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 xxv
... character of geometry in chapter III of the second part of the prologue.48 He indicates that although the principal concern of math- ematics is " dianoetic forms , " it also impinges on physics at its lower level and at its higher " it ...
... character of geometry in chapter III of the second part of the prologue.48 He indicates that although the principal concern of math- ematics is " dianoetic forms , " it also impinges on physics at its lower level and at its higher " it ...
Side xxvii
... character of his audience explains the tedious detail with which he goes through the propositions of Elements I in the last half of the commentary . 55 The sec- ond explains his emphasis on the uplifting effect of mathematical study ...
... character of his audience explains the tedious detail with which he goes through the propositions of Elements I in the last half of the commentary . 55 The sec- ond explains his emphasis on the uplifting effect of mathematical study ...
Side xlix
... character of geometry as a hypothetical science , which starts from first principles ( apxaí ) which it does not demon- strate — namely , axioms , definitions , and postulates . He expounds Aristotle's explanation of the difference ...
... character of geometry as a hypothetical science , which starts from first principles ( apxaí ) which it does not demon- strate — namely , axioms , definitions , and postulates . He expounds Aristotle's explanation of the difference ...
Side l
... character ( 245.24-246.5 , 251.11-19 , 253.20-254.3 , 390.12-392.8 ) . The role of the infinite and of in- finite divisibility in mathematical discourse is taken up in two lengthy passages ( 277.25-279.11 , 284.4-286.11 ) . And we are ...
... character ( 245.24-246.5 , 251.11-19 , 253.20-254.3 , 390.12-392.8 ) . The role of the infinite and of in- finite divisibility in mathematical discourse is taken up in two lengthy passages ( 277.25-279.11 , 284.4-286.11 ) . And we are ...
Side lvii
... character and validity of the pro- cedures used by mathematicians in handling these objects . These are basic problems in what we would now call the philosophy of mathematics . Proclus ' essay is the only systematic treatise that has ...
... character and validity of the pro- cedures used by mathematicians in handling these objects . These are basic problems in what we would now call the philosophy of mathematics . Proclus ' essay is the only systematic treatise that has ...
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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