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

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149125

LEMMA XII. PROP. LXXX.

Si fuerit rectangulum ABC, ęquale rectangulo DEF, ſitque AC
maior DF, erit BC minor EF.

115[Figure 115]

SI enim dicatur BC æqualem, vel maiorem
eſſe EF, cum ſit data AC maior DF, eſſet
omnino AB maior DE, & BC dicitur æqualis,
vel maior EF, ergo rectangulum ABC eſſet om-
nino maius rectangulo DEF, ſed æquale poſi-
tum fuit. Ergo patet propoſitum.

THEOR. XXXVIII. PROP. LXXXI.

Si recta linea ad alterũ terminũ cuiuſdam applicatæ coni-ſectio-
nem, vel circulũ cõtingat, ipſa omnino ſecabit ſibi adſcriptã eiuſdẽ
nominis ſectionẽ circa eandẽ applicatam, & cum æquali tranſuerſa
diametro, ſi ſectiones fuerint Hyperbolæ, vel Ellipſes, aut circuli.

ESto quæcunque coni-ſectio, vel circulus ABC, cuius diameter BD, yo
vna applicatarum ſit AC. & ad ipſius terminum A, ſit recta contingens
EAF, quæ diametro occurret in F; & ſumpto in diametri ſegmento 1124. 25.
pr. conic. quolibet puncto G, cum diametro GD, & applicata AC in qualibet figura,

116[Figure 116] ſed etiam, pro Hyperbola in ſecunda, & pro Ellipſi, vel circulo, in tertia,
cum dato tranſuerſo latere GM, quod æquale ſit tranſuerſo BL datæ ſectio-
nis, deſcribatur eiuſdem nomin@s ſectio AGC: dico hanc omnino 2257. h. contingente EAF.

Ducatur enim per A recta IAH, quæ ſectionem continget AGC, cum
eius diametro conueniat in H.

Iam in prima figura exhiben@ Parabolas, cum AF contingat

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