The philosophical and mathematical commentaries of Proclus ... on the first book of Euclid's Elements, and his life by Marinus, tr. with a prelim. dissertation on the Platonic doctrine of ideas by T. Taylor. (To which are added, A history of the restoration of the Platonic theology, by the latter Platonists: and a tr. of Proclus's Theological elements by T. Taylor).
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according afferts affirm alfo ancient angles appears becauſe Befides body bound called caufe cauſe centre circle circular circumference cogitation collected commentaries common comprehended concerning conclufion confider contained contemplation contrary definition demonftration divided divifion divine effence effential elements endued energy equal evident excellent exiſtence external extremes fame fays fcience fenfe fenfible feparated fhall fhould fides figures fimilar fimple fince firſt folid fome forms foul fpecies fubfift fubject fuch fuperficies geometry gods Hence ideas images infinite intellect intelligible interval itſelf kind knowledge likewife manner mathematical matter means middle moſt motion multitude muſt nature neceffary never objects opinion origin participate particular perfect philofopher plane Plato poffefs predicated prefent principles Proclus produced progreffion proper propofitions proportion quantity reafon receive relation right line right-line terminated thefe themſelves theſe things thofe thoſe tion triangle true truth unity univerfal various whole
Page xxxix - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 134 - A plane angle is the inclination of two lines to each other in a plane, which meet together, but are not in the same direction.
Page 170 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.
Page 169 - A RHOMBUS is that which has all its sides equal, but its angles are not right angles.
Page 38 - Platonic theology, and a mingler of much unintelligible stuff1 with it) does himself assert a monad or unity, superior to this whole trinity ; yet does he seem nevertheless rightly to contend against Amelius, that it was not the...
Page vi - ... they muft be coexiftent with their caufe, ie they muft be eternally beautiful, antecedent to the reafoning energy. Again, if we fuppofe the fupreme intellect, the demiurgus of the world, to operate by enquiry, his energy could not be fpontaneous, and truly his own; but his eflence would be fimilar to that of the artificer, who does not derive his productions from himfelf,. but procures them as fomething adventitious by learning and enquiry. But if the univerfe was not formed by deliberation,...
Page xxiv - A cypher being added to, or taken from a number, does neither increafe nor diminifli it ; from it is taken the beginning of computation, while itfelf is not computed ; and it bears a manifeft relation to the principal properties of a geometrical point." But in what manner are we to conceive the nothing which intervenes •between any two numbers, to be their term or boundary ? •For Euclid defines .a term to be the extremity of any thing; implying by the extremity, fomething belonging to that of...
Page 141 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a, right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.
Page 169 - An oblong, is that which has all its angles right angles, but has not all its sides equal.
Page 19 - ... so? indeed, at first sight, it appears ; but he who has penetrated the depths of ancient wisdom, will find in it more than meets the vulgar ear. The religion of the Heathens, has indeed, for many centuries, been the object of ridicule and contempt ; yet the author of the present work is not ashamed to own, that he is a perfect convert to it in every particular , so far as it was understood and illustrated by the Pythagoric and Platonic Philosophers.