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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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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51 views
Aristotle's and Plato's even and odd numbers, sets and actual infinity [closed]
Plato and Aristotle both use the terms even and odd about numbers (and have a separate discussion of the number 1).
From this point, it seems, there would be no great distance to the sets of even and ...
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1answer
85 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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1answer
92 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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54 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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148 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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117 views
When Did the Notion of ``Limit'' Arise and for What Purpose?
It is my understanding that Cauchy was the first to incorporate the notion of a ``$\delta\epsilon$ limit in his proofs, although a definition was not formulated until Weierstrass did so.
My question ...
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1answer
154 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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106 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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92 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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154 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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447 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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272 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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83 views
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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1answer
102 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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1answer
101 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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1answer
158 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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1answer
339 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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1answer
76 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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297 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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213 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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158 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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422 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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1answer
95 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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155 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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267 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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2answers
184 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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1answer
88 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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335 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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1answer
202 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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297 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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88 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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3answers
331 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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230 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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1answer
67 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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238 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 ...
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3k views
Sphericity of Earth from lunar eclipses - is Aristotle's argument valid?
Aristotle is often credited with proving the sphericity of Earth from the fact that the shadow of the Earth on the moon during lunar eclipses is always an arc of a round circle (as opposed to arcs of ...
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Did Aristotle note that ships disappear over the horizon hull-first?
I have run across several references to Aristotle's arguments for a spherical earth which claim that he noted that ships sink over horizon hull-first. For instance, Isaac Asimov writes in his essay ...
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245 views
How old is the Pythagorean Theorem? [closed]
More specifically, what is the oldest evidence of human awareness of what we now call the Pythagorean Theorem?
The phrase, "evidence of human awareness" was used to exclude a different question of ...
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102 views
Was Aristotle first to talk about gravity?
Aristotle was chatting about forces we later identified as gravity at about 300BC. He made a few mistakes regarding heavy objects falling faster etc, but that is by the by. Was he the first ever to ...
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1answer
112 views
What field will we be remembered for developing? [closed]
I had a course on History of Mathematics this semester and it seemed that each civilization became known for developing a particular area of mathematics. For example, Arithmetic and Ancient Egypt/...
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346 views
How was the Antikythera Mechanism moved?
I understood all the gears and cogwheels in the Antikythera Machine, but I am not sure what make all these stuffs works inside the box.
Is it mechanical movement done in hand-wound style?
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1answer
251 views
Was a regular heptagon ever constructed by ancient Greeks?
Today it is well known that a regular heptagon cannot be constructed with straightedge and compass, since it would require to solve an equation of third degree which is not possible with the standard ...
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Did Indian astronomers realize the sphericity of the earth independently of the Greeks?
Reading Wikipedia's articles on the flat earth, spherical earth, and history of geodesy makes it clear that virtually every society recognizing the spheroidal shape of the earth today owes the ...
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198 views
Straightedge and compass
According to most discussions of Euclid's Elements, this work - and indeed, much of Ancient Greek geometry - should be seen as engaged in the game of figuring out what can be done with straightedge ...
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129 views
What did the Greeks call the “trial and error” reasoning process?
What did the Greeks call the "trial and error" reasoning process?
Bruce Aune's review of Wilson's Peirce's Empiricism: Its Roots and Its Originality claims "The name 'empirici' is in fact traceable ...
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85 views
Whether Euclid considered squares to be rectangles
When I look up
'that which is right-angled but not equilateral'
there are translations that show the word before the above phrase to 'oblong', some that show 'rectangle' and some that show both ...
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Compass and straightedge: why?
Why is it that, in ancient Greece, mathematicians tried to solve geometrical problems using compass and straightedge only and, apparently, only if that failed, they tried to use other tools? Note that ...
