According to most accounts, geometry was first discovered among the Egyptians, taking its origin from the measurement of areas. For they found it necessary by reason of the flooding of the Nile, which wiped out everybody's proper boundaries. Nor is there anything surprising in that the discovery both of this and of the other sciences should have had its origin in a practical need, since everything which is in process of becoming progresses from the imperfect to the perfect.

The Pythagoreans considered all mathematical science to be divided into four
parts: one half they marked off as concerned with quantity, the other half with
magnitude; and each of these they posited as twofold. A quantity can be
considered in regard to its character by itself or in relation to another
quantity, magnitudes as either stationary or in motion. Arithmetic, then,
studies quantity as such, music the relations between quantities, geometry
magnitude at rest, spherics magnitude inherently moving.*A Commentary on
the First Book of Euclid's Elements*

Wherever there is number, there is beauty.

Quoted in M Kline,
*Mathematical Thought from Ancient to Modern Times*

This, therefore, is mathematics: she reminds you of the invisible form of the
soul; she gives light to her own discoveries; she awakens the mind and purifies
the intellect; she brings light to our intrinsic ideas; she abolishes oblivion
and ignorance which are ours by birth.

Quoted in M Kline, *Mathematical
Thought from Ancient to Modern Times*

It is well known that the man who first made public the theory of irrationals
perished in a shipwreck in order that the inexpressible and unimaginable should
ever remain veiled. And so the guilty man, who fortuitously touched on and
revealed this aspect of living things, was taken to the place where he began and
there is for ever beaten by the waves.

Scholium to Book X of Euclid V.

Main index | Quotations index | Biographies
Index | |

History Topics | Societies, honours, etc. | Famous
curves | |

Time lines | Birthplace Maps | Search
Form | |

Mathematicians of the day | Anniversaries
for the year |

JOC/EFR February 2000
The URL of this page is: | School of
Mathematics and Statistics University of St Andrews, Scotland | |

http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Proclus.html |