THE WEDDING AND THE OMPHALOS STONE

compiled by Dee Finney

Euclid

Euclid was a Greek mathematician. His book the Elements of Geometry set down how geometry was to be taught for the next 2000 years. He was born in 365BC and died in 275BC.

[1189] But even in physics where correspondence rules are used to 'explain’ by a four dimensional geometry the cosmic space-time structure, the data of measurements referred to can hardly be regarded as the same as those used to derive geometry initially. So far as this is so, the derivative references of geometry will differ from the correspondence references. Of course, nothing would prevent derivative references to be used also as correspondence references. During the long period while Euclidean geometry maintained sole jurisdiction over the conceptualization of space, there was no practical distinction between the two. And that is why the Euclidean axioms were taken to be a priori determinations of cosmic space relations.

Euclid, who put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first, makes mention of Euclid; and further they say that Ptolemy once asked him if there was in geometry any shorter way that that of the Elements, and he replied that there was no royal road to geometry. He is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, the latter having been contemporaries, as Eratosthenes somewhere says.

(Plato died 347 B.C.; Archimedes lived 287-212 B.C.)

Latin author, Stobaeus (5th Century A.D.):

Someone who had begun to read geometry with Euclid, when he had learnt the first theorem, asked Euclid, "what shall I get by learning these things?" Euclid called his slave and said, "Give him threepence, since he must make gain out of what he learns."

Sarton, p. 19: Athenian philosopher, Proclus (410 A.D. - 485): Ptolemy I, king of Egypt, asked Euclid "if there was in geometry any shorter way than that of the Elements, and he answered that there was no royal road to geometry."

Heath, History p. 355: Arabian author, al-Qifti (d. 1248):

Euclid, son of Naucrates, and grandson of Zenarchus, called the author of geometry, a philosopher of somewhat ancient date, a Greek by nationality, domiciled at Damascus, born at Tyre, most learned in the science of geometry, published a most excellent and most useful work entitled the foundation or elements of geometry, a subject in which no more general treatise existed before among the Greeks: nay, there was no one even of later date who did not walk in his footsteps and frankly profess his doctrine... For this reason the Greek philosophers used to post up on the doors of their schools the well-known notice, "Let no one come to our school, who has not first learnt the elements of Euclid."

Heath notes that ancient Arabian scholars describe many important Greek scholars as Arabian.

Heath, History p. 356: Pappus (end of 3rd Century A.D.): Apollonius [another mathematician] "spent a very long time with the pupils of Euclid at Alexandria"; also: "The four books of Euclid's Conics were completed by Apollonius, who added four more and gave us eight."

Heath, The Thirteen Books of the Elements, p. 6: The Arabians pronounced Euclides "Uclides" and thought his name came from two Arabic words: Ucli, which means "key," and Dis, which means "measurement." They thought Euclid's name meant, essentially, "key to geometry."

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