Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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10484GEOMETRI Æ nitè ſecat baſis productum planum in recta, 2, Z, perpendiculari
triangulo per axem, ACF, & ſint adhuc per puncta, N, S, ipſi, C
F, ductæ parallelæ, TL, HR, igitur quadratum, ℟ S, erit ęquale
1114. Secunn.
Elem.

58[Figure 58] rectangulo, TSL, & quadra-
tum, MN, æquale rectangulo,
22Ex Sexta
lib. 2. feq.
velex 23.
Sext. El. HNR, at rectangulum, TSL,
ad, HNR, habet rationem com-
poſitam ex ea, quam habet, T
S, ad, HN, . i. SB, ad, BN,
quia trianguli, BTS, BHN,
ſunt æquianguli, & ex ea, quam
habet, SL, ad, NR, . i. SV,
ad, VN, quia pariter trianguli,
SVL, NVR, ſunt æquiangu-
li, duę autem rationes, SB, ad,
BN, & , SV, ad, VN, componunt rationem rectanguli, BSV,
33Ex Sexta
lib. 2. feq.
vel ex 23.
Sexti El. ad rectangulum, BNV, ergo rectangulum, TSL, ad, HNR, . i.
quadratum, ℟ S, ad quadratum, MN, vel quadratum, ℟ D, ad
quadratum, MO, erit vt rectangulum, VSB, ad rectangulum, V
NB, quod oſtendere opu erat; hæc autem ab Apollonio vocatur
Ellipſis.

SCHOLIVM.

_H_Aec circa ſectiones conicas appoſui, tum vt quod menti meæ ſuc-
currit in lucem proferrem, tum vt eluceſcat, quam facilè paſſio-
nes, quæ ab. Apollonio in Elementis conicis circa earundem diametros,
vel axes quoſcumque demonſtrantur, circa eos, qui axes, vel diametri
princibales, ſiue ex generatione vocantur modo ſupradicto oſtendantur.
His tamen contenti ex Apollonio recipiemus pro dictarum ſectionum
axibus, vel diametris quibuſcumq; quod ipſe colligit ad finem Trop. 51.
primi Conicorum, ſcilicet.

In Parabola vnamquamque rectarum linearum, quę diametro ex
generatione ducuntur æquidiſtantes, diametrum eſſe: In hyperbola
verò, & ellipſi, & oppoſitis ſectionibus vnamquamque earum, quę
per centrum ducuntur, & in parabola quidem applicatas ad vnam-
quamq; diametrum, ęquidiſtantes contingentibus, poſte rectangula
ipſi adiacentia: In hyperbola, & oppoſitis poſſe rectangula adiacen-
tia ipſi, quę excedunt eadem figura: In ellipſi autem, quę eadem de-
ficiunt: Poſt@@mò quęcumque circa ſectiones adhibitis principalibus
diametris demonſtrata ſunt, & alijs diametris aſſumptis eadem con-
tingere.

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