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 xlix
... theorems and their kinds come up for explanation later ( 394.11- 396.9 ) . And when the student is introduced to the ... theorem receives repeated attention ( 77-81 , 201.3-15 , 210.5-10 , 220.6-222.19 , 241.19-244.9 ) , the discussion ...
... theorems and their kinds come up for explanation later ( 394.11- 396.9 ) . And when the student is introduced to the ... theorem receives repeated attention ( 77-81 , 201.3-15 , 210.5-10 , 220.6-222.19 , 241.19-244.9 ) , the discussion ...
Side liii
... theorems by means of which the theorem in question is established ( for a good example , see 240-241 ) . He turns then to objections that have been brought against Euclid's construction or his proof , usually identifying the author of ...
... theorems by means of which the theorem in question is established ( for a good example , see 240-241 ) . He turns then to objections that have been brought against Euclid's construction or his proof , usually identifying the author of ...
Side liv
... theorem capable of proof , which Ptolemy even claims to have demonstrated in one of his books . Moreover , it is a proposition whose converse he maintains Euclid himself proves later ; 35 and surely a proposition whose converse is ...
... theorem capable of proof , which Ptolemy even claims to have demonstrated in one of his books . Moreover , it is a proposition whose converse he maintains Euclid himself proves later ; 35 and surely a proposition whose converse is ...
Side lxi
... theorems , between a theorem and its converse- entire or partial - and a variety of technical terms whose use must be mastered in the handling of these procedures . With each of these Proclus is familiar , and they all appear at ...
... theorems , between a theorem and its converse- entire or partial - and a variety of technical terms whose use must be mastered in the handling of these procedures . With each of these Proclus is familiar , and they all appear at ...
Side 6
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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