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 xviii
... things Scholars often call the upper three levels of this schema , hypostases , nonsensible realms of reality . The fourth level is derived from Plato's Timaeus ( 34cff . , 41dff . ) , where the soul is said to be fashioned out of a ...
... things Scholars often call the upper three levels of this schema , hypostases , nonsensible realms of reality . The fourth level is derived from Plato's Timaeus ( 34cff . , 41dff . ) , where the soul is said to be fashioned out of a ...
Side xxi
... things into other things . " He goes on to explain that " opinion receives a scientific method of making distinctions from dianoia and applies it to other things . Opinion [ in this sense ] is not uncertain , it is not divided up by the ...
... things into other things . " He goes on to explain that " opinion receives a scientific method of making distinctions from dianoia and applies it to other things . Opinion [ in this sense ] is not uncertain , it is not divided up by the ...
Side xxii
... things . " I am now in a position to give the more precise account of the Pro- clean hierarchy toward which I have been working . At the highest level there is the One , which is apprehended only by a merging of the self which ...
... things . " I am now in a position to give the more precise account of the Pro- clean hierarchy toward which I have been working . At the highest level there is the One , which is apprehended only by a merging of the self which ...
Side xxiv
... things and by teaching it to reason about spiritual things . 43 See , for example , Philoponus , Commentary on Aristotle's Categories 4.23-35 . 44 See , for example , Olympiodorus , Prolegomena 8.39-9.1 . On this inscription sec H. D. ...
... things and by teaching it to reason about spiritual things . 43 See , for example , Philoponus , Commentary on Aristotle's Categories 4.23-35 . 44 See , for example , Olympiodorus , Prolegomena 8.39-9.1 . On this inscription sec H. D. ...
Side lvi
... things mentioned but exists as a combination of all these categories " ( 123.19 ) . The reference is clearly to Syrianus and points to a time when he was still head of the School . This does not help us much , since the date of Syrianus ...
... things mentioned but exists as a combination of all these categories " ( 123.19 ) . The reference is clearly to Syrianus and points to a time when he was still head of the School . This does not help us much , since the date of Syrianus ...
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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