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 affections affirm ancient angles animal appears arithmetic become body bound called cause centre circle circular circumference cogitation collected common composed comprehended concerning conclusion consequence considered contained contemplation contrary conversant defines definition demonstration desire discourse divided divine division elements endued energy enquiry equal essence essential evident excellent exhibits existence external extremes fame fense figures forms foul geometry gods Hence ideas images infinite intellect intelligible kind knowledge known lastly less likewise magnitude manner mathematical matter means middle motion multitude nature necessary never objects observes opinion origin participate particular perfect philosopher plane Plato possess predicated present principles Proclus produced progression proper proportion propositions quantity reasons receive relation requisite respect right line right-line sensible separate sides similar simple solid soul species subsist superficies terminated things tion triangle true truth unity universal various whole
Página 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.
Página 162 - 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.
Página 161 - A RHOMBUS is that which has all its sides equal, but its angles are not right angles.
Página 32 - 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...
Página 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,...
Página 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...
Página 133 - 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.
Página 161 - An oblong, is that which has all its angles right angles, but has not all its sides equal.
Página 13 - ... 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.