“But Hermotimus, the Colophonian, rendered more abundant what was formerly published by Eudoxus and Theætetus, and invented a multitude of elements, and wrote concerning some geometrical places. But Philippus the Mendæan, a disciple of Plato, and by him inflamed in the mathematical disciplines, both composed questions, according to the institutions of Plato, and proposed as the object of his enquiry whatever he thought conduced to the Platonic philosophy.”

—  Proclus

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV.

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Greek philosopher 412–485

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“Again, Amyclas the Heracleotean, one of Plato's familiars, and Menæchmus, the disciple, indeed, of Eudoxus, but conversant with Plato, and his brother Dinostratus, rendered the whole of geometry as yet more perfect. But Theudius, the Magnian, appears to have excelled, as well in mathematical disciplines, as in the rest of philosophy. For he constructed elements egregiously, and rendered many particulars more universal. Besides, Cyzicinus the Athenian, flourished at the same period, and became illustrious in other mathematical disciplines, but especially in geometry. These, therefore, resorted by turns to the Academy, and employed themselves in proposing common questions.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV.

“After Pythagoras, Anaxagoras the Clazomenian succeeded, who undertook many things pertaining to geometry. And Oenopides the Chian, was somewhat junior to Anaxagoras, and whom Plato mentions in his Rivals, as one who obtained mathematical glory. To these succeeded Hippocrates, the Chian, who invented the quadrature of the lunula, and Theodorus the Cyrenean, both of them eminent in geometrical knowledge. For the first of these, Hippocrates composed geometrical elements: but Plato, who was posterior to these, caused as well geometry itself, as the other mathematical disciplines, to receive a remarkable addition, on account of the great study he bestowed in their investigation. This he himself manifests, and his books, replete with mathematical discourses, evince: to which we may add, that he every where excites whatever in them is wonderful, and extends to philosophy. But in his time also lived Leodamas the Thasian, Architas the Tarentine, and Theætetus the Athenian; by whom theorems were increased, and advanced to a more skilful constitution. But Neoclides was junior to Leodamas, and his disciple was Leon; who added many things to those thought of by former geometricians. So that Leon also constructed elements more accurate, both on account of their multitude, and on account of the use which they exhibit: and besides this, he discovered a method of determining when a problem, whose investigation is sought for, is possible, and when it is impossible.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV.

“But Eudoxus the Cnidian, who was somewhat junior to Leon, and the companion of Plato, first of all rendered the multitude of those theorems which are called universals more abundant; and to three proportions added three others; and things relative to a section, which received their commencement from Plato, he diffused into a richer multitude, employing also resolutions in the prosecution of these.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV.

“And thus far historians produce the perfection of this science. But Euclid was not much junior to these, who collected elements, and constructed many of those things which were invented by Eudoxus; and perfected many which were discovered by Theætetus. Besides, he reduced to invincible demonstrations, such things as were exhibited by others with a weaker arm. But he lived in the times of the first Ptolemy: for Archimedes mentions Euclid, in his first book, and also in others. Besides, they relate that Euclid was asked by Ptolomy, whether there was any shorter way to the attainment of geometry than by his elementary institution, and that he answered, there was no other royal path which led to geometry. Euclid, therefore, was junior to the familiars of Plato, but more ancient than Eratosthenes and Archimedes (for these lived at one and the same time, according to the tradition of Eratosthenes) but he was of the Platonic sect, and familiar with its philosophy: and from hence he appointed the constitution of those figures which are called Platonic, as the end of his elementary institutions.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV. On the Origin of Geometry, and its Inventors.

Al-Farabi photo

“Farabi followed Plato not merely as regards the manner in which he presented the philosophic teaching in his most important books. He held the view that Plato’s philosophy was the true philosophy. To reconcile his Platonism with his adherence to Aristotle, he could take three more or less different ways. First, he could try to show that the explicit teachings of both philosophers can be reconciled with each other. He devoted to this attempt his Concordance of the opinions of Plato and Aristotle. The argument of that work is partly based on the so-called Theology of Aristotle: by accepting this piece of neo-platonic origin as a genuine work of Aristotle, he could easily succeed in proving the substantial agreement of the explicit teachings of both philosophers concerning the crucial subjects. It is however very doubtful whether Farabi considered his Concordance as more than an exoteric treatise, and thus whether it would be wise of us to attach great importance to its explicit argument. Secondly, he could show that the esoteric teachings of both philosophers are identical. Thirdly, he could show that “the aim” of both philosophers is identical.”

Al-Farabi (872–951) Philosopher in 10th century Central Asia

Leo Strauss, Farabi's Plato http://contemporarythinkers.org/leo-strauss/essay/farabis-plato/, Louis Ginzberg Jubilee Volume, American Academy for Jewish Research, 1945. Reprinted, revised and abbreviated, in Persecution and the Art of Writing.

“Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', 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 (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.”

Proclus (412–485) Greek philosopher

As quoted by Sir Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol.1 https://books.google.com/books?id=UhgPAAAAIAAJ Introduction and Books I, II p.1, citing Proclus ed. Friedlein, p. 68, 6-20.

Ralph Waldo Emerson photo

“Plato was synthesis of Europe and Asia, and a decidedly Oriental element pervades his philosophy, giving it a sunrise color.”

Ralph Waldo Emerson (1803–1882) American philosopher, essayist, and poet

Source: Abhedananda, Swami India and her people, a study in the social. political, educational and religious conditians of India. [6th ed.] Calcutta, Ramakrishna Vedanta Math [1945]

Thomas Little Heath photo

“Theodorus of Cyrene and Theaetetus generalised the theory of irrationals, and we may safely conclude that a great part of the substance of Euclid's Book X. (on irrationals) was due to Theætetus. Theætetus also wrote on the five regular solids, and Euclid was therefore no doubt equally indebted to Theætetus for the contents of his Book XIII. In the matter of Book XII. Eudoxus was the pioneer. These facts are confirmed by the remark of Proclus that Euclid, in compiling his Elements, collected many of the theorems of Eudoxus, perfected many others by Theætetus, and brought to irrefragable demonstration the propositions which had only been somewhat loosely proved by his predecessors.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
Achimedes (1920)

Edith Hamilton photo

“Through Plato, Aristotle came to believe in God; but Plato never attempted to prove His reality. Aristotle had to do so. Plato contemplated Him; Aristotle produced arguments to demonstrate Him. Plato never defined Him; but Aristotle thought God through logically, and concluded with entire satisfaction to himself that He was the Unmoved Mover.”

Edith Hamilton (1867–1963) American teacher and writer

Source: The Echo of Greece (1957), Chapter 4, "The School Teachers"

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“There is no author to whom my father thought himself more indebted for his own mental culture, than Plato, or whom he more frequently recommended to young student. I can bear similar testimony in regard to myself. The Socratic method, of which the Platonic dialogues are the chief example, is unsurpassed as a discipline for correcting the errors, and clearing up the confusions incident to the intellectus sibi permissus.”

John Stuart Mill book Autobiography

Source: Autobiography (1873)

https://archive.org/details/autobiography01mill/page/21/mode/1up pp. 21–22

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