## 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). |

### Common terms and phrases

according afferts affirm alfo alſo angles becauſe Befides bound caufe cauſe centre circle circular circumference cogitation compofed compofite comprehended concerning conclufion confequence confidered confifts conftituted contains contemplation converfant definition defire demiurgus demonftration difciplines difcourfe divifion divine effence effential endued energy enquiry equal Euclid exift exiſtence faid fame fays fcience fenfe fenfible feparate fhall fides figures fimilar fimple fince firft firſt folid fome forms foul fpecies fpeculation fubfift fubject fuch fufficiently fuperficies fuperior fuppofe geometry greateſt Hence herſelf himſelf impoffible infinite infinity intellect intelligible inveſtigation itſelf knowledge laft laftly lefs likewife manner mathematical meaſure mixt moft moſt muft multitude muſt nature neceffary obferves paffions perfect phantafy philofopher Philolaus plane Plato Plotinus poffefs poffible predicated prefent principles Proclus produced progreffion propofitions purpoſe Pythagoras reafon refide refpect requifite right line right-line ſay ſhall ſhould ſuch Suidas Syrianus thefe themſelves theſe things thofe thoſe Timæus triangle underſtand unity univerfal uſe

### Popular passages

Page xxxvii - 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 132 - 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 168 - 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 167 - A RHOMBUS is that which has all its sides equal, but its angles are not right angles.

Page 34 - 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 iv - ... 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 xxii - 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 139 - 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 167 - An oblong, is that which has all its angles right angles, but has not all its sides equal.

Page 15 - ... 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.