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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Σελίδα
Proclus (Diadochus.) THE Philofophical and Mathematical COMMENTARIES O F PRO CLU S ; SURNAME D PLATO'S SUCCESSO R , O N THE FIRST BOOK OF EUCLID'S ELEMENTS . AND HIS LIFE BY MARINUS . TRANSLATED FROM THE GREEK . WITH A PRELIMINARY ...
Proclus (Diadochus.) THE Philofophical and Mathematical COMMENTARIES O F PRO CLU S ; SURNAME D PLATO'S SUCCESSO R , O N THE FIRST BOOK OF EUCLID'S ELEMENTS . AND HIS LIFE BY MARINUS . TRANSLATED FROM THE GREEK . WITH A PRELIMINARY ...
Σελίδα lviii
Proclus (Diadochus.) circumfcribing the circle , which will be confèquently greater ; the other infcribed , which will be . confequently less than the given circle . Hence , becaufe the circle is a medium between the two given fquares ...
Proclus (Diadochus.) circumfcribing the circle , which will be confèquently greater ; the other infcribed , which will be . confequently less than the given circle . Hence , becaufe the circle is a medium between the two given fquares ...
Σελίδα xcvi
Proclus (Diadochus.) ་ parts in the first place , we confider how her nature is fa- bricated from their conjunction ; and fhe is a whole in the ... Proclus Proclus obferves , the confideration of the foul ought to xcvi DISSERTATION ON THE.
Proclus (Diadochus.) ་ parts in the first place , we confider how her nature is fa- bricated from their conjunction ; and fhe is a whole in the ... Proclus Proclus obferves , the confideration of the foul ought to xcvi DISSERTATION ON THE.
Σελίδα xcvii
Proclus (Diadochus.) Proclus obferves , the confideration of the foul ought to receive a quintuple distribution . Besides , as the foul con- fifts from a divifible and indivisible nature ; fo the quinary is compofed from the first even ...
Proclus (Diadochus.) Proclus obferves , the confideration of the foul ought to receive a quintuple distribution . Besides , as the foul con- fifts from a divifible and indivisible nature ; fo the quinary is compofed from the first even ...
Σελίδα xcviii
Proclus (Diadochus.) own proper nature ; and on this account fhe contains both a straight and circular figure . I omit other correfponden- cies of a circle and triangle with the foul , as they are exhibited in the following Commentaries ...
Proclus (Diadochus.) own proper nature ; and on this account fhe contains both a straight and circular figure . I omit other correfponden- cies of a circle and triangle with the foul , as they are exhibited in the following Commentaries ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 167 - A RHOMBUS is that which has all its sides equal, but its angles are not right angles.
Σελίδα 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...
Σελίδα 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,...
Σελίδα 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...
Σελίδα 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.
Σελίδα 167 - An oblong, is that which has all its angles right angles, but has not all its sides equal.
Σελίδα 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.