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

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

Table of contents

[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.

[311.] THEOR. XLII. PROP. LXVIII.

[312.] COROLL. I.

[313.] COROLL. II.

[314.] MONITVM.

[315.] DEFINITIONES. I.

[316.] II.

[317.] III.

[318.] IIII.

[319.] PROBL. XIV. PROP. LXIX.

[320.] SCHOLIVM I.

296110 longo erunt ipſę C D, E F, in prolato verò erunt axes minores) 11ibidem. tiaque ſolidas portiones C A D, E A F, quarum recti Canones erunt ipſæ
æquales portiones planæ C A D, E A F. Dico tales portiones ſolidas inter
ſe æquales eſſe.

Nam bifariam ſectis E F in G, & C D in H, patet puncta G, H eſſe cen-
tra circulorum, ſiue Ellipſium E O F, C P D; & ſi per punctum G deſcri-
224. ſec.
Conic &
5. 6. 7. pri-
mi huius. batur in vtraque ſigura eiuſdem nominis Coni-ſectio G H, que ſimilis & concentrica ſectioni E A D, & qualis in Monito poſt 68. h. definiuimus,
patet inquam ipſam ſectionem G H omnino tranſire per H, ſimulque E F,
& C D in punctis medijs G, H contingere.

3368. h.

Iam ductis per G, H, rectis I G L, M H N ad axem A B perpendicula-
ribus, concipiantur per ipſas duci plana ad planum per axem E A D erecta,
444. primi
Conic. &
12. Arch.
de Co-
noid. &c. quæ efficient in exteriori ſolido circulos circa diametros I L, M N, & communes eorum ſectiones cum planis per E F, C D ductis, erunt rectæ G O, H P, quæ ad planum E A D rectæ erunt (ſunt enim communes ſe- ctiones duorum planorum ad idem planum erectorum) hoc eſt, tùm O G
553. vnd.
Elem. cum vtriſque E F, I L, tùm P H cum vtriſque C D, M N rectos eſſiciet
6619. ibid. angulos; vnde in circulis tranſeuntibus per I L, M N, rectangulum I G L
æquabitur quadrato G O, & re-

241[Figure 241] ctangulum M H N quadrato H
P, atque ipſæ G O, H P erunt
circulorum, aut Ellipſium E O
F, C P D minores ſemi-axes,
in Cono tamen, vel Conoide
Parabolico, aut Hyperbolico,
vel in Sphæroide oblongo; nam
in prolato, erunt maiores ſemi-
axes: ſed rectangula I G L, M
H N ſunt æqualia, 773. Co-
roll. 46. h. enim æquatur quadrato ſemi-tangentis per verticem interioris ſectionis, & c.
ergo, & quadrato G O, H P æqualia erunt, ſiue ſemi-axis G O æqualis ſe-
mi- axi H P; ſed circulus, aut Ellipſis E O F ad C P D, eſt vt 887. Arch.
de Co-
noid. &c. lum ſub E F, G O, ad rectangulum ſub C D, H P, & rectangulum ſub E F,
G O ad rectangulum ſub C D, H P eſt vt E F ad C D (cum eorum latitu-
dines G O, H P ſint æquales) ergo circulus, vel Ellipſis E O F ad C P D
erit in ſolido Parabolico, vel Hyperbolico, aut Sphæroide oblongo, vt ma-
ior axis E F ad maiorem axim C D, vel in Sphæroide prolato, vt minor
axis E F ad minorem C D: ſed E F ad C D eſt vt altitudo Canonis C 9965. h. D, ad altitudinem Canonis E A F, cum ipſi ſint æquales portiones eiuſ-
dem coni-ſectionis, & horum Canonum altitudines ſunt eædem, ac 10103. Schol.
69. h. tudines ſolidarum portionum C A D, E A F, quare circulus, vel Ellipſis E
O F ad C P D, erit reciprocè vt altitudo ſolidæ portionis C A D, ad alti-
tucinem ſolidæ E A F: at huiuſmodi portiones ſunt ſolida 1111Coroll.
70. h. proportionalia, & ipſorum baſes altitudinibus reciprocantur, ergo ipſæ ſo-
lidæ portiones inter ſe ſunt æquales. Quod erat demonſtrandum.

121274. h.

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