmRoman stadium = 625 pes = 185 m

  600 stadiums = 1 degree = 111 km

  The Egyptian Degree

  1 cord of ht = 100 royal cubits = 1 khet =52.5 m

  1 cord of 3ht = 3 st3t of 100 royal cubits = 157.5 m

  1 itrw = 210 cords of ht = 70 cords of 3ht = 21,000 royal cubits = 11.025 km

  1 Egyptian degree = 700 cords of 3ht = 10 itrw = 110.25 km

  1 itrw is 1 hours river journey

  1 atur is 1 hour of March

  1 Egyptian Minute of March is 350 royal cubits of 525 mm = 183 m

  The Ptolomaic stadia is divided into remen instead of pous

  in Egypt Remen had always been used for land surveys.

  1 Ptolomaic Degree = 500 stadions = 111 km

  111 km divided into 500 stadions of 600 remen of 14.7" = 222m

  Erathosthenes Degree

  1 Persian degree = 700 stadia = 111 km

  10 Egyptian schoeni = 20 Persian parasangs = 600 furlongs

  1 Persian stadia = 157.5 m = 3 Egyptian st3t

• You refer to Herodotus, as if some riddle related Eratosthenes can be explained there. In describing the geography of Egypt, Herodotus simply mentions a number of distances within Egypt. That's it. His form is very clear and impossible to misunderstand.

The Primary source is Herodotus who says the Egyptian schoenus (itrw) is 60 stadions

Below you will see cites that each stadion is 600 Greek feet = 185 m. (pous)

The Egyptian itrw is thus 60 x 185 m = 11.1 km

If that's true then the Egyptian itrw like the Greek schoenus is geocommensurate.

Now if you were knowledgable enough to recognize those numbers your brain would be screaming...

But wait !!! How does Herodotus manage to guess the correct Great Circle circumference?

Eratosthenes hasn't made his calculation yet.!!!

The Egyptian royal cubit is 525 mm, 525 x 21,000 =11.025 km

You do the math, 20,000 royal cubits doesn't work.

Let me also warn against "the opinion of the many" when it comes to facts.

You need to check facts even when everybody agrees with you .

I like the following source but it is not without error.

H Arthur Klein "World of Measurement" Simon and Schuster, 1974 SBN 671-21565-5 Chapters 4-9 in Particular.

p 55 "The digitus in and around Rome was about 1.854 cm or .73 inch long. It was related to the largest Roman length units by an interesting sequence of ratios. (Aproximate metric equivalents are given in parenthesis)

4 digiti = 1 palmus (7.4 cm)

4 palmi = 1 pes (29.5 cm)

5 pes = 1 passus (1.48 m)

125 passus = 1 stadium (184.5 m)

8 stadia = 1 milliare (1476 m)

p 60 "To sum up the average or typical short pes (foot) of Rome measured 29.6 cm.

p 61 " The Greek Digit 1.84 cm was close to the the Roman digitus (1.845 cm)

1 orguia = 1.84 m

1 amma = 10 orquias = 18.4 m

1 digit based stadion = 10 ammas = 184.5 m"

p 69 " Arnold's Customs of London appeared about 1500. It contains the following sequence for which we have substituted Arabic for Roman numerals. The length of a barley corn 3 tymes makes an ynch and 12 ynches make a fote and 3 fote make a yerde and 5 quarters (of the yerde) make an elle, 5 fote make a pace, 125 pace make a furlong and 8 furlong make an English Myle. Thus in 1500, 1 ell = 3.75 feet; I furlong = 125 x 5 = 625 feet; and 1 mile = 625 x 8 = 5000 feet."

p 70 "The old English leauge was even longer, about 3 statute miles or 4830 m."

p 71 "The Greek stade (stadium) has been equated with 600 Greek "feet"

[Greek Lengths]

I like Perseus but it is not without error in English translations from Greek

The only way to be sure you are getting the right information is to do your own field work, to learn the languages and scripts and read the originals yourself

[[http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.01.0126:book=2:chapter=7:section=1

Herodotus from Perseus]]

VI. autis de autês esti Aiguptou mêkos* to para thalassan hexêkonta schoinoi*, kata hêmeis diaireomen einai Aigupton apo tou Plinthinêteô* kolpou mechri Serbônidos* limnês, par' hên to Kasion oros teinei: tautês ôn apo hoi hexêkonta schoinoi eisi. [2] hosoi men gar geôpeinai eisi anthrôpôn, orguiêisi memetrêkasi tên chôrên, hosoi de hêsson geôpeinai, stadioisi, hoi de pollên echousi, parasangêisi, hoi de aphthonon liên, schoinoisi. [3] dunatai de ho parasangês triêkonta stadia, ho de schoinos, metron eon Aiguption, hexêkonta stadia.

VI. Further, the length of the seacoast of Egypt itself is sixty “schoeni”1 --of Egypt, that is, as we judge it to be, reaching from the Plinthinete gulf to the Serbonian marsh, which is under the Casian mountain--between these there is this length of sixty schoeni. [2] Men that have scant land measure by feet; those that have more, by miles; those that have much land, by parasangs; and those who have great abundance of it, by schoeni. [3] The parasang is three and three quarters miles, and the schoenus, which is an Egyptian measure, is twice that.

Stecchini can be a great source of things to check out. If you distrust him and attempt to prove him wrong by checking his facts you will definitely learn a few things in the process. For just one example take references to a Roman degree of 75 miles. Check that out.

"Through medieval times there had been preserved the memory of the Roman calculation of the meridian of degree as 75 Roman miles."

"Seventy-five Roman miles indicate a degree of 110,979 m. "

"The common practice of Roman times was to divide the Roman mile not into 10 stadia of 600 Roman feet, but into 8 stadia of 600 artabic feet, equal to 625 Roman feet."

"The artabic foot is particularly fitted to the calculation of geographic distances, since 100 such feet are equal to a second of degree. Hence a plethron of 100 artabic stadia fits exactly into the sexagesimal division of the degree. The Persian parasang, equal to an hour of march, is equal to 18,000 artabic feet, and is divided into the triple unit called milia in Roman times; since there are 20 parasangs to a degree, there are 60 milia to a degree."

"The corresponding degree would be the one of 75 Roman miles of 20 parasangs."

"all these figures express in different ways the value of 75 Roman miles or 20 parasangs to the degree."

"Since the Greeks before the time of Aristotle did not possess the state organization necessary to proceed to the measurement of the degree, it follows that the degree had been calculated before Greek times. If the degree had been calculated before Greek times, it follows that it was not the Greeks that discovered that the earth is a sphere."

"Kleomedes reports that Eratosthenes calculated the latitude of Alexandria in Egypt and that of Syene at the First Cataract, and found that this distance, which is the entire length of Egypt, would be 1/50 of the circumference of the earth. Eratosthenes would have calculated the distance between Alexandria and Syene as 5000 stadia, so that the circumference is 250,000 stadia. At the beginning of the nineteenth century it was determined that the Egyptian royal cubit is 525 mm. and hence it was concluded that Eratosthenes calculated by stadia of 300 Egyptian royal cubits."

"Ancient metrological tables state that the Philetairic or Ptolemaic royal cubit (which is the Babylonian-Egyptian royal cubit according to Boeckh’s terminology) is 9/5 of the Roman foot, so that the figure of Eratosthenes comes to be the usual figure of 75 Roman miles to the degree."

"But several authors of the Roman period mention a degree of 700 stadia. This degree value should not be confused with that of Eratosthenes and is based on a stadion of 300 royal cubits of the Pharaonic period; these two points have been made by Letronne. I have reported that the correct Egyptian royal cubit was 525 mm., but it was at times computed as 524. mm. and at times as mm. Assuming a cubit of 525 mm. the degree would be 110,250, and assuming a cubit of 526.3 mm. It would be 110, It is easy to see why the figure of 700 stadia to the degree was chosen: it well fits the pattern of septenary reckoning in the Egyptian royal cubit.""

[[http://www.metrum.org/measures/measurements.htm

I would propose that the best way to handle the information that needs to be there about the history of the Mile, who invented it, where and when, how long was it to begin with, what else has it been called, how has its definition changed over the years, is to use the names of the arcane units that will be missed by somebody who just wants to know about a statute mile but still be there for somebody who really really wants to know everything about the mile in excruciating detail and be able to see a list of footnoted cites for each fact that don't refer back to secondary sources.

Might I suggest that you familiarize yourself with Occams Razor. Then, read what the National Geodetic Survey has to say about the matter at hand: [3]

Have a splendid day. -- Egil 19:23, 23 August 2005 (UTC)

PS: Although I had a hard time believing it, it seems you have found some competition: See [4]

I think I'm going to give up on you Egil, you can't admit when you are wrong

and you consider math skills pseudoscience. Rktect 23:02, September 5, 2005 (UTC)

Fraction of the circumference

Wasn't the number Eratosthenes actually used 1/50 the circumference of the Earth, rather than 7 degrees? Sure, lots of commentators have rounded that off to 7 degrees, but that isn't what he used, is it? Gene Nygaard 15:44, 22 August 2005 (UTC)

Correct: 1/50, which translates to 7.2 degrees. The actual value is 7.08, so the measurement of the angle was within an accuracy of 2%. -- Egil 03:49, 23 August 2005 (UTC)

The number Eratosthenes used was 700 stadia of 300 royal cubits to a degree, or 252,000 stadia to the earths great circle. This was later rounded off to 250,000.

This was computed based on a supposed measure of the distance between Alexandria and Syene as 5000 stadia which is reported by Herodotus in Book II of his History. 7 degrees of 700 stadia would be 4900 stadia implying the cities were established to a geo-commensurate standard.

700 stadia of 300 royal cubits is 10 Egyptian itrw of 21,000 royal cubits or 110.25 km to a degree and 39690 km to the circumference. That is not a bad value, just slightly off from the Roman value of 111.0 km

The Egyptian royal cubit as a standard of measure goes back to before the pyramids and the atur is used in the campaign reports of the 18th dynasty. Herodotus reports on the schoenus as being an Egyptian measure and gives its value as 60 stadia or 1/10 degree. Rktect 10:17, August 23, 2005 (UTC) [Egyptian geo ma3t ry] Rktect 10:22, August 23, 2005 (UTC)

Who "rounded [it] off to 250,000 stadia"? When? Where do we find that 252,000 number from Eratosthenes? Gene Nygaard 13:52, 24 August 2005 (UTC)

Maybe the best question is what numbers did Cleomedes use, in the earliest surviving description of Eratostheses work, some two to six centuries afterwards? Gene Nygaard 13:56, 24 August 2005 (UTC)

A very plausible explanation I've seen has it the other way around, and it seems quite logical. 5000 stadia and 1/50 cirle would certainly give a result of 250,000 - and this was subsequently adjusted to 252,000 - a more convenient number for circle measures at the time since it was divisable by 60. (Btw, the 360 degree division of the circle was not used at the time of E.). But of course like anything connected to this, we must be aware that we do not have any first hand sources, so this is a plausible explanation. -- Egil 16:04, 24 August 2005 (UTC)

Latest Revert

I've just reverted Rktect's latest changes, primarily because they are POV. They describe opinions that various ancient people are supposed to have held - without any supporting sources. I also was not impressed by the 'ad hominem' attack on Egil's goodwill. Ian Cairns 01:43, 24 August 2005 (UTC)

My apologies - I did not set a 'minor edit' on the reversion - but that is how it appears in the history. Ian Cairns 01:47, 24 August 2005 (UTC)

I just discovered that the method of Eratosthenes measurement is also clearly described in the article History of Geodesy. This article is from a very reliable source indeed. There is no point in repeating the same description twice in Wikipedia, so I simply suggest that we leave out the explanation here, and instead refer to the other article. -- Egil 06:31, 24 August 2005 (UTC)

Some comments from Rktect moved from User_talk:Icairns:

Here is some feedback Ian. Please consider it a formal complaint and request for protection. I'm hoping that I have stated the facts in a way that is NPOV

As a person with NPOV yourself I'm sure you would be suprised if you were to begin by counting how many times Egil, Ken Gene, Drini and Zoe have reverted a page I have attempted to add some content to since Aug 5.

Please let me know how you would with NPOV account for their collective reversions of these pages being at so much higeher a rate than the rest of Wikipedia combined.

I'll give you the benefit of the doubt and allow your reverts are intended to restore what you consider a better page.

I'm sure that the several cites of other people who agree that Eratosthenes could not have made the measurements attributed to him escaped your notice.

I also doubt that you considered how the effect of your revert is to leave the article with one point of view (POV) in place having systematically removed all others.

Its hard to make that case for someone who repeatedly reverts references and wikification. As Drini points out it is not just him but that doesn't make the situation any better.

This began with Egil who apparently has a strong POV regarding what he speculates but has yet to prove, might be pseudo science and original research.

I entered mediation with Egil but it failed when he continued to recruit people to act on his behalf. The people Egil recruited (Ken, Gene, Drini and Zoe) now act together with Egil to take actions that remove cited content from Wikipedia and whose consensus for action lies chiefly among themselves.

This particular bit of information being spread about Egil recruiting people is completely misleading and has no grounds, I think it's hard for Rktect to believe that several people can act independently and disagree with his positions. -- < drini | ∂drini > 16:03, 24 August 2005 (UTC)

• When the same group of people vote for deletion on every standard of measure page and account for 26 of 27 votes to delete on those pages and vote to delete a total of over 30 pages started by the same user and collectively account for more than 400 separate attacks on that one user all I can say is thta when it is connected in series it no longer a parallel circuit. Rktect 00:31, August 31, 2005 (UTC)

Or it can also mean that the single user is so stubborn to realize he is wrong. -- (drini|☕) 00:52, 31 August 2005 (UTC)

They (Egil, Ken, Gene, Drini and Zoe) routinely make accusations of pseudo science and original research based on speculation and a lack of basic background in the primarily mensurational topics they attack.

As a group they have have a track record of marking for deletion a large number of pages that they revert in concert to avoid the three revisions rule, systematically deleting content, removing images, removing wikification, removing references and falsly acuse of copyright infringements.

If you refer to [5] then the copyvio is not a false statement. It's taken from [6] where it states:

Copyright Screen prints may be made of these maps for non-commercial educational and private purposes. Written permission must be obtained in advance to reproduce any digital material from the Library's collections, whether in hard copy or electronic forms.

First, obtaining written permission doesn't mean that you just copy and paste that paragraph. It means you need to provide a real paper permission form. And second, after the ruling of Jimbo a few months ago, free for noncommercial and educational is not free enough for wikipedia. Read [7] where it clearly states that noncommercial and "with permission only" MUST be deleted in sight. -- < drini | ∂drini > 16:03, 24 August 2005 (UTC)

Whenever attacked they also defend eachother in concert. Rktect 02:47, August 24, 2005 (UTC)

Thanks for your comments, which I've moved back to the relevant article's discussion page.

It is clear thay you, Egil, Kem, Gene, Drini, Zoe and I all have some common interests in the same articles. It is also clear that everyone has their own idea of what would improve these articles. This is no secret, and is how Wikipedia progresses. Everyone should be allowed to express their own ideas (as far as possible, within Wiki policies and guidelines). Then, with edits, reversions, new edits, etc. a consensus article should build. What I have seen over the past few weeks is some users working to a similar line. You have stated that these users are working in concert. My view, for what it is worth, is that they are working independently, but in parallel, with similar standards of what constitutes a good Wikipedia article - I do not believe there is any action in concert and have seen no evidence. As a comparison, I created a number of categories higher up in Wikipedia recently - several hours work - and these were rejected by other Wikipedians. They were formally considered for deletion and have been deleted. I have accepted this and their goodwill. The time I spend on Wikipedia is important to me and I cannot justify spending further time revisiting such areas where there is clear consensus by other Wiki users that my contribution was incorrect or just not acceptable. It happens - I deal with it.

My recent reversion in this article was because you included a full discussion of various Egyptian units of measurement (which made it start to look like several of your previous article edits), which did not seem immediately relevant to this article; you ascribed unsourced opinions to Eratosthenes and your edit comment was a clear personal attack on another Wiki user.

The policy for protecting articles is described in Wikipedia:Protection_policy. Note that Admins should not protect articles in which they have been involved (reversions, etc.) - so I'm ineligible. I'm not aware of any protection for users, which is what I understood that you requested. Ian Cairns 07:20, 24 August 2005 (UTC)

Time to remove the disputed tag?

Due to the finding of the arbitration commity (see Wikipedia:Requests_for_arbitration/Rktect#Remedies) there should be an opportunity to reach sufficient consensus so that the disputed tag can be removed. Anyone disagrees? --Egil 17:09, 22 October 2005 (UTC)

What is or was disputed? --Bubba73 (talk) 00:06, 23 October 2005 (UTC)

Afaik only contributions from Rktect, see Wikipedia:Requests_for_arbitration/Rktect/Evidence. I just want to make sure there is nothing else. -- Egil 00:35, 23 October 2005 (UTC)

Things appear to be adequate. Lose the tag already. --Mashford 19:58, 20 November 2005 (UTC)

cleanup and disputed

Well, someone had to do it... :) So I started. I think I've merged most new content, left some out. For instance:

"There are two theories concerning Plato's machine..."

because that's not related to Eratosthenes life at all (it's about doubling the cube which rktect was pushing) and because the latter part it's taken verbatim from another website (which is mentioned, but still it's copyvio). I could use some help to put in shape the earth's measurement section. I also removed the part taken verbatim from the math biographies page at the Erastothenes contributions section (for the same reasons outlined above) I finally took out the Strabo thing since I couldn't really understand its relevance (maybe on the entry of Strabo if there is one wold be more appropiated). --( drini's _vandalproof page ☎ ) 17:03, 30 November 2005 (UTC)

(1) Add a link to the famous map? (2) The map has a mystery

(I offer apologies in advance if i'm not adding my comment properly.)

(1) The article describes one of Erato's important contributions as, "A map of the entire known world". Such described map seems to be the map displayed at <http://en.wikipedia.org/wiki/Image:Iran.jpg#filelinks>; such displayed map is also shown at <http://en.wikipedia.org/wiki/Persia> and is there attributed to Erato. I don't know how to cite that link in the Erato article, so maybe someone else will do it. Thanks.

(2) The displayed map has words in English, such as "Northern Ocean". So Erato did not write such words on the map that is attributed to him. (Erato probably wrote Greek, I gather from the article.) So perhaps the English words were added centuries after Erato drew the map?? Bo99 23:11, 1 March 2006 (UTC)

A drawing would help

I think, a drawing would help to understand the method of Eratosthenes. Who can make and insert it? --84.136.239.196 01:23, 1 May 2007 (UTC)

"He also made what he thought was a map of the Earth."

The above text appears in the first paragraph - it implies that Eratosthenes was somehow wrong, and that he hadn't actually created a map of the Earth. I think it needs better wording - just because it wasn't particularly accurate, doesn't make it any less a map of the Earth. David 10:34, 23 May 2007 (UTC)

Fleet of Circumnavigation

The report should at least be mentioned of a fleet equipped by Eratosthenes in 232 BC to circumnavigate the Earth heading East through the Indian Ocean and reaching the Isthmus of Panama. The crew was Cyrenaican (Libyan), captain Rata and navigator Maui. Inscriptions around the Pacific and Maori Legends tell of events. The controversial name of Barry Fell, who grew up with Maori children, is attached to this. This reference is in Italian: http://www.liutprand.it/Eratost.htm hgwb 19:17, 9 June 2007 (UTC)

5000

In the text, in an article by Rawlins, "5000" appears twice. In the original, it appears once. —Preceding unsigned comment added by 86.141.242.167 (talk) 13:09, 22 December 2007 (UTC) This depends on the computer used.

(re)sources

You may want to check this passage from The Story of Geographical Discovery How the World Became Known by Joseph Jacobs, at []=112130 gutenberg. --MATIA 22:21, 30 August 2005 (UTC)

Two passages from John Lord:

• []=42620 http://www.gutenberg.org/catalog/world/fulltext-context?fulltext=eratosthenes&fk_files[]=42620
• []=11535 http://www.gutenberg.org/catalog/world/fulltext-context?fulltext=eratosthenes&fk_files[]=11535

By William Stevenson, A General History and Collection of Voyages and Travels - Volume 18

• []=99196 http://www.gutenberg.org/catalog/world/fulltext-context?fulltext=eratosthenes&fk_files[]=99196

Williams, Edward Huntington, Williams, Henry Smith, History of Science, a — Volume 1

• []=38860 http://www.gutenberg.org/catalog/world/fulltext-context?fulltext=eratosthenes&fk_files[]=38860

Apollonius Rhodius,

• []=36838 http://www.gutenberg.org/catalog/world/fulltext-context?fulltext=eratosthenes&fk_files[]=36838

--MATIA 22:56, 30 August 2005 (UTC)

beta

ERATOSTHENES, "THE SURVEYOR OF THE WORLD" from Williams' A History of Science gutenberg 1hci10.txt

An altogether remarkable man was this native of Cyrene, who came to Alexandria from Athens to be the chief of Ptolemy Euergetes. He was not merely an astronomer and a geographer, but a poet and grammarian as well. His contemporaries jestingly called him Beta the Second, because he was said through the universality of his attainments to be "a second Plato" in philosophy, "a second Thales" in astronomy, and so on throughout the list. He was also called the "surveyor of the world," in recognition of his services to geography. Hipparchus said of him, perhaps half jestingly, that he had studied astronomy as a geographer and geography as an astronomer. It is not quite clear whether the epigram was meant as compliment or as criticism...

Kerr's General History and Collection of Voyages and Travels gutenberg 13606-8

Ptolemy Euergetes was particularly attentive to the interests of the library at Alexandria. The first librarian appointed by Ptolemy the successor of Alexander, was Zenodotus; on his death, Ptolemy Euergetes invited from Athens Eratosthenes, a citizen of Cyrene, and entrusted to him the care of the library: it has been supposed that he was the second of that name, or of an inferior rank in learning and science, because he is sometimes called Beta; but by this appellation nothing else was meant, but that he was the second librarian of the royal library at Alexandria. He died at the age of 81, A.C. 194. He has been called a second Plato, the cosmographer and the geometer of the world: he is rather an astronomer and mathematician than a geographer, though geography is indebted to him for some improvements in its details, and more especially for helping to raise it to the accuracy and dignity of a science. By means of instruments, which Ptolemy erected in the museum at Alexandria, he ascertained the obliquity of the ecliptic to be 23° 51' 20". He is, however, principally celebrated as the first astronomer who measured a degree of a great circle, and thus approximated towards the real diameter of the earth. --MATIA 21:42, 5 September 2005 (UTC)

i've got a question how did eratosthenes get the name bata??? Aasin (talk) 18:10, 25 March 2008 (UTC)

Herodotus

In Book II of the History Herodotus gives an accurate measure of the Earths equatorial circumference which he attributes to the Egyptians. Since Herodotus lived before Eratosthenes how was it that the Egyptians arrived at their figures? Furlong refers to the Greek stadion of 185m. So Herodotus is making the proportion of the schoene of the Egyptians = 1/10 degree of the Earths equatorial circumference as accurately as can be determined.

The length of the country along shore, according to the bounds that we assign to Egypt, namely from the Plinthinetic gulf to Lake Serbonis, which extends along the base of Mount Casius, is sixty schoenes. The nations whose territories are scanty measure them by the fathom; those whose bounds are less confined, by the furlong; those who have an ample territory, by the parasang; but if men have a country which is very vast, they measure it by the schoene. Now the length of the parasang is thirty furlongs, but the schoene, which is an Egyptian measure, is sixty furlongs. Thus the coastline of Egypt would extend a length of three thousand six hundred furlongs.

Rktect (talk) 02:15, 27 January 2009 (UTC)

Sieve of Eratosthenes

Should the Sieve of Eratosthenes be in this article somewhere? —Preceding unsigned comment added by 78.32.103.197 (talk) 21:09, 25 September 2008 (UTC)

I have now added the Sieve in a brief section called Prime Numbers. This is in addition to the mention in Named after Eratosthenes, which was not really satisfactory since the Sieve is something he actually discovered himself, as opposed to the other entries which were just named in his honour long after his death. Dirac66 (talk) 02:56, 15 March 2009 (UTC)

Birth date

Just want to double-check that we're all on the same page here and that it's the correct page.

Article previously had his dates shown as 276 BC - 194 BC.

In this edit, User:W.A._Ribeiro_Jr. changed this to 285 BC - 194 BC.

I see a number of online sources with the "276 BC" date, and many of these appear not to be clones of this article.

What's the correct date and cite for same, or what are the sources for various guesses for the date?

-- 201.37.230.43 (talk) 23:13, 6 February 2009 (UTC)

You are quite right. User:W.A._Ribeiro_Jr. should have given a source for his change. I don't know the ancient source for the date, but most pages on the internet seem to agree on 276 BC, including the article on Eratosthenes maintained by The MacTutor History of Mathematics of the School of Mathematics and Statistics, University of St Andrews, Scotland, which seems reliable enough. I will therefore change the year back to 276. --Fabullus (talk) 07:59, 7 February 2009 (UTC)

I looked this up. The ancient source for the date seems to be the Suda, which gives 276-272 BC (Olympiad 126) for his year of birth. The question of whether he was born earlier seems to hinge on a comment by Strabo that Eratosthenes was a "γνωριμος" of Zeno of Citium (who died c. 262 BC). "γνωριμος" often means "pupil", which would imply that Eratosthenes must have been born a bit earlier to have been old enough to study Stoic philosophy under him, but, on the other hand, "γνωριμος" can also mean "acquaintance." The Dictionary of Scientific Biography, where I got most of this from, even states that one scholar puts the year-of-birth as early as 296 on the basis that there was copyist error in the Suda and he was actually born in the 121st Olympiad. Singinglemon (talk) 20:16, 12 February 2009 (UTC)

I like Eratosthenes alot he is cool —Preceding unsigned comment added by 194.83.96.26 (talk) 10:47, 24 March 2009 (UTC)

Eratosthenes and the Alexandria lighthouse ...

Its not too hard to explain why this section is so hard to read: If you go back to a version of Jan 2009 all is well. But then somebody must have deleted the preceeding paragraph ... Regards --Boobarkee (talk) 13:14, 17 August 2009 (UTC)

There was a section deleted by a vandal at 15:56, 11 March 2009 and then there was another vandalism which was not reverted far enough. See history --Alastair Rae (talk) 14:46, 7 October 2009 (UTC)

Measurement of the Earth

How did Erathothenes know that the Sun was very far away, in comparison to the size of the Earth? If you don't know that the Sun is far away, the observations can also be explained by a flat Earth and the Sun being close to the Earth (or a combination of the two). --Bubba73 (talk) 05:03, 4 October 2005 (UTC)

The moon is far away, by parallax. This rquires simultaneous observation at distant points; but simultaneity can be obtained by waiting for a lunat eclipse. The Sun is even further away (at half-moon, the triangle EMS has a right angle at M; the angle at E can be measured directly; the ratio of the two distances is the cosine of that angle.) --Septentrionalis 05:16, 4 October 2005 (UTC)

I assume that this was known at the time. Is that right? --Bubba73 (talk) 00:05, 23 October 2005 (UTC)

If I recall correctly, but I don't have a source in front of me; any history of Greek astronomy should do. --Septentrionalis 22:32, 23 October 2005 (UTC)

Yes, I'm sure I've read that the Greeks tried to determine the ES-to-EM distance ratio, and got it wrong on the short side by a factor of about 5 or 10, the difficulty being in accurately identifying exact first-quarter phase, and in measuring the slight difference between the MES angle and 90 degrees. (The actual distance ratio is just about 400). They did, however, by this means, find that the Sun was many times more distant than the moon. --Fredgds (talk) 06:39, 29 December 2009 (UTC)

Sorry to say this, but mathematically, Eratosthenes did not really proof that the earth was not flat, but like a ball. Because in his "evidence" he assumed that the rays, which come from the sun, are parallel. If I were a solicitor of the ancient Greek world view, I could say that the rays needn ´t be parallel. The sun can also be round (as a solicitor of the ancient Greek view of the world, I would only have to defend the thesis that the earth is flat). So the sun rays can also be anti-parallel. But then the earth can be flat and it is no contradiction, if the stick of Eratosthenes cast a cloud in Syene, but not in Alexandria during the same time.

If you put 2 pens on a desk and an electric light bulb exactly over 1 pen, then this pen will surely not cast a cloud, but the other pen, which is not directly over the light bulb, does.

So Eratosthenes did not give an evidence. If one argued that then the sun would then be too close to the earth (because the distance sun earth can be measured with the sentence of Pythagoras) and therefor the earth would be burnt, one could say (as a solicitor of the ancient Greek view of the world) that nobody knows how hot the sun is and via the Gods, like Zeus the hot rays of the sun are cooled :-).

However, Eratosthenes did not give any mathematical evidences of the earth of being round and no evidences of the length of the equator. —The preceding unsigned comment was added by 134.95.141.49 (talk) 14:58, 25 April 2007 (UTC).

This contention (that Eratosthenes didn't really prove the Earth not to be flat) is refuted by the Greeks' knowledge at that time that the Sun was much more distant than the moon (based on the very nearly right-angle separation of the two bodies at half-moon phases), which in turn was known (by parallax; star backgrounds seen from widely separated places during the same lunar eclipse) to be many times more distant than, say, the Alexandria-Syene distance. (This is pointed out above, in a little less detail, by Septentrionalis.) So it was known that the Sun's rays in those two places were virtually parallel. --Fredgds (talk) 06:39, 29 December 2009 (UTC)

My understanding is that a spherical Earth was the accepted opinion among Greek scientists. Eratosthenes was therefore not concerned with proving that the Earth was not flat, he was merely attempting to measure it. 193.203.156.239

The Greeks knew. By looking at their ports and out to sea one can easy notice that the earth is not flat (by the way ships disapear). --Firebird 01:14, 16 October 2007 (UTC)

They also considered the roundness of Earth's shadow on the moon during every lunar eclipse as evidence of a spherical Earth. I believe the progressive disappearance of ships' masts as they sailed out was cited by Galileo? Don't know whether he had learned of this line of evidence from ancient Greece? Perhaps someone can answer whether the Greeks in fact used this argument for a round Earth. I believe Firebird is correct on this. --Fredgds (talk) 06:39, 29 December 2009 (UTC)

I think the part about the sun appearing as disk, as opposed to a point, is rather irrelevant. A disk is fine, as you can simply measure based on the center of it. So just saying that the sun is not infinitely far away is sufficient.--Robbrown 05:04, 2 August 2007 (UTC)

Furthermore, it's not particularly difficult to measure the angular size of the sun's disk (about 1/2 degree), so that can be accounted for in any angular measure of the shadow. Never assume these people were stupid.

True, they were far from stupid, but it's not really that easy. What the Sun's non-point nature does is to blur out the shadow of a point object, making it difficult to locate its center. In that era they could have determined the shadow location better than the +/- 1/4 degree imposed by the size of the blur, but not by a whole lot. Still, if done carefully, maybe they could get the location to within +/-0.1 deg, and this should introduce only a few percent error in the result -- based on use of a great-circle arc of 7.5 degrees. --Fredgds (talk) 06:39, 29 December 2009 (UTC)

Fred Hoyle, a recently deceased and well-respected astronomer, points out that the distances in ancient Egypt were fairly well known. Runners were used to carry messages between cities and they had, over time, developed the knowledge of the distances to a fair level of accuracy - about 1%. The Itinerary stadia is suitable for runners' distances and since it gives an error for the size of the Earth (IIRC) of about 4%, Hoyle argues, reasonably IMNSHO, that Eratosthenes "got-it-right".

And I think I read, long ago in a book of Hoyle's, that Eratosthenes lucked out by making largely compensating errors. It must be remembered that, at that time, there wasn't yet any concept of error analysis in physical measurements. --Fredgds (talk) 06:39, 29 December 2009 (UTC)

I think the section should be changed to be more neutral, with a proper discussion of the interpretation of his work. It currently reeks of POV. Michael Daly 21:23, 13 September 2007 (UTC)

There can be no justification for having a "citation needed" that the Sun appears as disk for goodness sake. It might be argued that he could judge the centre of the sun anyway but if you leave the text in it just makes a mockery of the article to ask for a citation. Similarly with the "citation needed" for distances not being accurate in this period. Most people would be hard pressed to measure a distance over several miles to better than 1% even today. To say this needs citing is plain stupid. You'll be asking for a citation that the world exists at all next.

Collaborative projects

Following in the footsteps of Eratosthenes (La Main à la Pâte)

- Project: lamap.inrp.fr/eratos/

Since sept 2000, thousands pupils in intermediate course have measured the Earth's circumference from their classroom, simply by observing the shadow of a vertical stick at noon local solar time. Schools of many countries join together to reproduce the observations of the Greek scientist who, more than 2000 years ago, was the first to propose a simple method to measure our planet's size.

The Noonday Project (Center for Innovation in Engineering and Science Education (CIESE))

- Project : ciese.org/curriculum/noonday/

The Goal of the Noon Day Project is to have students measure the circumference of the earth using a method that was first used by Eratosthenes over 2000 years ago. Students at various sites around the world will measure shadows cast by a meter stick and compare their results. From this data students will be able to calculate the circumference of the earth. —Preceding unsigned comment added by Perbosc (talk • contribs) 23:03, 11 July 2010 (UTC)

Zombie Eratosthenes?

"By 194 B.C, Eratosthenes became blind. He died in 195 B.C, at the age of 80-82."

So he became blind a year after he died? 186.124.195.192 (talk) 19:10, 21 April 2010 (UTC)

Your remark is valid, although you swapped the numbers above. Of course being dead implies being blind, but that's not an accepted way to relate to facts in a serious encyclopedic something. Rursus dixit. (^mbork³!) 20:21, 10 October 2010 (UTC)

Sorry, me stupid! (BC) Rursus dixit. (^mbork³!) 20:22, 10 October 2010 (UTC)

One question about measurement of the Earth

One thing I've wondered is, how was Eratosthenes able to determine the exact time to make the measurement places 800 km from each other? I can think of a few ways it could be done, but all would have a high degree of error given what would be available at the time, I'm wondering if there is any evidence showing how he did it himself. -- Suso 03:28, 12 June 2007 (UTC)

If you measure at noon, the shadow of a vertical stick is going to be shortest. So, just trace the tip of the shadow in sand or on a paper. An added advantage is that you don't have to line up one spot exactly north of the other - the error is not that important if you know exactly how far apart they are going straight up north. (measuring the funny shadow line can be done later, in the afternoon or the next day. retostamm 13:57, 20 Aug 2007 (PST).

The original claim that Eratosthenes had heard (he did not make this observation himself) was that there was a well in Syene (near modern Aswan) where one could see the Sun reflected from the bottom of the well at (local) noon on the date of the summer solstice. That means that the Sun was directly overhead at noon on that date. The same measurement at Alexandria, where Eratosthenes lived, on the same date gives an altitude that is not 90 degrees (if memory serves, it is 7.5 degrees short, which means that the latitude of Alexandria is 31 degrees, which is about right.) I believe that this is documented with sources in Arthur Koestler's The Sleepwalkers.

So, there is no ambiguity in the data Eratosthenes was relying on. Bill Jefferys (talk) 23:18, 18 June 2011 (UTC)

Shape of Earth

Did Eratosthenes necessarily assume a spherical earth to make his math work? I always assume he did from my understanding. I assume also that Plato had a spherical earth in his philosophy because of the ideal of the sphere as perfect. Mike Logghe

Seems so likely that it's barely worth doubting, I'd suspect. AFAIK it's only in the last century or three that it's been known that the earth isn't spherical. Petrouchka 11:13, 22 February 2006 (UTC)

I have reverted the claim made in the antecedent edit, which appears to be original research.

(dubious claim removed - it is impossible to prove the Earth is round while staying around one point on its surface. It COULD be HALF a sphere for all he knew. It was his ASSUMPTION, under which he derived the circumference value.)

This is wrong. I am an astronomer and have taught this subject for over 40 years. It is well known that you CAN prove that the Earth is round while staying around one point on its surface. The reason is that lunar eclipses can take place at any position in the sky. If the Earth were hemispherical, for example, at some positions of the eclipse you will see a round shadow at ingress and a straight shadow at egress (or vice versa). This will happen whenever the eclipse takes place near the horizon. Similarly, a flat Earth would produce straight shadows at both ingress and egress when the eclipse takes place near the horizon. Only a spherical shape produces curved shadows (of constant or near constant curvature) regardless of the position of the Moon at the eclipse. This is explained in numerous elementary astronomy texts. This fact was known to the ancients. I'm pretty sure we mentioned it in my own text, Discovering Astronomy (Jefferys and Robbins, mid-70s. I'm sitting at the car dealer right now and don't have the exact reference available). Bill Jefferys (talk) 13:37, 17 June 2011 (UTC)

great, so is THIS what Eratosthenes did to prove it? How do we know? The claim in the article, which you so valiantly restored, gives us no source nor citation - nothing. How's THAT for the original research! And btw, OR only pertains to the article contents, not some remarks on history lists, is it not?

so if there's no evidence or citation for Eratosthenes actually doing what is claimed there, I think that OR claim in the text of the article about him proving it, however it may seem likely to you and now me also that he understood it, should be removed. Would you agree? WillNess (talk) 19:05, 18 June 2011 (UTC)

My reversion of your removal was based on your incorrect claim that the shape of the Earth cannot be inferred from observations made from one point on the Earth's surface, and not from the lack of a citation, which you didn't mention. I agree, the lack of a citation is a problem that needs to be fixed.

I do not know what sources, if any, that the person who originally posted this claim was using. (I am not that person). I presume that that individual had some source in mind for this claim. But it is not given; a request for a citation is already in the article. I would agree with you that if, within a reasonable period of time (now that this is the issue), no citation is forthcoming, then removal of this claim would be appropriate. But sufficient time should elapse until that action is taken, from the time that it has become evident that it is an issue (that is to say, from now).

I therefore request the person who added this material to come up with an appropriate citation, and I suggest that a deadline of two weeks (that is to say, until July 2, 2011) be set, for this citation to be forthcoming. Bill Jefferys (talk) 23:08, 18 June 2011 (UTC)

By the way, there is no need to be nasty or sarcastic. WikiPedia is a cooperative adventure, and snide comments do not promote its ends. Simply state the facts as you know them.

My guess is that the spherical shape of the Earth was well known long before Eratosthenes made his measurement of the size of the Earth, though I do not know this for a fact offhand and the person who originally posted this claim needs to come up with a citation. An authoritative source here doesn't say anything about Eratosthenes having proven that the Earth was spherical.

I know some historians of astronomy and will consult with them for more authoritative information. Bill Jefferys (talk) 23:33, 18 June 2011 (UTC)

I agree totally and wholeheartily apologise. I snapped and it was totally without merit. My bad. I don't want it to sound like an attempt at justification, but I did remove it because of the lack of citation, although not stating it. I thought about it in the context of his method of measurement of Earth's circumpherence, where the local sphericity would correspond to his local (Alexandria and to the south) measurements, but stretching this over to the whole Earth seemed like a stretch (although guided by the Occam's razor). Shades of Earth on the Moon is something that just didn't jump into my head though it seems obvious, now. Interesting, the capacity of the mind to treat something as natural and without need for an explanation, just because it is always there.

Erhm, not so obvious at all, as it is only during Lunar eclipses that Earth casts its shadow on the Moon, d'oh. WillNess (talk) 12:29, 19 June 2011 (UTC)

Another thing is the OR charge, which is all too frequently wielded on Wikipedia to my taste. For instance, I don't need any sources to support your "claim" that Earth shadows on the Moon prove its sphericity. Although were I to believe the Moon and its phases to be just some gods' play thing, a magical show, some picture up in the skies (especially as it seems to be not rotating), that would still prove nothing to me. Then I could only have my proof by actually seeing the Earth and the Moon as seen from some orbiting rocket. So we still need a prove that Eratosthenes didn't hold these beliefs, that he actually made notice of Earth's shadow on the Moon's face and interpreted it in that way. We can't just assume that. WillNess (talk) 12:25, 19 June 2011 (UTC)

I have put into my calendar a note to resolve the issue on July 2, unless someone posts a citation and/or I receive appropriate information from my correspondents that the current information is correct.

Fair enough? Bill Jefferys (talk) 14:16, 19 June 2011 (UTC)

yes, thank you. WillNess (talk) 19:31, 19 June 2011 (UTC)

According to Spherical Earth, Aristotle, in the century before Eratosthenes, gave three proofs of the shape of the Earth, including the one I mentioned about the uniformly circular shape of the shadow of the Earth during an eclipse. Citations to Aristotle's work are given.

Accordingly, it appears very clear that Eratosthenes was "not" the first to give a proof of the spherical shape of the Earth, and I will therefore remove that claim from the article. Bill Jefferys (talk) 01:44, 22 June 2011 (UTC)

Can someone explain something to this non-astronomer (biologist/toxicologist by education)? The article states that one of Eratosthenes' erroneous assumptions was that the two locations lie on the same meridian—would that really make a significant difference? Assuming the respective measurements were made at sidereal noon in each place, the only error would be in the difference in azimuth caused by the earth's movement through it's orbit as it turns the ~7° on it's axis from Syene's noon to Alexandria's (I calculate ~9″ on average, though it seems intuitively that it would be much less at summer solstice). This seems to me well within the margin of error for the rest of the measurements. Can someone clear this up for me—what am I missing? Best Regards, Mike Horstman (horstmanmd@me.com)

Capital of Ptolemaic Egypt?

...wasn't the capital of Ptolemaic Egypt Alexandria, from Alexander all the way to Umar? Twin Bird (talk) 21:06, 23 June 2011 (UTC)

Point of the portrait?

I have never understood the need to post "portraits" of ancient people whose true likenesses are completely and utterly unknown to us. Why are they there? Can we remove them? In my opinion, they add absolutely nothing to the article. They would be useful in an article about the life of the artist, but that is all. Frankly, the guy in the picture doesn't even look particularly Greek!67.193.234.252 (talk) 22:40, 26 July 2010 (UTC)

I agree unless the artist based the portrait on some sort of description at least to to the likeness of the subject.--Mesokabe (talk) 06:17, 15 September 2011 (UTC)

baffling section '...Alexandria lighthouse...large earth radius...small AU

The two paragraphs under this heading are a baffling non sequitur as they don't give any context. The article is clear and readable up to this point. I have no idea who Eusebius is, it's not clear why we're talking about lighthouses, a mass of measurements and percentages are introduced, and the tone changes from being supportive of Erastothenes to criticising him. The lighthouse story sounds interesting, but the detailed arguments over numbers are perhaps best left to the academic papers outside Wikipedia. --Air (talk) 14:13, 18 May 2009 (UTC)

You are quite right, Air. The two disjointed paragraphs were added by 128.220.205.134 on 30/10/2008. — Preceding unsigned comment added by 92.27.109.117 (talk) 14:24, 25 November 2011 (UTC)

Note

Note that 128.220.205.134 is a sock-puppet of Dennis Rawlins at times. — Preceding unsigned comment added by 86.177.3.183 (talk) 17:39, 23 November 2011 (UTC)

There is no reason to suppose that Eratosthenes ever had the slightest dealings with a light-house. — Preceding unsigned comment added by 86.177.3.183 (talk) 17:44, 23 November 2011 (UTC)

Posidonius used a similar method with accurate results, without using any light-house. — Preceding unsigned comment added by 92.27.109.117 (talk) 14:29, 25 November 2011 (UTC)

No one mentioned a light-house in the case of Eratosthenes for about 2,222 years. — Preceding unsigned comment added by 92.27.109.117 (talk) 14:51, 25 November 2011 (UTC)

Earth measurement information

Should something be done about the fact that the measurement of the circumference of the Earth seems to contradict the information on the History of geodesy page? Simoneister (talk) 09:48, 21 February 2012 (UTC)

I will be accused of trolling if I give the reason for this. — Preceding unsigned comment added by 86.180.157.197 (talk) 13:17, 28 February 2012 (UTC)

I agree, that the article on the History of geodesy is much more opposed to Eratosthenes than this one. — Preceding unsigned comment added by 86.180.157.197 (talk) 13:20, 28 February 2012 (UTC)

Improper Citation

Concerning this from the article:

"Eratosthenes criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, and that the Greeks should keep themselves racially pure, believing there was good and bad in every nation."

The W.W. Tarn book is not available on line, but I found it at a book store. I did not pay out the $100 for the two-volume set. However, on page 439 of volume two the discussion is about a fragment attributed to Eratosthenes in which he relates an interchange between Aristotle and Alexander the Great. Aristotle reportedly counseled Alexander to treat Greeks one way, foreigners another. Alexander reportedly disagreed and felt that all humanity should more or less get along and marry whomever. It's interesting, but it is Eratosthenes' account of an interchange between two different people. Racial "purity" is not part of the discussion. Please note, the fragment is basically hearsay. — Preceding unsigned comment added by 8.21.181.27 (talk) 11:56, 6 April 2012 (UTC)

Date of librarianship

When did Eratosthenes become the Library's head Librarian? This article says 236 BC, but I looked over at Britannica, and it says 255 BC- a pretty important difference. --maru (talk) Contribs 02:24, 6 January 2006 (UTC)

Lots of dates in antiquity are disputed or uncertain -- it'd take a bit of research to find out exactly what the possible range of dates is, which I don't have time to do just at the minute, but I can well believe it's uncertain to +/- 20 years or even more. In addition, ancient Greek dates are normally in the form "236/235 BCE" because the year ran from midsummer to midsummer. Petrouchka 11:10, 22 February 2006 (UTC)

Also, the article says "In 236 BC he was appointed by Ptolemy III Euergetes as librarian of the Alexandrian library, succeeding the second librarian, Apollonius of Rhodes," but the Library of Alexandria article lists Apollonius as the third librarian (after Zenodotus and Callimachus), with Eratosthenes fourth. Can someone more knowledgeable than I correct the discrepancy in one place or the other? Dodiad (talk) 20:52, 29 November 2012 (UTC)

Formula

I thought it might be a great idea to add the formula that Eratosthenes used to calculate the circumference of the Earth. He used the rod to find that in Alexandria it casted a shadow 7.5 degrees, this same day it would cast no shadow in Syene, due south of Alexandria. He then formulated that Earth's circumference divided by distance in stades from Syene to Alexandria (5250) would equal 360 degrees (Earths diameter) divided by the shadow casted in Alexandria, 7.5 degrees. Cross multiply these values 360 and 5250 and divide by 7.5 to get 252,000 stades. Which is so very close to Earth's real circumference. ToothFairyJenny (talk) 03:09, 20 September 2013 (UTC)

Citation request

The citation request is for the given sources of inaccuracy. The paragraphs commenting on the inaccuracies in E's estimates for the circumference of the earth are not sourced. I of course agree with the other editor's comment about not needing a source to say that the sun is not a point source. It's the main paragraph before (and after for that matter) that is not sourced. Who stated for instance that one error comes from the location of Syene? Who stated that it was difficult to measure distances accurately. I do not doubt that the statements are correct, but an inline citation would be nice. --AnnekeBart (talk) 16:37, 31 March 2011 (UTC)

Will be trying to help improve this article as a paper for my History of Science class. I want to use these sources as premises to expound on Eratosthene's Bibliography.

• Lukoševičius, Viktoras, and Tomas Duksa. "Eratosthenes' Map of the Oecumene." Geodesy & Cartography 38.2

(2012): 81-85

• Lindberg, David C. The Beginnings of Western Science: The European Scientific Tradition in Philosophical,

Religious, and Institutional Context, Prehistory to A.D. 1450. 2nd ed. Chicago: University of Chicago, 2007.

• Zeigler, Donald J. "From Prime Numbers to Place Names: A New Use for Eratosthenes' Sieve." California Geographer

43.(2003): 55-63.

• Bailey, Ellen. "Eratosthenes of Cyrene." Eratosthenes of Cyrene (2006): 1-3.
• Spruch, Grace Marmor. "The Legend Of Christopher Columbus." American Scholar 71.4 (2002): 61. Literary

Reference Center.

• Gow, Mary. Measuring the Earth: Eratosthenes and His Celestial Geometry

Ancient perspectives : maps and their place in Mesopotamia, Egypt, Greece, and Rome

• Talbert, Richard J. A. Ancient Perspectives: Maps and Their Place in Mesopotamia, Egypt, Greece, and Rome.
• Eratosthenes. Eratosthenes' Geography/fragments collected and translated, with commentary and additional

material, by Duane W. Roller

• Nicastro, Nicholas. Circumference: Eratosthenes and the Ancient Quest to Measure the Globe.

ToothFairyJenny (talk) 04:06, 1 October 2013 (UTC)

Computer Scientist?

Shouldn't computer scientist be part of the opening description as well? I tried adding it but it got reverted.

Computer scientist should be added given his contributions of several algorithms, most notably the Sieve of Eratosthenes. — Preceding unsigned comment added by 64.134.174.239 (talk) 22:02, 8 December 2012 (UTC)

Because of the algorithms he designed, he is usally called a mathematician! --Boobarkee (talk) 10:39, 1 October 2013 (UTC)

Jenny

I think the article is really good. I'm not sure what all you added but there is so much about this guy to know. The only thing I can think to ask is was he ever married or have any kids? Is there anything more to know about his life that didn't have anything to do with his profession? — Preceding unsigned comment added by Kycarp20 (talk • contribs) 21:32, 13 November 2013 (UTC)

Hey Jenny, the last sentence of the third paragraph in the "Life" section may need to be looked at. You could possibly reword it to say something like "As head of the library, Eratosthenes had many tasks that he was required to do such as...". There also seems to be an Oxford Reference problem in that section but I'm not sure if that is related to you. In the "Geography" section, you might shorten the third sentence by making it two sentences. You might also make a link to Geographika. Bill Nye OU (talk) 21:34, 17 November 2013 (UTC)

History of Science Edits

I really find this article fascinating. I do have some suggestions to clean up the biography. The opening introduction talks about all of his work. Maybe add more on who he was as person versus just explaining his work in the opening introduction.

Life: In this paragraph I found it sometimes hard to follow the sequence of events. It has very good information here, but maybe just a little clean up with the timeline of his life.

Measurement of the Earth's Circumference: I particularly enjoyed this section. I am very nerdy for statistics and numbers, this paragraph fulfilled my needs. The picture showing part of the globe from space was a very good add. The only suggestion for this section is to add some sources of where you found these statistics of Eratosthenes calculations. Without proper sources I just assume these numbers are made up.

Geography: Very good flow of sources listed in this section. I would suggest moving the History of Geodesy from the top of the ==geography== section to your ==external links== section. This provides a neat and clean order/flow to the page for the reader to follow. I found this section difficult to read, due to some grammatical errors. For instances, "In the Library of Alexandria he had access to scattered books of travel inside them countless information and representations that needed to be pieced together in some organized format," does not flow well. Maybe put a comma or a period between the words "travel" and "inside." Clean up minor grammatical errors like this and this section will be stellar.

Other Astronomical Distances: Looks like the Wikipedia Gods have already punished this article haha. I don't have much to say other then repeat what the Wiki Gods have already suggested. This section could be deleted, and use space the information out in this section amongst the entire article. This would clean up the article, and also not make it as beefy. Also, a picture would be nice here to spice up the section.

Prime Numbers: I like the moving digital picture explaining prime numbers. I see the article explains prime numbers, but where did Eratosthenes generate this algorithm? Why did he come up with this algorithm? Expand more on this paragraph, and add sources to where you found this information.

Switch the ==Works== Section and the ==Things named after Eratosthenes==. Maybe put the things named after Eratosthenes as a subsection of further readings or external links. This would clean the page up a bit more.

Final Notes: Jenny I really liked your article on Eratosthenes. He sounds like a very fascinating individual, with many contributions to the fields of mathematics and science. The article has plenty of information. The only suggestions are minor and should be taken with a grain of salt. Other then cleaning up the layout of the article, adding some sources, fixing minor grammatical changes, and elaborating more on some sections and cutting out some of the beef in other sections, this page was very well written. I disagree with the Wikipedia Gods rating this page as a C-class importance page. This man sounds like his discoveries were pivotal for the creation on geography, advance mathematics, and advanced science. This page should be Class-A with very high importance. Mavorik1 (talk) 17:56, 18 November 2013 (UTC)

Where was he born?

I am so confused about where he was born.

As I understand it, he was from Syrene, which was a small town near Elephantine. This is Aswan Egypt now.

This makes sense to me, because it is the right distance due south of Alexandria, and in the right country at the time.

I think that everyone is confusing Cyrene Libya with Syrene Egypt.

-- Jonathan

Do you have some evidence, or is this just a hunch? There is a preposterously long list of sources cited in the article (and a good few beyond these) that say the Greek colony in what is now Libya is where he was from. Of course they could all be wrong, but without some fairly impressive reliable sources refuting this position, we will have to go on believing them.—Jerome Kohl (talk) 17:44, 31 August 2015 (UTC)

Music theory

Music theory is mentioned in the initial summary of his achievements, but no example is given in the body of the text. Jplvnv~enwikisource (talk) 14:17, 12 April 2016 (UTC)

Berber Origines

Eratosthenes was a berber, there is berber tribes in Eypte and Libya and he have not been came with greeks, he was born in Libya, so he is not greek, he is berber. Why all people stole from us our scientists. — Preceding unsigned comment added by Berber027 (talk • contribs) 15:58, 31 March 2014 (UTC)

Is there oral history among the Berber about this fellow or his discoveries? Jplvnv~enwikisource (talk) 14:21, 12 April 2016 (UTC)

On the size of the earth

Excellent article on Eratosthenes. I love the layout and the structure. I would however add my hapenny on the context of the size of the earth. A more thorough explanation can be found here...

The main contention is over the length of Egypt as 5000 stade, syene to Alexandria being 5000 stade and 1/50th earth. This is actually a much deeper confusion over the metrology of the time, and is almost said tongue in cheek, where you can have your cake and eat it. The british : roman foot was in the ratio 35:36. The greek : roman foot was in the ratio 24:25. The Total length of Egypt was 7 degrees upper + lower. Using 1/50th Earth or 7.2 degrees gives the alternative 36:35 ratio. This is a different unit of measure than conventional egyptian.

The stade could be 300 royal cubits or 400 common cubits, but these come in multiple lengths depending on the geodesy module being used. [Note Herodotus stating the common was 3 finger short of the royal of 28 fingers (ie 24:25)] Herodotus gives the length of Lower Egypt as 6 degrees or 1/60th earth as 60 schoene of 60 stade of 600 feet or 400 common cubit. The Egyptians have the shen ring representing, all that was ruled under the path of the sun, constructed from coiled rope with a diameter bar at base.

Coiled rope = 100... Path of the sun = 1 day... Diameter of 'ruled' Earth = 100 days march.

At 1 passus / second of 60"...

24hour x 60min x 60sec x 60" x 100 days = 518,400,000 thumb inches.

With Pi as 25/8 to go with the base 60 system and as typified by Vitruvius (See Vitruvian Man for the importance of 25/8).

The Earth becomes 1,620,000,000 inches and 7 degrees is thus 31,500,000 = 5000 x 300 x 21" (5000 stade)

Thus we get:

1,555,200,000" Herodotus 1/60th Earth or 6 degrees (Ratio 864 - Geodetic Greek)

1,575,000,000" Eratasthenes 1/50th Earth or 7.2 degrees (Ratio 875 - Anglo Sumerian)

1,620,000,000" Egyptian Shen Ring. Length of Egypt 7 degrees (100 Atur). Length of lower Egypt 6 degrees. ACos 6/7 = 31 degree latitude boundary (Ratio 900 - Romano Egyptian).

There is no error in the size of the earth. It was known. All of these versions of the earths elliptical circumference (North/South length) are the same size using different modules. What changes, is the value of Pi used, and if the module refers to base, polar, equatorial, 2d mean or 3d mean.

Using 576 base : 577 polar : 577.33 3D Mean : 577.5 2D Mean : 578 equatorial

250,000,000 x 864/275 x 2 = 1570909090.9 Base Circle

1570909090.9 * 577.5/576 = 1,575,000,000" 2D Mean

Pi = 6/5th Phi^2 = 6/5th (Phi + 1) & Phi = 89/55 Fibonacci Series & Phi + 1 = 144/55

True Ellipticity = 601/600 x (6/5 Phi^2)/pi = 594.52559 polar : 596.52559 equatorial = 1/298.2627953 — Preceding unsigned comment added by Michael saunders (talk • contribs) 21:35, 1 August 2016 (UTC)

Working with 600 and generating the Phi proportion is much easier than trying to create a Pi proportion and a 594.53559 module. Especially when they give the same circumference. — Preceding unsigned comment added by Michael saunders (talk • contribs) 21:40, 1 August 2016 (UTC)

The 252,000 stade Strabo Earth presents us with three issues:

7.2/360 x 252,000 = 5040 stade for the length of Egypt.

7.0/360 x 252,000 = 4900 stade for the length of Egypt.

6.0/360 x 252,000 = 4200 stade for the length of Egypt.

However, 1,555,200,000 / 252,000 / 300 gives us a cubit of 144/7 Greek Geodetic inches or 7 cubit to 12 feet.

All of these measures give various cubits of 21", 20.57" and 20.16" Greek Geodetic and all of which originate from the Remen Cubit area. The diagonal of a 20 unit square is 28.28427 and 28.28427 : 28 is 99%. Thus dividing the hypotenuse by 28 scales the cubits into 1% increments. 21" @ 100% (Major cubit) ~ 20.79 (Nile cubit) @ 99% ~ 20.58" @ 98% (144/7 Mapping cubit) ~ 20.37" @ 97% (Remen diagonal cubit) ~ 20.16" @ 96% (28 finger Minor cubit) You can use 21 finger and 30 finger diagonal to complete the 20:21:29 system Sumerian half with 20" cubits.

96% of 900 = 864.

96% of 600 = 576.

The rabbit hole goes much deeper. How far down do you want to go ? Michael saunders (talk) 21:41, 1 August 2016 (UTC)

The well story

Seems the well story is a later misunderstanding and Eratosthenes himself never used a well.

http://articles.adsabs.harvard.edu//full/1914Obs....37..352D/0000352.000.html

188.238.42.194 (talk) 16:14, 4 July 2017 (UTC)

Pronunciation of the name (stress placement)

The article says:

(Greek Ἐρατοσθένης, pronounced er-ə-TOS-thə-neez

This seems inconsistent. The Greek stress here is on the penult syllable, but the English stress is on the antepenult. Which is correct?

It is an English article, about a notable person so it is wholly appropriate to include a suitable English pronunciation scheme. People, who speak English say his name all the time, wrongly. I sought out this sight to exclusively determine the pronunciation of his name in English so I could correspond. So what is with the mystery Greek letters in the pronunciation part? I have no idea what the Greek letters mean in terms of phonemes. I don't think one should have to learn Greek to pronounce a famous man's name in English. — Preceding unsigned comment added by 24.89.225.234 (talk) 11:11, 28 August 2016 (UTC)

The final Greek vowel is long. Greek didn't like accent placement further from the end than 3 short-vowel units. So, (and not to get too pedantic), the acute is forced to the penult. However, somewhere along the historical pronunciation line perhaps the heavy consonant cluster [sth] amounted to phonetic speed-bump and people just paused on the ó. Some people do pronounce it quasi-classically however, adding to the confusion. There's no right or wrong way about it, at any rate. JohndanR (talk) 02:18, 31 July 2017 (UTC)