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 xiii
... four high - paying chairs of philosophy in Athens , one for each of the four major sects , Platonists , Peripatetics , Stoics , and Epicureans , as well as at least one chair in rhetoric . These chairs were official appointments ...
... four high - paying chairs of philosophy in Athens , one for each of the four major sects , Platonists , Peripatetics , Stoics , and Epicureans , as well as at least one chair in rhetoric . These chairs were official appointments ...
Side liii
... Euclid's restriction of " parallelogram " 33 Propositions in Euclid's first book will normally be referred to hereafter by Roman numerals only . to four - sided figures is justified . Despite his liii PROCLUS AS A COMMENTATOR ON EUCLID.
... Euclid's restriction of " parallelogram " 33 Propositions in Euclid's first book will normally be referred to hereafter by Roman numerals only . to four - sided figures is justified . Despite his liii PROCLUS AS A COMMENTATOR ON EUCLID.
Side liv
Proclus Glenn R. Morrow. to four - sided figures is justified . Despite his twice - announced inten- tion ( 84.12 , 200.16 ) , he deals with a great variety of " cases " in his comments , and some of them are evidently inserted as ...
Proclus Glenn R. Morrow. to four - sided figures is justified . Despite his twice - announced inten- tion ( 84.12 , 200.16 ) , he deals with a great variety of " cases " in his comments , and some of them are evidently inserted as ...
Side lv
... four propositions establish.37 With regard to the contested fourth postulate - that all right angles are equal - he argues for its validity on the ground that the right angle is the standard by which all other angles are measured and as ...
... four propositions establish.37 With regard to the contested fourth postulate - that all right angles are equal - he argues for its validity on the ground that the right angle is the standard by which all other angles are measured and as ...
Side lxix
... four books . These also I have put in the mar- gins , together with Barocius ' helpful division of the Prologue into chapters and the titles he assigned to them . Finally , since Proclus ' commentary presupposes that its readers will ...
... four books . These also I have put in the mar- gins , together with Barocius ' helpful division of the Prologue into chapters and the titles he assigned to them . Finally , since Proclus ' commentary presupposes that its readers will ...
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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