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 vii
... Prologue : Part One 3 Prologue : Part Two 39 Definitions 70 Postulates and Axioms 140 Propositions : Part One 156 Propositions : Part Two 276 Supplementary Note 344 Index 347 Foreword to the 1992 Edition Ian Mueller PROCLUS ' COMMENTARY ...
... Prologue : Part One 3 Prologue : Part Two 39 Definitions 70 Postulates and Axioms 140 Propositions : Part One 156 Propositions : Part Two 276 Supplementary Note 344 Index 347 Foreword to the 1992 Edition Ian Mueller PROCLUS ' COMMENTARY ...
Side xxv
... definitions , is full of indications of the metaphysical and theological truths imaged in geometrical concepts and proposi- tions.50 In chapter II of part one of the prologue Proclus describes the Limit and the Unlimited as the common ...
... definitions , is full of indications of the metaphysical and theological truths imaged in geometrical concepts and proposi- tions.50 In chapter II of part one of the prologue Proclus describes the Limit and the Unlimited as the common ...
Side xxix
... definition - by con- trast , notably , with causal and symptomatic argument ( 69.9–19 ) .59 Probably the most frequently cited passage in the Euclid commentary is chapter IV of the second part of the prologue , where Proclus gives an ...
... definition - by con- trast , notably , with causal and symptomatic argument ( 69.9–19 ) .59 Probably the most frequently cited passage in the Euclid commentary is chapter IV of the second part of the prologue , where Proclus gives an ...
Side xlix
... definitions , and postulates . He expounds Aristotle's explanation of the difference between these three types of ȧpxaí ( 76.6-77.6 ) and later gives a résumé of the contro- versy over the distinction between postulates and axioms ...
... definitions , and postulates . He expounds Aristotle's explanation of the difference between these three types of ȧpxaí ( 76.6-77.6 ) and later gives a résumé of the contro- versy over the distinction between postulates and axioms ...
Side liv
... definition of plane angle . To call it " the inclination to one another of two lines " is to put angle under the category of relation , an opinion which is open to numerous objections ( 122.21-123.13 , 128.3-22 ) . Again Euclid's fourth ...
... definition of plane angle . To call it " the inclination to one another of two lines " is to put angle under the category of relation , an opinion which is open to numerous objections ( 122.21-123.13 , 128.3-22 ) . Again Euclid's fourth ...
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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