65 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 ...
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59 votes
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What is Ptolemy holding in this picture?

It is called "Jacob's staff". It was an old astronomical tool used for trigonometric purposes.
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32 votes
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Why did the ancient Greeks originally become interested in conic sections?

The truth is that we do not know. We do know of the person who is credited with the discovery, Menaechmus (c. 350 BC), a student of Eudoxus of Cnidus and a friend of Plato's, one of the most prominent ...
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  • 67.1k
28 votes
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Why is the Pythagorean Theorem so ubiquitous?

The main question is why the Pythagorean theorem for right triangles: $$ a^2+b^2=c^2$$ is such a central tool of Euclidean geometry. There are many different approaches one can take to this; I'll give ...
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  • 3,681
25 votes

Irrationality of the square root of 2

I do not agree on some details of the interpretation regarding the discovery of the irrationality of $\sqrt{2}$ as a confutation of the Pythagoreans [...] belief that all numbers could be ...
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23 votes
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Was Aristotle really wrong about gravity?

I'll try with some calculations : please, check it and the formulae used ... A solid ball with a mass $m$ of $1$ kg falls (with the usual approxiamtions : no drag, etc.) with an acceleration $a$ that ...
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19 votes
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Pythagoras vs. the idea of Pythagoras

Yes the stories of Pythagoras that were common a few decades ago have all been been disproved, largely by Walter Burkert in Lore and Science in Ancient Pythagoreanism (1972). In short, Pythagoras ...
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18 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 (...
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17 votes

Was Aristotle really wrong about gravity?

In short, you were taught that Aristotle was wrong because he was wrong. He didn't make a prediction, he made an observation about rock and feather, and then sloppily generalized it to all objects ...
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17 votes
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How did Babylonians figure out that the evening star is the morning star?

I doubt that many Babylonians or Greeks or any others who cared about such things ever thought Hesperus and Phosphorus were different objects any more than we think the Morning Star and Evening Star ...
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17 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 ...
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  • 67.1k
15 votes

Irrationality of the square root of 2

According to this link, Legend has it that Hippasus first discovered the irrationality of $\sqrt{2}$. The second link in fact mentions a legend that held that supporters of Pythagoras murdered ...
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14 votes

Why did the ancient Greeks originally become interested in conic sections?

This question has been discussed several times on math overflow: https://mathoverflow.net/questions/191909/discovery-and-study-of-conic-sections-in-ancient-greece It also has references. One theory ...
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13 votes
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Why wasn't probability developed in ancient Greece?

This is a good point, I mused about it too. First, Pythagoreans and Plato had a very high minded idea of mathematics, gambling would have been seen as a lowly pursuit. This in itself does not explain ...
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12 votes

Irrationality of the square root of 2

These legends do exist, and have for along time. But few if any specialist historians of the subject believe Pythagoreans discovered irrationality of $\sqrt{2}$. See: Pythagoras vs. the idea of ...
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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 ...
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11 votes

Why were geometers dissatisfied with the parallel postulate?

The reasons are "simple". All other axioms and postulates appeal to our "everyday experience", at least in principle. The straight lines correspond to light rays in everyday experience. However it ...
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11 votes

Was Aristotle really wrong about gravity?

No. Aristotle was not necessarily wrong. This is in substance Carlo Rovelli's view in Aristotle’s Physics: a Physicist’s Look. As the abstracts announces it Aristotelian physics is a correct and ...
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  • 2,267
11 votes

Why did Aristotle make mistakes in his laws of motion?

Air or more generally medium resistance was not yet treated as a separate effect in Aristotle's time. Nor was there a clear idea of motion in a vacuum, in fact most ancient Greek philosophers, ...
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11 votes
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Why and when did some areas separate themselves from philosophy and some not?

The area of knowledge separates itself from philosophy as soon as a reliable method of obtaining exact knowledge in this area is invented. Thus mathematics separated from philosophy at its very ...
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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 ...
10 votes

Was Aristotle really wrong about gravity?

Yes, Aristotle was wrong about gravity. But I think it is unfair to say “that Aristotle was responsible for holding back physics for centuries”. The ones who held back physics for centuries were the ...
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  • 3,335
10 votes
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Concerning the measurement of the Earth's circumference by Eratosthenes

Certainly that the Earth is spherical was a commonplace (among the educated people) at the time of Eratosthenes. Once you start traveling on sea (or climbing mountains) you immediately notice that the ...
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10 votes
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Could the industrial revolution have happened in Hellenistic Alexandria?

This is a very interesting question which occupied me for a long time. I agree with L. Russo that a "scientific revolution" really happened in Hellenistic Greece. It actually happened 2 centuries ...
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10 votes

How did ancient Greeks explain moon phases without reflection of sunlight?

Yes. According to this, we don't know who it was to explain the phases using a spherical model, though it was before 600 B.C: The first person to correctly explain the phases of the Moon is lost ...
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9 votes

Did geometric patterns in nature suggest the early notions of proportion and ratios?

It seems that originally ratio and proportion emerged not so much "from nature", as from human activities, first practical and later more theoretical. We often find things in nature only after we ...
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  • 67.1k
9 votes

What was the aftermath of the proof of irrationality of $\sqrt 2$ for the Greeks?

Irrational numbers were not anathema to Pythagoreans, they never thought of them at all, or of rational numbers for that matter. The only numbers they acknowledged before, during, and after the ...
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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 ...
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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 ...
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