Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER V. dempto quadrato, ME, quia verò tripla, BE, eſt compoſita ex, E
X, & dupla, EN, ſi a rectangulo ſub compoſita ex, EX, & dupla,
EN, & ſub, EM, abſtuleris quadratum, ME, . i. rectangulum ſub,
MF, & , ME, remanebit rectangulum ſub compoſita ex ipſa, XE,
EN, NM, & ſub, EM, illas ergo tres componentes rationes in has
duas reſolutas habemus, ſcilicet in eam, quam habet rectangulũ
ſub, XEN, integra, & ſub, EN, ad rectangulum ſub integra, XE,
EN, NM, & ſub, ME, & in eam, quam habet, NE, ad, EM, quæ
duæ rationes componunt rationem parallelepipedi ſub, NE, & ſub rectangulo integræ, XEN, ductæ in, EN, ideſt parallelepipe-
di ſub integra, XEN, & quadrato, NE, ad parallelepipedum ſub,
ME, & rectangulo integræ, XE, EN, NM, ductæ in, ME, . i. ad
parallelepipedum ſub integra, XE, EN, NM, & quadrato, ME,
ergo omnia quadrata, AF, demptis omnibus quadratis hyperbo-
læ, DNF, ad omnia quadrata, SF, demptis omnibus quadratis
fruſti, HDFG, erunt vt parallelepipedum ſub integra, XEN, & quadrato, NE, ad parallelepipedum ſub integra, XE, EN, NM,
& quadrato, ME, quod erat oſtendendum.

538.1.

Is huius.
Defin. 12.
1. I.
10, 1.2.
0392-01
3. huius.
3.6. .1.

539. PROBLEMA I. PROPOS. VI.

A Data hyperbola portionem abſcindere per lineam
ad eiuſdem axim, vel diametrum ordinatim appli-
catam, cuius omnia quadrata, regula propoſitæ hyperbo-
læ baſi, ad omnia quadrata trianguli in eadem baſi, & cir-
ca eundem axim, vel diametrum cum portione, ſiue hyper-
bola abſciſſa, exiſtentis, habeant datam rationem, quam
oportet eſſe quidem maioris inæqualitatis, ſed tamen mi-
norem ſexquialtera.

Sit ergo data hyperbola, FEG, cuius axis, vel diameter, E M & larus tranſuerſum, CE, cuius ſit, AE, ſexquialtera, baſis, & regu-
la, FG, data ratio, quam habet, HR, ad, RL, maioris inæquali-
tatis, ſed minor ſexquialtera, oportet ergo ab hyperbola, FEG,
per lineam ad, EM, ordinatim applicatam . i. baſi, fiue regulæ,
FG, parallelam, portionem, ſiue hyperbolam abſcindele, cuius
omnia quadrata ad omnia quadrata trianguli in eadem baſi, & circa eundem axim, vel diametrum cum ipſa habeant rationem,
quam habet, HR, ad, RL; quia ergo ratio, HR, ad, RL, eſt mi-
nor ſexquialtera, erit minor ea, quam habet, AE, ad, EC, & etiã

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