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 xxvi
... Limit . These mathematical facts do not strike us as profound , but for Proclus they are a way of introducing the student to deep metaphysical truths . 51 Having discussed the common principles of mathematics , Proclus turns in chapters ...
... Limit . These mathematical facts do not strike us as profound , but for Proclus they are a way of introducing the student to deep metaphysical truths . 51 Having discussed the common principles of mathematics , Proclus turns in chapters ...
Side xxviii
... Limit and the Unlimited as ultimate principles . Given Proclus ' adulation of Pythagoras and Plato , one might have expected him to be satisfied with the Pythagorean division alone . But he gives another , which he ascribes to Geminus ...
... Limit and the Unlimited as ultimate principles . Given Proclus ' adulation of Pythagoras and Plato , one might have expected him to be satisfied with the Pythagorean division alone . But he gives another , which he ascribes to Geminus ...
Side lxv
... Limit ( répas ) and the Unlimited ( aπepov ; 5.15-7.12 ) . The Limit expresses the character of boundedness or determinateness that belongs to every intelligible object ; the Unlimited represents the fecundity of being , ever going ...
... Limit ( répas ) and the Unlimited ( aπepov ; 5.15-7.12 ) . The Limit expresses the character of boundedness or determinateness that belongs to every intelligible object ; the Unlimited represents the fecundity of being , ever going ...
Side 4
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Side 5
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A Commentary on the First Book of Euclid's Elements Proclus,Proclus Diadochus,Proclus Proclus Ingen forhåndsvisning tilgjengelig - 1970 |
Vanlige uttrykk og setninger
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