A Commentary on the First Book of Euclid's ElementsPrinceton University Press, 8. nov. 1992 - 355 sider In Proclus' penetrating exposition of Euclid's methods and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strength of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere. This is virtually the only work surviving from antiquity that deals with what we today would call the philosophy of mathematics. |
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Side xiv
... Plato - that is , the truth - was understood in an imperfect way by unnamed early philosophers , 18 and expressed in a perfect way by Plato ; it then became for the most part invisible to persons who called themselves philosophers ...
... Plato - that is , the truth - was understood in an imperfect way by unnamed early philosophers , 18 and expressed in a perfect way by Plato ; it then became for the most part invisible to persons who called themselves philosophers ...
Side xvi
... Plato . Phi- losophy for Proclus is Platonic exegesis because Plato knew all the phi- losophy there is to know . Scholars disagree about the accuracy of Neoplatonic conceptions of Platonic philosophy , but there is fairly gen- eral ...
... Plato . Phi- losophy for Proclus is Platonic exegesis because Plato knew all the phi- losophy there is to know . Scholars disagree about the accuracy of Neoplatonic conceptions of Platonic philosophy , but there is fairly gen- eral ...
Side xvii
... Plato's Republic . The metaphysical picture starts from a dichotomy between the intelligible world of being , the Forms , apprehended by intellect or mind ( nous ) in- dependently of the senses , and the world of becoming , apprehended ...
... Plato's Republic . The metaphysical picture starts from a dichotomy between the intelligible world of being , the Forms , apprehended by intellect or mind ( nous ) in- dependently of the senses , and the world of becoming , apprehended ...
Side xviii
... Plato's Parmenides , and with the ultimate God . 30 Adding this realm and making some terminological adjustments to bring vocabulary somewhat closer to Proclus ' , we obtain the schema of figure 2 . FIGURE 2 Domain the One Object the ...
... Plato's Parmenides , and with the ultimate God . 30 Adding this realm and making some terminological adjustments to bring vocabulary somewhat closer to Proclus ' , we obtain the schema of figure 2 . FIGURE 2 Domain the One Object the ...
Side xix
... Plato also uses mathematical ratios to describe the construction of the soul . Aristotle already knows of Platonists who call the soul a self - moving number . And there are indi- cations of a tradition stretching down to Proclus ( see ...
... Plato also uses mathematical ratios to describe the construction of the soul . Aristotle already knows of Platonists who call the soul a self - moving number . And there are indi- cations of a tradition stretching down to Proclus ( see ...
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A Commentary on the First Book of Euclid's Elements Proclus,Proclus Diadochus,Proclus Proclus Ingen forhåndsvisning tilgjengelig - 1970 |
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angle ABC angle BAC angles are equal angles equal Aristotle axioms Barocius base bisected called circle circular circumference coincide commentary common constructed contained demonstration diameter divided divisible drawn Eecke Elements equal angles equal sides equal to AC equal to angle equal to triangle equilateral triangle Euclid Euclid's Elements Eudemus exterior finite follows forms Friedlein Geminus geometer geometry given straight line greater than angle Greek Grynaeus Heath Hence hypothesis Iamblichus ideas indefinitely indivisible infinite intelligible interior angles isosceles triangle less Limit magnitude mathematics matter Neoplatonic Neoplatonists parallel lines parallelogram partless perpendicular philosophy plane Plato porism postulate principles problem Proclus produced propositions proved Pythagorean Reading with Barocius reason rectilinear angle rectilinear figures reduction to impossibility reference right angles sides equal soul square starting-points subtends surface Syrianus theorem things Timaeus tion triangle ABC understanding unequal Unlimited whole