“But after these, Pythagoras changed that philosophy, which is conversant about geometry itself, into the form of a liberal doctrine, considering its principles in a more exalted manner; and investigating its theorems immaterially and intellectually; who likewise invented a treatise of such things as cannot be explained in geometry, and discovered the constitution of the mundane figures.”

— Proclus

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

Adopted from Wikiquote. Last update Sept. 14, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "But after these, Pythagoras changed that philosophy, which is conversant about geometry itself, into the form of a libe…" by Proclus?

Proclus 18

Greek philosopher 412–485

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.

“conventional terms such as service work, intellectual labor, and cognitive labor all refer to aspects of immaterial labor, but none of them captures its generality. As an initial approach, one can concieve immaterial labor in two principle forms. The first for refers to labor, that is primarily intellectual or linguistic such as problem solving, symbolic and analytical tasks, and linguistic expressions. This kind of immaterial labor produces ideas, symbols, codes, texts, linguistic figures, images and other such products. We call the other principle form of immaterial labor "affective labor."”

Antonio Negri book Multitude: War and Democracy in the Age of Empire

Affective labor, then, is labor that produces or manipulates affects such as a feeling of ease, well-being, satisfaction, excitement, or passion.
108
Multitude: War and Democracy in the Age of Empire

“A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid.”

Freeman Dyson book Infinite in All Directions

Source: Infinite in All Directions (1988), Ch. 2 : Butterflies and Superstrings, p. 17
Context: Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry?... It cannot be answered by a definition.

“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.

“"All things excellent are as difficult as they are rare." These words which bring to a close Spinoza's masterpiece Ethics, after the manner of Geometry, sum up the experience of a life as rare as it was difficult.”

Edgar A. Singer, Jr. (1873–1954) American philosopher

Source: Modern thinkers and present problems, (1923), p. 37: Chapter 2. Benedict de Spinoza, 1632-1677

“I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof”

Pierre de Fermat (1601–1665) French mathematician and lawyer

Letter to Frénicle (1657) Oeuvres de Fermat Vol.II as quoted by Edward Everett Whitford, The Pell Equation http://books.google.com/books?id=L6QKAAAAYAAJ (1912)
Context: There is scarcely any one who states purely arithmetical questions, scarcely any who understands them. Is this not because arithmetic has been treated up to this time geometrically rather than arithmetically? This certainly is indicated by many works ancient and modern. Diophantus himself also indicates this. But he has freed himself from geometry a little more than others have, in that he limits his analysis to rational numbers only; nevertheless the Zetcica of Vieta, in which the methods of Diophantus are extended to continuous magnitude and therefore to geometry, witness the insufficient separation of arithmetic from geometry. Now arithmetic has a special domain of its own, the theory of numbers. This was touched upon but only to a slight degree by Euclid in his Elements, and by those who followed him it has not been sufficiently extended, unless perchance it lies hid in those books of Diophantus which the ravages of time have destroyed. Arithmeticians have now to develop or restore it. To these, that I may lead the way, I propose this theorem to be proved or problem to be solved. If they succeed in discovering the proof or solution, they will acknowledge that questions of this kind are not inferior to the more celebrated ones from geometry either for depth or difficulty or method of proof: Given any number which is not a square, there also exists an infinite number of squares such that when multiplied into the given number and unity is added to the product, the result is a square.