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

Table of contents

< >
[121.] THEOR. XXVI. PROP. XXXXVIII.
[122.] MONITVM.
[123.] THEOR. XXVII. PROP. XXXXIX.
[124.] THEOR. XXVIII. PROP. L.
[125.] COROLL.
[126.] PROBL. XVII. PROP. LI.
[127.] PROBL. XVIII. PROP. LII.
[128.] ALITER.
[129.] ALITER breuiùs.
[130.] PROBL. XIX. PROP. LIII.
[131.] ALITER.
[132.] ALITER breuiùs.
[133.] PROBL. XX. PROP. LIV.
[134.] ALITER breuiùs.
[135.] PROBL. XXI. PROP. LV.
[136.] PROBL. XXII. PROP. LVI.
[137.] COROLL. I.
[138.] COROLL. II.
[139.] PROBL. XXIII. PROP. LVII.
[140.] COROLL.
[141.] THEOR. XXIX. PROP. LIIX.
[142.] ALITER.
[143.] THEOR. XXX. PROP. LIX.
[144.] THEOR. XXXI. PROP. LX.
[145.] THEOR. XXXII. PROP. LXI.
[146.] THEOR. XXXIII. PROP. LXII.
[147.] SCHOLIVM.
[148.] THEOR. XXXIV. PROP. LXIII.
[149.] THEOR. XXXV. PROP. LXIV.
[150.] PROBL. XXIV. PROP. LXV.
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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.
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.
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-
, &
c.

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