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

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128104 cum quadrato intermediæ partis DC; rectangulum ergo ACB ſuperat re-
ctangulum ADB; & hoc ſemper; ergo rectangulum ACB, ſub æqualibus
partibus compræhenſum, eſt _MAXIMV M._ Quod primo, & c.

Item, quadrato dimidiæ A C æquatur

93[Figure 93] rectangulum A D B, vna cum quadrato
DC, & eidem quadrato AC æquatur re-
ctangulum AED vna cum quadrato EC,
ergo rectangulum A D C cum quadrato
DC, æquale erit rectangulo AEB, cum
quadrato EC, eſt autem quadratum DC
minus quadrato EC, cum ſit linea DC mi-
nor EC, ex hypoteſi; ergo rectangulum
ADC maius erit rectangulo AEB. Quod ſecundò, & c.

THEOR. XXXII. PROP. LXI.

Si fuerint duæ quæcunque coni-ſectiones, non excepto circulo,
eiuſdem, vel diuerſi nominis per diuerſos vertices ſimul adſcriptæ,
quæ in eiuſdem communis ordinatim ductæ extremis punctis ſimul
conueniant, è quorum altero eadem recta linea vtranque ſectionem
contingat, ea coni-ſectio cuius vertex cadit infra verticem alterius
erit alteri inſcripta, & in ijſdem tantùm applicatæ extremis ſe con-
tingent.

SInt duæ quælibet coni-ſectiones ABC, ADC non excepto circulo, eiuſ-
dem, vel diuerſi nominis per diuerſos vertices B, D ſimul adſcriptæ,

94[Figure 94] quarum communis diameter ſit BH, communiſq; applicata ſit AC, in cuius
extremis A, C, ſectiones ſimul occurrant, & ex eorum altero veluti ex

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