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.

Filter by
Sorted by
Tagged with
2
votes
1answer
66 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 ...
4
votes
4answers
220 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 ...
4
votes
1answer
137 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 ...
1
vote
1answer
151 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. ...
0
votes
1answer
323 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 ...
2
votes
0answers
64 views

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 ...
1
vote
1answer
87 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 ...
3
votes
1answer
141 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 ...
0
votes
0answers
118 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 ...
0
votes
1answer
102 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 ...
0
votes
1answer
82 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 ...
3
votes
3answers
540 views

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 ...
5
votes
1answer
203 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] ...
3
votes
1answer
180 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 ...
4
votes
2answers
191 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: ...
0
votes
0answers
66 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 ...
4
votes
3answers
170 views

Did Eudoxus really set out to partition irrationals (Dedekind cuts) with rationals or was that a mere side effect we perceive through our modern POV?

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, ...
3
votes
1answer
66 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,...
5
votes
3answers
219 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 ...
4
votes
1answer
867 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 ...
7
votes
2answers
1k views

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 ...
2
votes
0answers
223 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 ...
0
votes
0answers
88 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 ...
0
votes
1answer
111 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/...
7
votes
3answers
203 views

How was the Antikythera Mechanism moved?

I understood all the gears and cogwheels in the Antikythera Machine, but I not sure what make all these stuffs works inside the box. It's mechanical movement done by hand-wound style?
8
votes
1answer
180 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 ...
6
votes
1answer
469 views

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 ...
3
votes
1answer
134 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 ...
1
vote
1answer
82 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 ...
1
vote
2answers
73 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 ...
4
votes
3answers
1k views

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 ...
5
votes
2answers
691 views

How was the focus/directrix property of conic sections discovered?

I've always thought that defining conic sections by a locus of points w.r.t the ratio of the distance to the focus and directrix was always "too artificial" - how does one actually discover this ...
2
votes
2answers
325 views

Was Babylonian Mathematics as sophisticated as Greek mathematics?

Why its true that the Egyptians did not see much developments. It has been said that the Babylonians were equal to the Greeks in mathematical achievement in terms of having an axiomatic, deductive ...
2
votes
2answers
777 views

How did Ptolemy calculate the distance to the moon

I've read that Hipparchus measured the distance to the Moon using the lunar and solar eclipse and obtained a value around 67.3 Earth radii. It also says that soon after Ptolemy gave a more accurate ...
3
votes
3answers
909 views

How did Aristotle influence Euclid?

In other words, how is Aristotle's logic represented in Euclid's Elements? I have read many articles where Euclid's Elements is linked to Aristotle's logic, but I do not understand, and I can't find ...
4
votes
1answer
462 views

What are Philolaos' “even-odd” numbers?

Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each ...
5
votes
2answers
470 views

how sophisticated was Egyptian and Babylonian mathematics compared to the Greeks

It seems like the focus always tends to be on the achievement of Greek math (which strikes of eurocentrism a little bit) while civilizations like the Egyptians and Babylonians are overlooked why do ...
5
votes
2answers
326 views

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

I'm reading "Professor Stewart's Incredible Numbers," by Ian Stewart and in there it is claimed that In early Greece, the list of numbers started $2, 3, 4,$ and so on: $1$ was special, not "really" ...
3
votes
2answers
186 views

How did Archimedes arrive at his principle in his time?

Archimedes principle: Any object, wholly or partially immersed in a stationary fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. I get that this can be ...
5
votes
0answers
136 views

Plato's chemical formula for water

In a paper about Plato's Timaeus I came across a cryptic note saying: "Academic research usually avoids noting that Plato's assertion about water consisting of two parts air and one part fire is ...
7
votes
2answers
5k views

Did the ancient Greeks have zero in their number system?

Roman numerals don't have 0. I was taught that the arabs introduced 0 in their arabic numerals and it is depicted as a decimal point. The arabs, in turn, got their number system from india in ...
2
votes
1answer
367 views

Instances of the use and application of mathematics in Ancient Greece

I am setting out to write a paper, the thesis of which only needs to have the property that it addresses "how was mathematics used in Ancient Greece". I have begun my own investigation (i.e. ...
3
votes
1answer
566 views

What is the history of angle quintisection (division into five equal parts)?

I was reading lately that the quintisection of an angle is possible with paper folding (origami). Now, in contrast to the trisection of an angle, a problem which was discussed historically, and was ...
9
votes
1answer
380 views

What did ancient near eastern protoscience believe about germination?

Two Bible verses seem to indicate that ancients believed germination was the death of a seed, and a resurrection or rebirth of that seed into a plant: Unless a grain of wheat falls into the earth ...
3
votes
2answers
214 views

Looking for source of foods associated with specific humors

Let's get this out of the way- I am aware that this is nonsense today. However, historically it would have been considered science, so I'm asking here rather than in the History SE. Classically, ...
2
votes
1answer
118 views

Which ancient mathematician was opposed to “application” of math?

I seem to recall reading about a mathematician from antiquity whose view was, roughly, that to "apply" math was to do it violence (or indeed, to expedite violence) and so looked down on applications. ...
7
votes
2answers
142 views

What manuscript is depicted in the HSM advertisement?

The following advertisement recently appeared in the sidebar on math.se: Is the Greek script on the left actually from a mathematical manuscript? What is its source?
13
votes
3answers
1k views

Why wasn't probability developed in ancient Greece?

The modern axiomatic approach to probability was established by Kolmogorov nearly 70 years ago. According to Wikipedia, the first ideas connected to a mathematical theory of probability arose with ...
2
votes
2answers
243 views

What are the earliest mentions of Prime Numbers?

Egyptians and Babylonians must have had some ideas about primes but what are the earliest mentions or comments? Where is the first list of primes? After Burkert's work on Pythagoreanism an answer ...
6
votes
1answer
475 views

Why does Aristotle write 'astrology' when Plato writes 'astronomy'?

Checking modern quotes from Aristotle almost everywhere the word astronomy is found to be replacing the original Greek or Latin astrology' (astrologia). In Plato'...