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 19
... prior to this , it enquires , by itself , concerning the if , and this especially in its determinations , agitating , whether the object of its enquiry is poffible or impoffible , what place it poffeffes , and in how many ways . It ...
... prior to this , it enquires , by itself , concerning the if , and this especially in its determinations , agitating , whether the object of its enquiry is poffible or impoffible , what place it poffeffes , and in how many ways . It ...
Σελίδα 34
... prior termination . At the fame time , therefore , in which he fays to a given point , he terminates both the given right line , and its equal which is inveftigated . But that the cafes of the prefent problem are formed from the va ...
... prior termination . At the fame time , therefore , in which he fays to a given point , he terminates both the given right line , and its equal which is inveftigated . But that the cafes of the prefent problem are formed from the va ...
Σελίδα 47
... prior to fymptoms . Likewise a problematical propofition is fimple , and re- quires no artificial intelligence . For this commands us to accomplish fomething evident , as to conftruct an equilateral triangle , or from two given unequal ...
... prior to fymptoms . Likewise a problematical propofition is fimple , and re- quires no artificial intelligence . For this commands us to accomplish fomething evident , as to conftruct an equilateral triangle , or from two given unequal ...
Σελίδα 48
... prior to problems . For Carpus affigns a precedency to problems , according to order : but Geminus to theorems , according to a more perfect dignity . But of this fourth theorem ,, we have al- ready obferved , that in a certain refpect ...
... prior to problems . For Carpus affigns a precedency to problems , according to order : but Geminus to theorems , according to a more perfect dignity . But of this fourth theorem ,, we have al- ready obferved , that in a certain refpect ...
Σελίδα 57
... prior demonstrations . For the prefent fixth theorem shews that which hap- pens to be impoffible , because it deftroys the common conception , af- firming that the whole is greater than its part . But the eighth the- orem.falls , indeed ...
... prior demonstrations . For the prefent fixth theorem shews that which hap- pens to be impoffible , because it deftroys the common conception , af- firming that the whole is greater than its part . But the eighth the- orem.falls , indeed ...
Συχνά εμφανιζόμενοι όροι και φράσεις
abides according affert affumed alfo alſo angles equal bafe baſe beauty becauſe Befides bifected body cafe caufe cauſe compofed confequent conftituted conftruction contains converted dæmon defcribed defire demonftration divine effence effentially energy eternity exifting faid fame manner fays fcience fecondary feparated fhall fhew fhewn fides fimilar fimple fince firft firſt fituated fome fomething foul fpirit fubfifts fubject fubtend fuch fufficient fuperior gods greater Hence himſelf Iamblichus ifofceles imparticipable impoffible infinite inftitutor intellect intelligible internal angles inveſtigation itſelf laſt lefs leſs likewife manifeft meaſure moſt multitude muſt nature neceffary obferved oppofite parallelogram participates perfect philofopher Plato Plotinus poffefs poffible pofterior Porphyry prefent prefent theorem prior Proclus produced progreffion propofed PROPOSITION reafon refide refpect requifite right angles right line ſay ſeparate ſhall ſhould ſpace ſubſiſt ſuch thefe themſelves theorem theſe things thofe thoſe triangle Ulyffes underſtand unity univerfal whole
Δημοφιλή αποσπάσματα
Σελίδα 6 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 12 - If equals be taken from equals, the remainders are equal. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Σελίδα 294 - The front appear'd with radiant splendours gay, Bright as the lamp of night, or orb of day, The walls were massy brass : the cornice high Blue metals crown'd in colours of the sky ; Rich plates of gold the folding doors incase ; The pillars silver, on a brazen base ; Silver the lintels deep-projecting o'er, And gold the ringlets that command the door.
Σελίδα 296 - And hateful he who breathes a foreign air. These did the ruler of the deep ordain To build proud navies, and command the main ; On canvas wings to cut the watery way ; No bird so light, no thought so swift as they.
Σελίδα 12 - THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders are equal.
Σελίδα 280 - Capricorn is fouthern, and accomodated to afcent : and, indeed, the GATES of the cave, which look to the North, are with great propriety...
Σελίδα 285 - Two urns by Jove's high throne have ever flood, The fource of evil one, and one of good ; From thence the cup of mortal man he fills...
Σελίδα 293 - The Pleiads, Hyads, with the northern team; And great Orion's more refulgent beam; To which, around the axle of the sky, The Bear, revolving, points his golden eye, Still shines exalted on th' ethereal plain, Nor bathes his blazing forehead in the main.
Σελίδα 279 - ... to human life. From the confine, therefore, in which the zodiac and galaxy touch each other, the soul, descending from a round figure, which is the only divine form, is produced into a cone by its defluxion.
Σελίδα 279 - Hence he asserts, that the nutriment of milk is first offered to infants, because their first motion commences from the galaxy, when they begin to fall into terrene bodies. On this account, since those who are about to descend are yet in Cancer, and have not left the milky way, they rank in the order of the gods.