Clavius, Christoph
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Geometria practica
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Quoniam enim triangulum B C F, ad triangulum D E F, duplicatam
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portionem habet lateris B F, ad latus D F, hoc eſt, rectæ L M, ad rectam O:
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<
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L M, ad O, quod L M, O, M N, ſint continuè proportionales. </
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<
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triangulum B C F, ad triangulum D E F, ita L M, ad M N; </
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<
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xml:space
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nem rationis, vt triangulum B C F, ad Trapezium B E, ita L M, ad L N. </
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Cum ergo ſit, vt LM, ad LN, ita quadratum K, ad quadratum G, quod
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ſexti.</
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H I, L N, continuè ſint proportionales, erit quo que vt triangulum B C F, ad
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trapezium B E, ita quadratum K, ad quadratum G, hoc eſt, ita triangulum
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BCF, quod ipſi K, æquale eſt, ad rectilineum A, ipſi G, æquale. </
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triangulum B C F, ad trapezium B E, & </
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portionem; </
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<
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"> æqualia erunt trapezium BE, & </
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xml:space
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">rectilineum A, quod eſt
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ſitum.</
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deinde ſuper B C, verſus R, S, vbianguli R B C, SCB, duobus re-
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ctis ſunt maiores, non autem verſus punctum concurſus F, conſtruendum trape-
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zium rectilineo A, cuiuſcunque magnitudinis ſit, æquale, habens latus oppo-
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ſitum rectæ B C, parallelum. </
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tum K, cuius latus L M; </
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<
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">rectilineo A, aliud quadratum G, æquale, cuius
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latus HI, per ea, quæ ad propoſitionem 14. </
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Num. </
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<
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<
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<
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xml:space
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">Dein de lateribus L M, HI, inueniatur
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tertia proportionalis MP, quæ ipſi LM, in continuum & </
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ta: </
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poſtremo, vt Q, ad L P, ita fiat FB, ad F R: </
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<
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BCF, ad triangulum R S F, proportionem habet duplicatam lateris F B, ad
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latus F R, hoc eſt, proportionis Q, ad L P; </
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L P, duplicata proportionis L M, ad Q, vel Q, ad L P, quod tres rectæ L M,
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Q, L P, ſint continuè proportionales. </
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<
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triangulum R S F, ita L M, ad L P; </
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trariam in ſcholio propoſ. </
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">à nobis demonſtratam, vt trian-
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gulum BCF, ad trapezium BS, ita L M, ad M P. </
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ſexti.</
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eſt quadratum K, ad quadratum G, quod tres L M, H I, M P, ſint continuè
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proportionales. </
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<
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ita quadratum K, ad quadratum G. </
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ſit æquale quadratum K: </
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hoc eſt, rectilineo A, cui quadratum G, conſtructum eſt æquale. </
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<
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poſitum.</
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ſi quando duæ rectæ B F, C F, in tam remoto puncto concurrant,
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vt vix haberi poſsit, (quod quidem tunc accidet, cum ipſæ rectæ ferè pa-
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rallelæ ſunt) abſoluemus problema, etiamſi punctum concurſus F, non habea-
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mus, huncin modum. </
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in C F, agatur T V, alteri BF, parallela; </
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proportionalis X. </
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potius, vt Num. </
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<
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<
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neo A, inueniatur tribus BC, X, H I, quarta proportionalis IY, agatur que Y Z,
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lateribus qua drati parallela. </
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<
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"> Et quoniam eſt, vt triangulum B C F, (ſi
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ſexti.</
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ficeretur) ad triangulum V C T, ita recta B C, ad rectam X, hoc eſt, ita H </
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