Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

A C ad ſibi ſimilem M N, ita quadratum D F ad O P, vel ita circulus, aut
Ellipſis D F ad ſibi ſimilem O P, & permutando, ſectio A C ad D F erit
vt ſectio M N ad O P, & hoc ſemper vbicunque ſolidorum Acuminatorum
axes ſint proportionaliter ſecti: quare, ex tertia præmiſſarum definitionum,
Acuminata ſolida A B C, D E F erunt ſolida Acuminata proportionalia. Quod erat primò, & c.

326.1.

Coroll.
7. Arch.
ibid.

PRæterea ſint A B C, D E F
duæ portiones eiuſdem, vel
diuerſorum Conoidum Hyper-
bolicorum, vt in tertia figura, vel
eiuſdem, aut diuerſorum Sphæ-
roidum, vel Sphærarum, vt in
quarta, (quæ portiones ſunt pa-
riter ſolida Acuminata per 1. Schol. 69. h.) quarum baſes ſint
circuli, aut Ellipſes A C, D F. Patet quod ſi per axes ſolidorũ,
quorum ſunt portiones ducantur
plana, quæ portionum baſibus ſint erecta, fient in ſolidis portio-
nes genitricium ſectionum A B C, D E F, hoc eſt in tertia por-
nes Hyperbolarum, & in quarta portiones Ellipſium, quas vocamus Ca- nones, & communes horum Canonum ſectiones cum baſibus erunt rectæ A C, D F, quæ ipſarum baſium erunt axes. Sint iam Canonum A B C, D E F intercepta diametrorum ſegmenta B G, E H, (quæ & ſolidarum
portionum axes vocantur ab Archimede) quibus productis vſque ad earum
centra Q, R, habeat ſegmentum G B ad ſemi-diametrum B Q, eandem
rationem, ac ſegmentum H E ad ſemi - diametrum E R. Dico in vtraque
harum figurarum, portiones ſolidas, vel ſolida Acuminata A B C, D E F
eſſe Acuminata ſolida proportionalia.

326.1.

0285-01
69. h.
ex 12.
Arch. de
Conoid.
1. Schol.
69. h.
3. vnd.
Elem.
ex 14.
& 15. Ar-
chim. ib.

Diuiſis enim ipſorum axibus B G, E H proportionaliter vtcunque in I,
L, ductiſque per I, L planis M N, O P ipſis baſibus A C, D F æquidi-
ſtantibus, erit ſectio M N in ſolido A B C ſimilis baſi A C, & ſectio O P in-ſolido D E F ſimilis baſi D F, & earum communes ſectiones cum planis
Acuminatis A B C, D E F erunt rectæ M N, O P ipſis A C, D F paralle-
læ vtraque vtrique, eruntque homologæ diametri earundem ſimilium ſe- ctionum.

326.1.

ex Co-
roll. 15.
eiuſdem.
3. & 16.
vnd. El.

Et quoniam, per conſtructionem, in Acuminatis planis A B C, D E F,
Hyperbolarum, vt in tertia figura, aut Ellipſium, vt in quarta, ſeginenta
diametrorum G B, E H ad proprias ſemi-diametros B Q, E R eandem ha-
bent rationem, erunt ipſa Acuminata, plana Acuminata proportionalia; ſuntque B G, E H proportionaliter ſectæ in I, L, ex conſtructione, quare
vt recta A C ad D F, ita recta M N ad O P (ex definitione planorum Acu-
minatorum proportionalium) & quadratum A C ad D F, hoc eſt circulus,
vel Ellipſis A C ad ſibi ſimilem D F, vt quadratum M N ad O P, vel vt circulus, aut Ellipſis M N ad ſibi ſimilem O P, & hoc ſemper vbicunque

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