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67 votes

What is Ptolemy holding in this picture?

This device was invented by a Jewish Rabbi, Levi Ben Gershon. It was used to measure the angular distance between two stars or, in general, any pair of celestial bodies. Ptolemy lived 1000 years ...
Riccardo.Alestra's user avatar
61 votes
Accepted

What is Ptolemy holding in this picture?

It is called "Jacob's staff". It was an old astronomical tool used for trigonometric purposes.
Euler_Salter's user avatar
40 votes
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How did Eratosthenes know the Sun was very far away?

We do not know for sure what Eratosthenes read, but at his time this was a common knowledge. This can be inferred from the book of Archimedes, The sand reckoner (Archimedes was Eratosthenes' ...
Alexandre Eremenko's user avatar
22 votes
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How did Ptolemy know that days were unequal lengths?

You are right: at the time of Ptolemy they could not measure the length of a day directly. Actually Ptolemy never discusses any clocks in his book, he probably used some crude devices record the ...
Alexandre Eremenko's user avatar
20 votes
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Why was the development of mathematics very slow between Ancient Greece and Descartes?

Making my comment into an answer: Was there a gap of knowledge or slow-down of progress in math as a whole between Ancient Greeks and the 17th century? The answer is probably no. Islamic Medieval ...
Mauricio's user avatar
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19 votes

What is Ptolemy holding in this picture?

And this tool has been known under many other latin names than baculus Jacob (or Jacob's staff): radius astronomicus (astronomic ray), crux geometrica (geometrical cross), revelatorem secretorum (...
Laurent Duval's user avatar
18 votes
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Did the ancient Greeks have zero in their number system?

During the classical and early Hellenistic period (until 200 BC) Greeks did not use any positional system, they had their own which was decimal but not positional. The units from 1 to 9 are assigned ...
Conifold's user avatar
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16 votes

How did Eratosthenes know the Sun was very far away?

This is a long answer, explaining more or less step to step why the data available to Eratosthenes indicted that the Sun should be a vast distance from the Earth, thus makings its diverging rays ...
M.A. Golding's user avatar
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12 votes
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The Greeks did not discover "a single scientific law"

It is a strange idea that scientific laws can be only expressed with algebraic means. The Greek did discover several scientific laws. The oldest one is attributed to Pythagoras himself: it relates the ...
Alexandre Eremenko's user avatar
11 votes
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What manuscript is depicted in the HSM advertisement?

User plannapus points out that the proposer of the ad links to the original source, which is the first page of Diophantus’s Arithmetica, specifically the 1621 translation by Claude Gaspard Bachet de ...
11 votes

Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

Feynman is being... liberally creative. What he says is his own interpolation that "makes sense" from the perch of today. "Must have been psychologically wonderful", perhaps, but &...
Conifold's user avatar
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10 votes
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What did the ancient Greeks know about the solar system, and how?

No they did not know this. The motion of the Sun, Moon and planets (as seen from the Earth) was known, in the sense that it could be predicted with reasonable accuracy. To do this, they used an ...
Alexandre Eremenko's user avatar
9 votes

When $1$ wasn't really a number in Greece

Euclid's Elements Book VII: Definition 1: A unit is that by virtue of which each of the things that exist is called one. Definition 2: A number is a multitude composed of units. See also: Aristotle ...
Mauro ALLEGRANZA's user avatar
9 votes
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What did ancient near eastern protoscience believe about germination?

The Encyclopedia of Seeds: Science, Technology and Uses, edited by J. Derek Bewley, Michael Black, Peter Halmer, CABI International 2006 (Entry: History of seed research) cites some ancient ...
Margaret Friedland's user avatar
9 votes

Did Indian astronomers realize the sphericity of the earth independently of the Greeks?

(I started writing this answer from memory, but on a second look at some sources it turns out to answer the question for the statement of a rotating earth rather than that of a spherical earth... but ...
ShreevatsaR's user avatar
9 votes
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How was the Antikythera Mechanism moved?

UPDATE (March 2021): A comprehensive new reconstruction of the Antikythera mechanism has been published in Nature, Freeth et al., A Model of the Cosmos in the ancient Greek Antikythera Mechanism. It ...
Conifold's user avatar
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9 votes
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What does "given in species" mean in old geometry textbooks?

Such terms as “given in species” are defined in Euclid’s Data (Greek, English): III. Rectilineal figures are said to be given in species, which have each of their angles given, and the ratios of ...
Michael E2's user avatar
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9 votes
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What dialect of ancient Greek was taught to natural philosophers?

Attic, the highest prestige dialect, hands down. For centuries, this has been the mainstay of Greek language education in Europe. There is no better reminder of this than Newton's Trinity College ...
Cosmas Zachos's user avatar
8 votes
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What is the history of angle quintisection (division into five equal parts)?

Not much history to it, I am afraid. It seems that methods of trisection rather obviously (to those who considered them) applied to quintisection as well, so the problem was of little theoretical ...
Conifold's user avatar
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8 votes

The Greeks did not discover "a single scientific law"

Euclid wrote an Optica (300 BC) — surely “Visual rays proceed in a straight line indefinitely” ranks with the best physical laws. So did Ptolemy (160 AD), and Hero wrote a Catoptrica (50 AD). ...
Francois Ziegler's user avatar
8 votes
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The abstraction of mathematics from physics

You are right, this happened in ancient Greece, and is credited to Thales and Pythagoras. Unfortunately, too little of their early work survived (nothing written by Thales or Pythagoras). The main ...
Alexandre Eremenko's user avatar
7 votes

Did the ancient Greeks have zero in their number system?

It depends on the definition of the "Ancient Greeks". Ptolemy, who lived in 2 century AD, lived on the territory of the Roman empire, but wrote in Greek, and probably worked in Alexandria (...
Alexandre Eremenko's user avatar
7 votes

Compass and straightedge: why?

The real reason is probably that straightedge and especially compass are the simplest, most primitive instruments, and also easy to make. At the same time they are quite accurate. (Straightedge is not ...
Alexandre Eremenko's user avatar
7 votes
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Was a regular heptagon ever constructed by ancient Greeks?

We have Archimedes's construction of regular heptagon due to Arab transcription by Thabit Ibn Qurra, see Mendell's translation. Aaboe gives modernized exposition and commentary in Episodes from the ...
Conifold's user avatar
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7 votes
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How was gravity explained in Ancient Greek and Roman times?

See Aristotle's Natural Philosophy. According to Aristotle, change in the natural world can be : [either] in accordance with the nature of the object — in which case the change is natural (phusei) or ...
Mauro ALLEGRANZA's user avatar
7 votes
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What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?

Students learned theorems, propositions and their proofs. A teacher would call a student to the blackboard and ask to reproduce a proof. A shorter test would be just to state the theorem. Many ...
Alexandre Eremenko's user avatar
7 votes
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Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

The answer to your question in the title is definitely yes. For example, Fermat wrote in a letter: "Perhaps, posterity will thank me for having shown that the ancients did not know everything". Fermat ...
Alexandre Eremenko's user avatar
7 votes
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Did Archimedes view fractions as "numbers"?

No, Archimedes, and ancient Greeks generally, did not see fractions as numbers, and they did not use fractions as we use them today, they did not use them at all. What they used was ratios of ...
Conifold's user avatar
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7 votes

Adrastus, Proclus, and 2+8+50+288+… versus 1+9+49+289+…

As nwr commented above, the original text by Proclus is his commentary on Plato's Republic, and Cambridge University Press is in the process of publishing an English translation. Unfortunately, I ...
Timothy Chow's user avatar
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7 votes
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How did Aristotle explain the motion of living things moving by themselves, and falling of objects, with his hypothesis of all motion needing a cause?

This issue is analyzed by Furley in Self-Movers. Aristotle's answer is somewhat convoluted due to conflicting motives, one from common sense and the other from his cosmology. For falling bodies we ...
Conifold's user avatar
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