Vitruvius
,
Marci Vitruvii Pollionis De architectura libri decem : ope codicis Guelferbytani, editionis principis, ceterorumque subsidiorum recensuit, et glossario in quo vocabula artis propria Germ. Ital. Gall. et Angl. explicantur
,
1800
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LIBER IX. (CAPUT I.)
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erit longus et latus pedes denos, efficit areae pedes centum. </
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<
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opus fuerit eum duplicare, et aream pedum ducentorum item ex paribus
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lateribus facere, quaerendum erit, quam magnum latus ejus quadrati fiat,
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ut ex eo ducenti pedes duplicationibus areae reſpondeant. </
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<
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">Id autem nu-
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mero nemo poteſt invenire: </
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<
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plicati pedes CXCVI. </
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<
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<
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xml:space
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">Ergo quoniam id non ex-
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plicatur numero in eo quadrato longo et lato pedes decem (a b c d), quae
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fuerit linea ab angulo (b) ad angulum (d) diagonios (b d) perducatur, uti
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dividatur in duo trigona aequa magnitudine (b a d et b c d), ſingula areae pedum quinquagenum: </
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<
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xml:space
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">ad ejus lineae diagonalis longitudinem locus
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quadratus (b e f d) paribus lateribus deſcribatur. </
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<
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">Ita quam magna duo
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trigona in minore quadrato quinquagenum pedum linea diagonia fuerint
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deſignata, eadem magnitudine, et eodem pedum numero quaturo in ma-
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jore erunt effecta. </
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<
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xml:space
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">Hac ratione duplicatio grammicis rationibus a Plato-
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ne, uti eſt ſchema ſubſcriptum, fuit explicata.</
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">Item Pythagoras normam ſine artiſicis fabricationibus inventam oſtendit,
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et quam magno labore fabri normam facientes vix ad verum perducere
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poſſunt, id rationibus et methodis emendatum ex ejus praeceptis expli-
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catur. </
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<
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">Namque ſi ſumantur regulae tres, e quibus una ſit pedes tres,
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(A B) altera pedes quatuor, (A C) tertia pedes quinque (C B): </
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<
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xml:space
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">haeque regulae inter ſe compoſitae tangant alia aliam ſuis cacuminibus extremis,
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ſchema habentes trigoni (A B C), deformabunt normam emendatam. </
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<
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xml:space
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eas autem regularum ſingularum longitudines, ſi ſingula quadrata paribus
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lateribus deſcribantur, quod erit pedum trium latus, (A B D E) areae ha-
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bebit pedes novem: </
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