La matematica del Rinascimento

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Between science and wisdom Pythagoras and the
beginning of Greek mathematics
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Autolico di Pitane
Ippocrate di Chio
Conone di Samo
Aristarco di Samo
Pitagora di Samo
Teeteto di Atene
Apollonio di Perga
Talete di Mileto
Eudosso di Cnido
Eudemo di Rodi
Archimede di Siracusa
Ipsicle di Alessandria Didimo di
Alessandria Filone di Alessandria Menelao di
Alessandria Erone di Alessandria Tolomeo di
Alessandria Diofanto di Alessandria Pappo di
Alessandria Teone di Alessandria
Eratostene di Cirene
Euclide di Alessandria
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Between science and wisdom
Thales of Miletus
Pythagoras of Samos
(VI century b. C.)
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Between science and wisdom
They say that Thales first proved that the circle
is divided into two equal parts by its diameter
Thales of Miletus
(VI century b. C.)
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Between science and wisdom
It is said that first he has established that the
angles at the base of each isosceles triangle are
equal.
Thales of Miletus
(VI century b. C.)
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Between science and wisdom
Thales of Miletus was able to measure the height
of the pyramids
Thales of Miletus
(VI century b. C.)
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Between science and wisdom
Thales led Pythagoras to sail to Egypt and meet
with the priests of Memphis and Diospolis,
because they were the ones who had instructed him
in those disciplines for which he was considered
wise by the people.
Porphyry, Vita Pythagorae
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Between science and wisdom
It is said that when Cambyses took possession of
Egypt, took prisoner Pythagoras who lived there
with the priests, and that Pythagoras, once in
Babylon, was initiated into the mysteries.
Cambyses lived precisely at the time of
Polycrates, to escape whose tyranny Pythagoras
had gone to Egypt.
Theologumena Arithmetica
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Between science and wisdom
They say that the one who first divulged the
nature of commensurability and incommensurability
to men who did not deserve to be made ??part of
this knowledge, was so hated by the other
Pythagoreans, that not only drove him from the
community, but also built him a tomb as if he had
died, he that once had been their friend
Iamblichus, De vita pythagorica
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Between science and wisdom
A proof of this type, for example, is that of the
incommensurability of the diagonal and the side
of the square, which is based on the fact that
if we assume that they are commensurable, odd and
even numbers are equal.
Aristotle, Prior analytics
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Between science and wisdom
Let ABCD be a square and suppose that the
diagonal BC is commensurable with the side AB.
Let E and Z be the smaller numbers that are to
one another in the ratio of BC to AB they are
relatively prime. But also their squares,
respectively, I and K are relatively prime. On
the other hand, the square of the diagonal is
twice the square of the side by Pythagoras
theorem. So I 2K, and I is even. In addition,
half of the square of an even number is also
even, and therefore I / 2, i.e. K, will be even.
But I and K are prime to each other, while two
even numbers can not be prime. Therefore either I
or K, or both, must be odd. On the other hand it
has been shown that both must be even. This is
contradictory, and thus the incommensurability is
proved.
Alexander of Aphrodisias, Analytica
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Between science and wisdom
In any right triangle, the square which is
described upon the side subtending the right
angle is equal to the squares described upon the
side which contain the right angle.
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Between science and wisdom
30
124,51,10
1,414213
4225,35
42,42639
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Between science and wisdom
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Between science and wisdom
C
B
A
D
ABC ACD CBD
AB2 AC2 CB2
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Between science and wisdom
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Between science and wisdom