## A Commentary on the First Book of Euclid's ElementsIn 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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angle ABC 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 ideas imagination 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 spiric sections square starting-points subtends surface Syrianus theorem things Timaeus tion triangle ABC understanding unequal Unlimited whole