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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 13, page id 898203430:0205
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ORDTHATARVM POTENEIDM CIMT. LIB. II.
quadratum F C aequale duobus quacratis A C cum duobuS CF, sed duo
AC cum duobus C F aequantur quadratis simUI A F, F B C guum (I AB
bitariam lecta in C, eique sic in directum addita BF) ergo ee quadratum
CF quadratis partium AF, FB, vel incegrancium dacam, vel coaddica-
rum aequale est. Et hoc de quacunque simili ordinata LC. Ouare conne.
num Hyperbola D F. est Locus propopolicae Ordinacionis. Ouod erac _c.
DROPOSITIOA
Ocus Ordinatarum potentium summam on quuti
a to data cum quadrato partis, est ad conuexum HIr
perbolae aequilaterae, cuius centrum sit occursus datae.
es partis, vertex vero ab eodem occursu perpendieu
lariter distet per semianem transuersum aqualem data.
IT data AB, cuius pars BF, e super AB concipiatur quadratum.
D ABCD, _ per verticem C Fsyperbola aequilatera C F, cuius cen-
trum sic punctum B occursus datae cum parte BF. Dicor (i ex F Ordinetur
FFI hanc posse summam ex quadrato datae AB cum quadrato partis BL.
ProduCatuE C B, eique lumatur requalis BI.
de per verricem I delcribarur alia Hyperbola
TL. IpE C F OppOlita, iuInSaTIE BD, de produca
tIr HIF ad MI, qua HIF ICCet DO in N, et DB
in O, _ tandem producta veringue AL FIYPer.
Bolis occurrat in F, L ex quibus agantuL P P,
L. O ip(I AB Parallelae it  st
Tam, ob Hlyperbolam aequilareram CRs est re.
ctangulum IPC, siuC QC P, vel. L DF. aequale
quadrato ordinata PE, vel quadrato DC, vel
DA. Sed rectangulum LD F ad, MI N H est
ve 2 quadracum AB ad BF, vel ve quadratum
AD ad F O, d permutando est rectangulum
I. DF. aequale quadrato P. D. ve modo octendi-
mus, ergo de rectangulum MIWEI quadrato FC
aequale est, sed quadratum PN aquatI qua
drato datae AB, ob laterum aequalitatem, cr80
his aequalibus verinque addicis erit rectangulum NL N II cum quadrato
F NIs hoc est unicum quadratum ordinatae L FI aequale quadrato FO,
vel quadrato partis sibi aequalis B F. cum quadeato datxe AB: e hoc de
qualibet alia simili ordinaia exc. Ouare conuerum huiusmodi Hyperbolx
C F est Locus propolita Ordinationis. Ouod dc.
prov.
imihuiuse
PRO.