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 94
... consequent pofition , and yet , towards the fame parts , may form angles belonging to that one right line , equal to two right , we may fhew with Porphyry , as follows . Let there be a certain right line a b , and any point in it c ...
... consequent pofition , and yet , towards the fame parts , may form angles belonging to that one right line , equal to two right , we may fhew with Porphyry , as follows . Let there be a certain right line a b , and any point in it c ...
Σελίδα 100
... consequent to a problém . But in the third place , they must be divided according to their oftenfions . For fome are ex- hibited , together with oftenfive methods , but others together with de- ductions to an impoffible . Thus the ...
... consequent to a problém . But in the third place , they must be divided according to their oftenfions . For fome are ex- hibited , together with oftenfive methods , but others together with de- ductions to an impoffible . Thus the ...
Σελίδα 109
... consequent to the ceding datum ; and that the triangle which has a greater and less fide , contains a greater angle , under the greater fide . pre- But because the geometrician , when in the conftruction he receives the triangle a b c ...
... consequent to the ceding datum ; and that the triangle which has a greater and less fide , contains a greater angle , under the greater fide . pre- But because the geometrician , when in the conftruction he receives the triangle a b c ...
Σελίδα 129
... consequent to principles . PROPOSITION XXIV . THEOREm XV . If two triangles have two fides equal to two , each to each , but the one angle contained by the equal right lines greater than the other they shall also have the base of the ...
... consequent to principles . PROPOSITION XXIV . THEOREm XV . If two triangles have two fides equal to two , each to each , but the one angle contained by the equal right lines greater than the other they shall also have the base of the ...
Σελίδα 149
... consequent to the three omitted hypothefes . Thus , in the pre- ceding figure , let both the external angles be b , dfg , be at the fame parts , I fay that these are equal to two right angles . For the angle dfe , is equal to the angle ...
... consequent to the three omitted hypothefes . Thus , in the pre- ceding figure , let both the external angles be b , dfg , be at the fame parts , I fay that these are equal to two right angles . For the angle dfe , is equal to the angle ...
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.