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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 15, page id 898203430:0207
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OADINATARVM POTENTIVM LMUT. LIB. II.
P R OPOSFFIO XXII.
Ocus Ordinatarum potentium summam ex quadra
a to datae cum quadrato superadditae, est ad conuexum
FIrperbolae aequilaterae, cuius centrum sit occursus dam
tae cum superaddita, data vero sit semiaxis coniuca
tus, adeo et semianis transuersus sit aequalis datae.
TT data A B, de superaddica quaelibet. A C, ex A vero SE 2d A B
a perpendicularis, ec aequalis AD, aC PeF VeHTICeM D CuM CCnTO A,
_ lemiaxe cransuerso AD tiac Hyperbola aquila.
tera D F, cuius propterca lemiaxis coniugatuS
exic A B. Dico hanc FErperbOlam esse Locum
PTOPOsItUM; hOC eAt (I Cx C OrdinCTIE C F, tanC
posse summam ex quadrato datie AB, cum qua-
drato luperaddita, AC.
tunsatur DC, quae (quum Fyper bola DF. sII
requilatera) ordinacae C P. aequalis erit 2 sed CD
Potest quacrata D A, AC, vel AB, AC, ersC
d C F Porerit eadem quadrata AB, AC data,
d superaddicae; & sic de lingulis similiter Ordina-
cis eec. Ouare converum huulmodi Hyperbolae est LocuS prOPOlicae Or-
dinationis. Ouod erat _c.
P R OPOS FTFO XZII
Ocus Ordinatarum potentium summam ex quadra-
to totius datae linea, (5 ex quadratis simul partium;
vel inteerantium, vel coadditarum; est ad conuexum
Firperbola, cuius centrum sit punctum bisecans datam,
vertex vero ab eodem perpendiculariter distet per se-
miaxem transuersum potentem sesquialterum quadrati
ex data, es qui sui semirecti sit duplum.
PIT data AB, cuius partes incegranes, vel COnddIEX GuXCUNqUA AF, F. B.
de secta AB bitariam in C, crisatur ex C perpendicularis CD PO-
rens quadratum selquialcerum ipsius A B, d cum centrO C, de lemiaxe
transuerso C D describatur per D Hyperbola D F, cuius rectum latus
subdu-
aCOrolL. 2Y