Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

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[281.] THEOR. XXVI. PROP. XLV.
[282.] COROLL.
[283.] THEOR. XXVII. PROP. XLVI.
[284.] COROLL. I.
[285.] COROLL. II.
[286.] THEOR. XXVIII. PROP. XLVII.
[287.] THEOR. XXIX. PROP. XLVIII.
[288.] THEOR. XXX. PROP. XLIX.
[289.] THEOR. XXXI. PROP. L.
[290.] COROLL.
[291.] THEOR. XXXII. PROP. LI.
[292.] SCHOLIVM.
[293.] THEOR. XXXIII. PROP. LII.
[294.] THEOR. XXXIV. PROP. LIII.
[295.] ALITER.
[296.] THEOR. XXXV. PROP. LIV.
[297.] THEOR. XXXIV. PROP. LV.
[298.] THEOR. XXXVII. PROP. LVI.
[299.] PROBL. VIII. PROP. LVII.
[300.] PROBL. IX. PROP. LVIII.
[301.] PROBL. X. PROP. LIX.
[302.] PROBL. XI. PROP. LX.
[303.] PROBL. XII. PROP. LXI.
[304.] PROBL. XIII. PROP. LXII.
[305.] MONITVM.
[306.] THEOR. XXXVIII. PROP. LXIII.
[307.] THEOR. XXXIX. PROP. LXIV.
[308.] THEOR. XL. PROP. LXV.
[309.] THEOR. XLI. PROP. LXVI.
[310.] LEMMA XIII. PROP. LXVII.
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THEOR. XLIII. PROP. LXX.
Portiones eiuſdem, vel diuerſorum Conorum, aut Conoidum
Parabolicorum, ſunt ſolida Acuminata proportionalia.
Item.
Portiones eiuſdem, vel diuerſorum Conoidum Hyperbolico-
rum, vel Sphærarum, aut Sphæroidum, quarum ſegmenta diame-
trorum in portionibus genitricium earum ſectionum ad baſes ere-
ctis intercepta, ad ſuas ſemi-diametros eandem homologam ha-
beant rationem, ſunt pariter ſolida Acuminata proportionalia.
SInt primò duæ quæcunque portiones A B C, D E F eiuſdem, vel diuer-
ſorum Conorum, vt in prima figura, vel eiuſdem, aut diu erſorum Co-
noidum Parabolicorum, vt in ſecunda, quarum axes ſint B G, E H, baſes
verò circuli, aut Ellipſes A C, D F, ipſæque portiones ſolidæ, (quæ iam
1169. h. per primum Scholium precedentis ſunt ſolida Acuminata) planis per eorum
22ibid. 1.
Schol.
ſolidorum axes ductis ad baſes rectis ſecentur, &
ſient in ſolidis recti 33ex 12.
Archim.
de Co-
noid. &
Comand.
ſuppleta.
nones A B C, D E F, qui erunt portiones ſectionum ſolida &
communes ſectiones ipſorum cum baſibus erunt rectæ A C, D F, quæ circulorum, aut Ellipſium erunt axes. Dico in vtraque ſigura ſolidas por- tiones A B C, D E F eſſe Acuminata ſolida proportionalia.
Etenim horum Acuminato-
443. vnd.
Elem.
233[Figure 233] rum ſolidorum axibus B G, E
H proportionaliter vtcunque
55ex 13.
Archim.
ibidem.
ſectis in I, L, ducantur per I,
L plana M N, O P baſibus A
C, D F æquidiſtantia, quæ in
ſolidis efficient ſectiones ipſa-
rum baſibus ſimiles earumq;
66ex Co-
roll. 15. ib.
communes ſectiones cum pla-
773. vnd.
Elem.
nis A B C, D E F erunt re- ctæ M N, O P ipſis A C, D
8816. ib. F parallelæ, &
earundem ſi- milium ſectionum homologæ
diametri.
Iam cum ſit G B ad B I, vt
H E ad E L, ob conſtructio-
nem, ſitque in prima figura A
C ad M N, vt G B ad B I;
&
D F ad O P, vt H E ad E L (cum Canones A B C, D E F ſint triangula)
erit A C ad M N vt D F ad O P, &
quadratum A C ad M N, vt
quadratum D F ad O P.
In ſecunda verò eſt quadratum A C ad M N, vt
re cta G B ad B I (cum Canon A B C ſit portio Parabolæ) vel vt recta H
99Coroll.
7. Arch.
ibid.
E ad E L, per conſtructionem, vel vt quadratum D E ad O P:
eſt ergo in
vtraque ſigura, vt quadratum A C ad M N, vel vt circulus, aut

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