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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 14, page id 898203430:0206
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=206
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VINCENLIL VINTANT DE LOCIS SOLIDIS
D R OPOSITIO NAM
Ocus Ordinatarum potentium summam ex quadra
to datae cum quadrato additae, est ad convexum
LIrperbola aequilaterae, cuius centrum sit occursus datae
cum addita, C5 a quo axis vertex perpendiculariter di
stet per distantiam aequalem datae, quae sit ejus semi-
axis transuersus.
NIT AB data, eique 2ddita BC, de ex B ducta BD super AC per
Pendiculari, ee aequali ipsi datxe AB, per verricem D, cum cenrO
B, de Lemiaxe transuerso BD, hac Hyperbola requilatera D F. Di.
co hanc esse Locum PrOPOTU: hoC eAt, SI ex C ordinetur C L, hanc pot
sc Cummam quadratorum AB, BC datae, de additae.
Tunsatur D C. Fc quoniam Hyperbola DF.
est aequilatera, de BD, B A sune aequales, ex
constructione, estque BD semiaxis cransuerlus,
eric B A semiaxis ConiugatUS; atque eA C F Or.
dinaca inter coniugacum axem, a Arperbolam.
r. huius. ergo quadraium C F. ad B D est ve d quadra-
tum CB cum BA, vel cum BB, vel ve vni
cum quadratum C D ad idem quadratum BA
semiaxis coniugati, vel ad idem quadratum B D: quare quadrata C E,
CD lunc aequalia, adeoque e latera C F, CD; Sed CD porest qua-
drata DB, BC, vel AB, BC, ergO_ C F eadem poterit quadeaca
AB, BC datae, e addicae: de hoc de qualibet alia simili ordinara dec. Ouam.
obrem convexum huinsmodi Fyperbolx est Locus propolux Ordinatio
nis. Quod erat _c.
 hac manifestum Ac, I HsPetora aGunatera, quemcunque ramum
Ca unis vertice ad ase coniugatarum Sectionum auc eGlale
edle oratala ad lo occursu inter cundem axem coniugacum, de da
cam Ryperbolam interceptum. Superius enim ostensum fuit rectam DC
ductam ex verrice axis EIyperbolae DE. ad coniugatam diametrum ABC
requalem ese ordinaa C. F. inter iplam coniugacum, ee Hyperbolam.
  
a