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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 26, page id 898203430:0054
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VINCENFH VIVIANI PRO LOCIS.
PR OPOSITIO XVII
WV quacunque Coni. sectione, vel Circulo. Si basis
trianculi circumscriptiinter focum, o sibi proximum
avis verticem ceciderit, 9 in Fillipsi prolata inter cen-
trum, 5 verticem, per quem, in sinoulis sectionibus,
sit verticalis contingens alteri lateralium occurrens, quae
a puncto dimidia basis trianculi applicetur subtendens
rectum anculum ab ipsa verticali, ( sectionis axe con
stiturum: haec in Circulo reliquae lateraiium tancen
tium aequidistabit.
In Paraboia vero, in Fryterbola, 5 Fllipsi oblonea ei
dem tanrenti oecurret ad partes sectioni contrarias.
Sed in FTyperbola occurret inter verticales tancentes sectio:
num opposiearum.
In prolata autem ad partes centri; altra tamen verrica-
lem tansentem priori oppositam.
Et si ab occursibus praedicta subtensa cum lateralibus con
tincentibus ad preductum axem ducantur ordinatae,
punctum bisecans seementum ab bis abscissum; cadet
in Parabola. FErperbola. C5 Fllipsi obtonea inter ver-
ticem trianculi circumscripii, es ordinatam a Sectio
nis vertice remotiorem.
In IErperbola vero, inter Sectionis centrum, C5 Ordina-
tam vc tici proviorem.
Sed in Ellipsi prolata inter ejus centrum; es ordinatam
a vertice remotiorem
Si autem, quae ordinatur in prolata F.llipsi, per centrum
sit ducta, praescripta subtensa cum viraque item late-
raii contincente conneniet, es ordinatim ad axem du-
eta ab acursious agamia axis seementa abscindent in
ter eusuem orams, es centrum dectionis.
ESO ABC quaelibet ex praedictis Coni - sectionibus, cuius axis BK,
L vertex B, Focus F, axls CaluertuS I B, cenrum O: hoc est in
criprum sic criangulum AF. C, cuus axis F D, balis AD C incer focum
F e
FI. ista figura, etto Circulus; utsecnta, Parabola; in certia, Hyperbo.
Id;  Guata; Flliplis obloas  eed Prolata, atque Cineulis circum