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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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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44 views
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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77 views
(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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102 views
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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49 views
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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102 views
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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41 views
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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62 views
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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94 views
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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247 views
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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66 views
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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41 views
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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89 views
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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76 views
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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47 views
How long is the "Great Year" in the Antikythera Mechanism?
Through antiquity it was understood that after a finite time interval the configurations of the planets will repeat and this was called a "Great year" or, eventually a "Platonic year&...
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115 views
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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107 views
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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67 views
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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226 views
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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195 views
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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323 views
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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106 views
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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158 views
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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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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384 views
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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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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137 views
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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161 views
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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388 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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371 views
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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80 views
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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342 views
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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324 views
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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169 views
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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456 views
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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100 views
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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160 views
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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351 views
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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215 views
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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104 views
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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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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401 views
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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212 views
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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339 views
What was the relation between Euclid's points and Democritus' atoms?
Geometry as described in Euclid's Elements originated roughly at the same same time as Democritus described his atomic theory.
I wonder how close these two points of view were related at those times: ...
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114 views
Was 360 considered a magic number, possibly?
The number $360$ as the number of units into which the circle is divided has some nice properties:
it has as many divisors as a number of its size can have
it's nearly the number of days per year
...
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424 views
Did Eudoxus really set out to present irrationals as Dedekind cuts?
I've been intrigued by the similarities between what Eudoxus' Theory of Proportions and Dedekind cuts.
However, I wish to question this "perceived similarity" and would like to where the flaws are, ...
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322 views
Why didn't Euclid try to assign numbers to lengths?
Preliminary note: With "Euclid" I don't mean a person but the mathematicians of the Euclidean period of which Euclid (if he had been one person) was a representative.
I imagine that Euclid could have ...
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72 views
Whereabouts of oldest extant source for Apollonius’ *Conics*, Books I - IV
Regarding Conics, it is widely written, e.g. Rutger's site, that:
The first four books have come down to us in the original Ancient Greek, but books V-VII are known only from an Arabic translation,...
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257 views
The Greeks did not discover "a single scientific law"
The title is drawn from a sentence in a Jim Holt article,
"The Dangerous Idea of the Infinitesimal,"
now a chapter in his book collection.1
I found this a striking claim, and perhaps true, as
the ...
