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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Resultat 1-5 av 47
Side xii
... divided their logic into dialectic and rhetoric ( Diogenes Laertius , VII.41 ) . According to Cicero ( Tusculan Disputations II.9 ) , Philo , the last known head of Plato's Academy , di- vided his teaching equally between rhetoric and ...
... divided their logic into dialectic and rhetoric ( Diogenes Laertius , VII.41 ) . According to Cicero ( Tusculan Disputations II.9 ) , Philo , the last known head of Plato's Academy , di- vided his teaching equally between rhetoric and ...
Side xvii
... Divided Line at the end of book VI of the Republic Plato complicates the bifurcation between sensible and intelligible by subdividing the two realms and correlating certain " con- ditions of soul " with them ( figure 1 ) . FIGURE 1 ...
... Divided Line at the end of book VI of the Republic Plato complicates the bifurcation between sensible and intelligible by subdividing the two realms and correlating certain " con- ditions of soul " with them ( figure 1 ) . FIGURE 1 ...
Side xviii
... divided into three realms , the One , Being or Nous , and Soul , where Soul serves in a quite complex and not easily fathomed way as the intermediary between the nonsensible and sensible realms . A version of this hierarchy - which ...
... divided into three realms , the One , Being or Nous , and Soul , where Soul serves in a quite complex and not easily fathomed way as the intermediary between the nonsensible and sensible realms . A version of this hierarchy - which ...
Side xxi
... divided up by the variety of sensibles , and its knowledge ( eidêsis ) is not limited to mere suppositions ; rather it receives its content from nous and dianoia , 36 For the term " passive nous " see 52.3-12 , 55.23-56.22 , and 185.25 ...
... divided up by the variety of sensibles , and its knowledge ( eidêsis ) is not limited to mere suppositions ; rather it receives its content from nous and dianoia , 36 For the term " passive nous " see 52.3-12 , 55.23-56.22 , and 185.25 ...
Side xxv
... Divided Line passage of Plato's Re- public discussed above . He emphasizes that mathematics deals with a realm intermediate between being and sensibles . Proclus discusses the intermediate character of geometry in chapter III of the ...
... Divided Line passage of Plato's Re- public discussed above . He emphasizes that mathematics deals with a realm intermediate between being and sensibles . Proclus discusses the intermediate character of geometry in chapter III of the ...
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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