Full text: Clavius, Christoph: Geometria practica

GEOMETR. PRACT. tionalis S N, quæ terminetur in N, (qualis fuit tertia proportionalis S N, dua-
bus K N, & X, inuenta) vel cuius terminus vltra N, cadat. Quando enim ter-
minatur in N, erit rectilineum inter B I, & vltimam parallelam comprehenſum
æquale quadrato K M, hoc eſt, rectilineo A, vt oſtenſum fuit de rectilineo BH,
paulo ante hunc Num. 8. Quando autem terminus tertiæ proportionalis ca-
dit vltra N, videlicet in b. ita vt rectangulum Y d, ſit æquale vltimo quadrato
inuento, hoc eſt, rectilineo D H; ac proinde totum rectilineuminter BI, & vlti-
mam parallelam, hoc eſt, rectangulum K d, maius quadrato K M, vel rectilineo
A; erit vltimum rectilineum D H, maius rectangulo N d, propterea quod K Z,
ipſi BH, æquale eſt, & Y d, ipſi D H. Quare ſi ſuper rectam D a, inter rectas D V,
a H, conſtituatur trapezium D f, per parallelam e f, rectangulo N d, æquale, vt
ſupra Num. 3. traditum eſt: erit rectilineum inter B I, & e f, parallelas conten-
tum æquale quadrato K M, hoc eſt, rectilineo A.

243.1.

274-01

Cætervm non eſt neceſſe, vt ſemper à proximo angulo parallela duca-
tur in figura B F. Quando namque ſenſus iudicaret plus minus, parallelam ex
aliquo angulo non proximo ductam auferre rectilineum minus quadrato
K M, vel non multò maius, ducenda eſſet parallela ex eo angulo, & recti-
lineo abſciſſo conſtruendum æquale quadratum, & reliqua perficienda, vt
prius.

Deniqve ſi aliquando deprehenderetur, rectilineum abſciſſum non eſſe
multo minus quadrato, conſtituendum eſſet, vt Num. 3. docuimus, ſuper paral-
lelam illam trapezium æquale rectangulo, quo quadratum KM, rectilineum ab-
ſciſſum ſuperat.

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