Questions tagged [ancient-greece]

For questions about events occurring in Greece and the immediate areas around it between 800 B.C. and 600 A.D.

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Discussions of why the Greeks "squared the..." geometrically

The Wikipedia article on squaring the circle has a relatively good history of their efforts on this particular problem, but it fails to mention why the Greeks were interested in this methodology on a ...
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1 vote
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Exhaustion method blocked by religious aspects?

Eudoxus developed the exhaustion method for calculating areas that continued with Archimedes and then only in the 16th century with Stevin and Cavalieri. Why did it take so long? Was there any ...
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2 votes
1 answer
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The abstraction of mathematics from physics

When and how did mathematics come to be abstracted away from the physical world? At first, mathematics would originate in its simplest form of counting and addition as to keep track of certain ...
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7 votes
1 answer
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Adrastus, Proclus, and 2+8+50+288+… versus 1+9+49+289+…

According to the MacTutor essay "D'Arcy Thompson on Greek irrationals" (which I take to be a version of Thompson's original essay whose only liberty with the original text is giving English ...
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What was the difference between Number and Magnitude in Ancient Greece [duplicate]

I've been reading Infinite Powers by Steven Strogatz and in it, he writes about how the greeks differentiated between numbers as being discrete and magnitudes as being continuous. However, all of ...
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Al-Fihrist survivals

I wonder if there is any estimate about the percentage of the books that survived from Islamic ancient time listed in Ibn Nadim's Al Fihrist? Is there any counterpart of this work belonging to ancient ...
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Classification of "Epitaph of Diophantus" problem

The well-known riddle of the Epitaph of Diophantus, attributed to Metrodorus, is one of the style of simple problem in algebra whose pattern when expressed in contemporary algebraic notation is: $$x = ...
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What is Aristotle's view on Plant generation?

I am new to Aristotle study, In Book 1 of Generation of Aristotle give his view on plant generation, In Book 1.1 Aristotle writes " But all those creatures which do not move, as the Testacea and ...
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What date is assigned to Hippocratic treatises "On Generation" and "On the Nature of the Child"?

On the nature of the Child is quoted by Galen in his Book "On Semen". I want to know what date is given to these two books, especially "On Generation"?
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(Where) does Plato define perfect number?

I've read several texts suggesting that Plato defines "perfect number" in his Republic, book VIII 546 b. However, there's no definition as we can see from - for example - this translation: &...
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Did the ancients construct higher genus curves?

I know that the ancients had several ways to construct geometric shapes. I know two of them: the biggest one, ruler and compass, with which you can build some polygons, bisect an angle, etc, but not ...
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Incommensurables and their effects on ratios [duplicate]

I am currently reading "The History of Mathematics" by Uta C. Merzbach. I'm confused on the significance and the disruption caused by the discovery of incommensurable numbers. I get that all ...
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2 votes
1 answer
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What is "female seed" in Galen's work?

On the last page (page 84) of Anthony Preus's paper$^\star$ on Galen's criticism of Aristotle's Conception Theory, the author writes that Galen discussing the second book of "On Seed", which ...
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Historicity of Euclid. Looking for the references of Euclid in ancient texts that has survived [duplicate]

The general consensus is that Euclid was a real historical figure. Wikipedia https://en.wikipedia.org/wiki/Euclid concludes on the hypothesis that Euclid was not a real person, "This hypothesis ...
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Nachmanides and the Greek proof that the earth is mostly covered with water

In the Biblical account of creation, G-d divided the waters. The rabbi and Biblical commentator Nachmanides wrote about this that he believes the Greek demonstration that the earth is mostly covered ...
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To what extent was astronomical knowledge in ancient Greece common knowledge?

I have a question about ancient Greek astronomy. We know certainly that the likes of Pythagoras, Aristotle, Anaximander, et al had much to say about the motions of the stars, planets, comets, etc, ...
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What happened to the original sources of Euclid's Elements?

I am aware of the fact that Euclid's Elements is a compilation of the works of previous Greek mathematicians like Thales, Pythagoras (his school), Eudoxus, Theaetetus, etc. However, I want to know the ...
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Is it true that there were "wooden guiding structures" proposed, by the ancient Greek, to account for the motions of the planets?

I can remember after attending a philosophy of science class, I put forward the thought ancient Greek had about the motion of the planets. I had read about them thinking there are wooden circular ...
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How did Eratosthenes know the difference between two cities? [duplicate]

First, be familiar with how Eratosthenes first got an estimation of the earth's circumference. My questions is fairly simple: how did they know the distance between two cities back in the days? ...
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-1 votes
2 answers
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Do we know of any ancient 'Introduction to Mathematics' in Ancient Greece, besides "The Elements"? [duplicate]

Given that Euclid's work is titled "The Elements", it is safe to imply that it is a compendium of elementary results of Ancient Greek Geometry. Other works, such as those of Apollonius, ...
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Greek fire explosive I assume -- did an accident lead any inventor to consider using it as a propellant?

I would guess that occasionally pots of Greek fire did explode and if so, one would have seen how far shards were sent. Assuming this is true, did anyone suggest something like a cannon or a bomb ...
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Greek astronomy vs astrology

I wonder if would be right to say that while most ancient astronomical activities, such as building and improvement of observational structures, had a strong astrological component, the Greek ...
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1 answer
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Are the ancient Egyptians and the ancient Mesopotamians really the cradles of civilization? [closed]

Is it true that ancient Greek knowledge of mathematics, science, astronomy, engineering, architecture, civilization came from the ancient Minoan civilization and ancient Mycenaean civilizations and ...
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1 answer
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Gravity of Plato

What is the description of the gravitational interaction in the philosophy of Plato? Are there some drastic differences from Aristotle's physics?
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What dialect of ancient Greek was taught to natural philosophers?

Ancient Greek had a large impact on scientific and mathematical language and thinking leading into the Enlightenment period and beyond. But "ancient Greek" could refer to any dialect ...
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2 votes
1 answer
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When did mathematicians suspect that $\pi$ is irrational?

The title says it all. The irrationality of $\pi$ was proved by Lambert in the 18th century, but the Greeks at the time of Pythagoras already knew that $\sqrt2$ and the golden ratio were irrational. ...
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1 vote
1 answer
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What did the ancient Greeks know about the solar system, and how?

I'm aware that it was known to the ancient Greeks that the planets were somehow different from the stars. But in what depth did they know the solar system? In particular, did they know: that the sun ...
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1 vote
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Why didn't the ancient Greeks consider 1 to be odd?

The Wikipedia page on parity currently says: The ancient Greeks considered 1, the monad, to be neither fully odd nor fully even Why didn't they consider 1 as odd? (I am assuming they already had the ...
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-1 votes
2 answers
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Why isn't the history of mechanics dated from Archimedes time?

It's often said - and more often written - and perhaps, even more spoken of - that modern physics began with Galileo due to his application of mathematics to motion. This is the position taken by ...
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7 votes
2 answers
481 views

What does "given in species" mean in old geometry textbooks?

I recently came across the term "triangle given in species" in Hatton's Projective Geometry. Searching in archive.org turned up other examples (such as this) of 19th century texts, and it ...
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Did Archimedes view fractions as "numbers"?

For quite some time I had the wrong impression that classical Greek mathematicians didn't use fractions. (I don't remember where I had this from.) But I recently looked into Heath's book about ...
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6 votes
1 answer
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Are there commented English translations of Pappus's works on conics?

I'm investigating the conics in ancient Greece, I have the works of Apollonius, Diocles and Euclid, written with great commentary (both explaining the math and the historical context) that make them ...
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-1 votes
1 answer
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How did the Greeks label their axes?

In the current era, we label the Cartesian plane in x and y as our basis vectors, but what did the Greeks use to label their axis? The Greeks were around long before Descartes, so did they even use ...
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What are the sources for Democritus’ experiment of dividing a shell down to its atoms?

It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits ...
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8 votes
2 answers
535 views

How did Eratosthenes know the distance between Aswan and Alexandria?

In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
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Did Ptolemy and other Greek scientists actually measure the distance to the Sun?

According to Subhash C. Kak: Early Theories on the Distance to the Sun: “Pancavimsa Brahmana states that the heavens are 1000 earth diameters, de, away from the earth. The sun was also taken to be ...
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2 votes
1 answer
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Superscripts and constants in Diophantus’ Arithmetica

Diophantus’ notation for higher powers of the unknown includes a superscript, usually written as a lowercase or uppercase upsilon - e.g., $\Delta^{\upsilon}$ as the square. It is not clear to me ...
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4 votes
4 answers
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Did Renaissance mathematicians once consider themselves inferior to the great ancient mathematicians?

In the book "What Do You Care What Other People Think?", Feynman talks about how in the 16th century Niccolo Tartaglia discovered a solution to cubic equations. He says while this was not a major ...
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4 votes
1 answer
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Are Euclid's theorems and proofs due to Euclid?

Some appear to argue that much of the Elements by Euclid is a compilation of knowledge handed down to Euclid from his predecessors. On the other hand, some credit the proof, of the Pythagorean theorem ...
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1 vote
1 answer
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I can't comprehend the sentence in Euclid Elements [closed]

I am Korean, and I thought I can understand majority of english sentences, but this is really hard to translate literally for me. Even though I asked it to my English teacher, he did not know either. ...
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Why 1 was source of numbers even though ancient Greeks knew about irrational number?

In Ancient Greek, most people like Pythagoras thought 1 (monad, unity) is no number, but it is ruler and beginning of all other numbers. And Pythagoras thought everything is number. But they found ...
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On Trigonometric Methods Available to Aristarchus

Approximately 2300 years ago, Aristarchus proposed a method for determining the relative distances of the sun and the moon in relation to the earth. Specifically, he asserted that when the moon is in ...
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1 vote
1 answer
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What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?

In modern textbooks, students are greeted with plenty of exercises. Usually they are also organized in such a way that you have examples and pointers to what concepts are most important. The elements ...
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3 votes
1 answer
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When did people start to state and justify properties of arithmetical operations?

I have question regarding the history of the idea of founding mathematics (specially arithmetic) on a logical basis. What I'm interested in knowing is, at what point historically people started to ...
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Does the story about Thales and the heights of pyramids illustrate that Thales did not know of AAA triangle similarity?

Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by ...
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What is the story behind the recently discovered gear fragment of Olbia?

Until yesterday i thought that nothing direct is known about the "Archimedes's planetarium" - an elaborate ancient planetarium based on complex gear mechanism that could represent the geocentric ...
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What geometric results were first proven by assuming all real numbers are rational?

Pythagoras and his followers believed that all magnitudes are commensurable; that is, the ratio of two magnitudes of the same kind, like two lengths or two areas, is equal to the ratio of natural ...
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4 votes
3 answers
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How was gravity explained in Ancient Greek and Roman times?

Gravity is of course something that we can all observe. Stuff falls towards the ground. But not everything: some things like steam or smoke defy this force and instead float up. During Ancient Greek ...
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5 votes
1 answer
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Why did Euclid define "a unit" instead of "the unit"?

I know Euclid's Definition VII.1 of a unit only from English and German translations: A unit is (that) according to which each existing (thing) is said (to be) one. [translation by Fitzpatrick] ...
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3 votes
1 answer
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Does any extant Greek text prove that the area of an inscribed regular polygon increases with the number of sides?

Does any extant Greek text prove that the area of a regular polygon inscribed in a fixed circle increases with the number of sides in the polygon? I can't find such a proposition in Euclid, but the ...
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