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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 25, page id 898203430:0217
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ORDIHATAAVM POTENTINMLIT. LIB. I.
differentia vero incer quadrata A B, A C est rectangulum H B C, sed
differentia inter FBF, e HBC est rectangulum FC F, live quadracum
ordinatae C D in lemicirculo, creo d ditterentia inter quadratum datxe
AB, rectanguio F BP aequalis ostenta, X rectansulum HBC, quae cA
distereneia imer quadearen datae A B, de superaciditae A C, est ipsum
quadratum ordita ae CD, de hoc de qualibet simili ordinata iner puncta
B, F. Duare concauum huius peripherix eAt Locus propolia Ordinatio.
nis. Ouod erat c.
e R O P OS L L LO AAAVIIL.
.
Ocus Ordinatarum porentium differentiam inter qua
dratum datae, (5 differentiam quadratorum datae
Cs superaddita, quae possit maius duplo quadrati ex da-
ta est ad concauum FErperbola aequilaterae, cuius cen
trum sit occursus datae cum superaddita, semiaxis ve-
ro transuersus possit duplum quadrati ex data; axis
autem sit ad productionem superadditae.
N IT data AB, e superaddica quaelibet A C, quae tamen poltic plul-
a quam duplum quadrati ipsius AB. lumpeaque AF, cuius quadratum
duplum (IE AB, Cum CenErO A, d semiaxe transverso AF. har Hy Peibola
ED. Dico hanc esse Locum propolicum: nimirum ordinatam CI polle
ditterenciam inter quadratum datae A B, ee ditterentiam quadratorum
AB, AC.
ProduCatuE B A. Super quam sU-
IaNtUE A F, A G, A HI, ip(IS AB,
AF, A C, aequales, singulae lingulis.
Jam rectangulum FIF C est diste.
rentia inter rectangulum HBC, e
OBF, sed HT BC est disserentia in-
ter quadratum superaddicae AC, et
quadratum datae AB, e rectanou
Ium CBF aequatur quadrao eiusdem datae AB (quoniam positum est
quadratum AF. duplum quadrati AB) ergo rectangulum II F. C est difie-
rentia inter quadratum datae, de disterentiam quadratorum datae, de supe.
radditae; scd HF. C aequale est rectansulo C C F. ( quum OH, F. C CInE
aequales, ex constructione) de rectangulum C C F XequatuI quadratO CD
(quum G F. Ic axis cransuertus deseripexe Hyperbolae aequilatera) ergo et
quadratum CD est differentia inter quadratum datae AB, d ditterenciam
quadratorum eiuldem dux, de luperaddirae A C: d hoc de qualiber (1.
mili ordinata vitra PuNCtuM P. Sec. Ouare concauum huius Hyperbolae est
Eocus propoliae Ordinacionis. Ouod et ac _c.
D
i
et.