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

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162138

Nam quadratum AF æquatur rectangulo ſub FB, & recto latere, 11Coroll.
1. h. ſub dupla FB, ſiue ſub EF, & dimidio recti, ſed idem quadratum A F æ- quatur rectangulo ſub eadem EF, & ſub FD; quare FD erit dimidium recti.
2235. pri-
mi conic. Quod primò, & c.

Amplius in Hyperbola ſecundæ figuræ, dico interceptam portionem FD
eſſe pluſquam dimidium recti lateris.

Nam reperto eius centro G, erit rectangulum GFE ad quadratum AF,
vel ad rectangulum DFE, vt tranſuerſum latus ad rectum, ſed 3337. pri-
mi conic. GFE ad DFE, eſt vt linea GF ad FD, ergo GF ad FD eſt vt tranſuerſum la-
tus ad rectum, vel vt ſemi-tranſuerſum GB ad ſemi-rectum, & permutando
GF ad GB, erit vt FD ad ſemirectum, ſed eſt GF maior GB, ergo FD erit
maior ſemi-recto latere. Quod ſecundò erat, & c.

Tandem in Ellipſi

128[Figure 128] tertiæ figuræ, in qua
intercepta axis portio
DF eſt de maiori axe,
vel in quarta figura, in
qua prædicta portio
DF eſt de minori axe,
dico item ipſam DF
minorem eſſe dimidio
recti lateris eius axis,
cui ductæ perpendicu-
lares occurrunt.

Sumpto enim Elli-
pſis centro G, eſt re-
ctangulũ EFG ad qua-
dratum AF, vel ad re-
ctangulum E F D, 44ibidem. tranſuerſum latus ad
rectum, ſed idem rectangulum EFG ad EFD eſt vt linea GF ad FD quare
GF ad FD eſt vt tranſuerſum ad rectum, vel vt GB dimidium tranſuerſi ad
dimidium recti, & permutando GF ad GB, vt FD ad dimidium recti, ſed eſt
GF minor GB, ergo & FD erit minor quàm dimidium recti. Quod vlti-
mò, & c.

COROLL. I.

HInc patet in Parabola, & Hyperbola contingenti perpendicularem in-
ter contactum, & axem, ſemper eſſe pluſquam dimidium recti lateris
ſectionis. Nam in triangulo AFD recta AD recto angulo oppoſita maior eſt
latere DF, ſed DF, vel æqualis eſt (in Parabola) vel maior (in Hyperbola)
prædicto dimidio, quare perpẽdicularis AD erit omninò maior ipſo dimidio.

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Scan	Original
101	77
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105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
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117	93
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121	97
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128	104
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130	106

Scan	Original
101	77
102	78
103	79
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106	82
107	83
108	84
109	85
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