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

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131107

THEOR. XXXIV. PROP. LXIII.

In quacunque coni-ſectione, etiam in triangulo, MAXIMA
diametro æquidiſtantium inter ſectionem, & quamcunque ordina-
tim applicatam interceptarum, eſt ipſa diameter; aliarum verò
ea, quæ propinquior eſt diametro, maior eſt remotiori.

ESto triangulum, vt in prima figura, vel circuli, aut Ellipſis, vel Parabo-
læ, vel tandem Hyperbolæ portio ABC, vt in ſecunda, quarum dia-
meter ſit BD, & ordinatim applicata ſit AC, ductiſque quotcunque EF,
GH, & c. parallelis ad BD. Dico BD eſſe _MAXIMAM_, diametro reliqua-
rum verò, propinquiorem EF, maiorem eſſe remotiori.

Nam ſi concipiatur ex B duci

96[Figure 96] quædam linea ordinatim appli-
catæ AC æquidiſtans quæ 1117. pri-
mi conic. cadet extra ſectionem, iungique
recta linea puncta E, B quæ 2210. pri.
conic. &
32. eiuſd. cadet intra, patet ipſam EB ad al-
teram partem productam (cum
ſecet in B eam, quæ ducta ſit ex
B parallela ad AC) conuenire
quoque cum CA ad partes A, & ſic BD maiorem eſſe recta EF, ſiue omnium
_MAXIMAM_. Quod primò, & c.

Item ſi puncta G, E, iungantur recta linea ipſa omnino cum 3322. pri.
conic. &
23. eiuſd. extra ſectionem conueniet, ac propterea ſecabit priùs eam, quæ ex B ducta
ſit ipſi A C ęquidiſtans; cum ergo GE ſecet vnam parallelarum, ſecabit quo-
que, ſi producatur, alteram CA ad partes A, & ſic EF erit maior ipſa GH.
Quod ſecundò, & c.

THEOR. XXXV. PROP. LXIV.

Ellipſium æqualium diametrorum, eidem angulo, vel Parabo-
læ, vel Hyperbolæ, aut portioni Ellipticæ, vel circulari, quæ non
ſit maior Ellipſis, vel circuli dimidio, inſcriptarum, ſe mutuò, ac
ſectionem contingentium, quæ propior eſt vertici, minor eſt re-
motiori.

ESto ABC, vel angulus rectilineus, vel Parabole, vel Hyperbole, aut por-
tio non maior dimidio ſemi-Ellipſis, vel ſemi-circuli, cuius vertex B,
diameter BD, & circa æqualia ipſius ſegmenta DE, EF adſcriptæ ſint dato
angulo, vel ſectioni Ellipſes DVE, ETF, ope diagonalium AG, IL, & ap-
plicatarum KHV, NMT, vt in præcedenti Scholio monuimus, quæ anguli
latera, vel ſectionem contingent in K, V, N, T, eique erunt inſcriptæ, & ſe
mutuò contingent in E (cum applicata LEG vtranque ſectionem contingat.)

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Scan	Original
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96	72
97	73
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