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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 42, page id 898203430:0234
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VINCLNTIL VIVLANI DE LOCIS SOLIDIS
ROPOSTT LO LLLEI.
Ocus Ordinatarum potentium differentiam inter qua
ratum data, (5 rectanculum coadditarum; quod
sit maius quadrato datae, est ad concauum ETyperbolae
equilatera, cuius vertex sit occursus illarum coaddi
tarum; quarum rectanculum aequale sit quadrato da-
ta centrum vero sit punctum bisecans datam.
IT data A B secta bitariam in C, de producta (IC sCCCtT in D, H
a rectangulum ADB aequale sit quadrato datae AB; d iterum vIIrZ D
vicunque in C. Constac rectansulum AC B, quum excedat rectangulum
AD B, excedere quoque quadratum AB. PIXterCA, per verricem D, cum
centro C describatur Fyperbola equilatera DHI. Dico hanic enle Locum
provolicum: hoc est ordinatam C HI posse differentidm inter quadratum.
datae AB, de rectangulum condditarum AC B.
ProdUCatUE C A, Sumaturque A F sequalis
BD: eric er 90 _ C F aequalis C, D, nempe DF
erit axis cransuersus Eyperbola DHI, qua quum
Tic sequilatera, crie rectangulum. FD C aequale,
quadrato GH, Sed rectansulum F C, D aequale Y
est rectangulo sub AC cum BD in GD C nam
AC Cum BD aequatur AC, cum AF ip EI BD aequali; ex construccione)
per Lem, ee rectangulum sub AC cum BD in GD est a differentia inter FCCtanGU
lum ACB, ee ADB, ergo e rectangulum FC D, fiuc aequale sibi qua
dracum C H est ditterentia inter rectangulum AC, B, quod eA conddita-
rum, e rectangulum ADB, vel huic aequale quadratum datre A B: et
hoc de lingulis similibus ordinatis dec. Ouare concauum huius Hyperbo
Ixe CA Locus propolica Ordinationis. Ouod erut ec.
PROPOSITIO LXV.
Ocus Ordinatarum potentium differentium inter re
ctanculum sub data in sermentum maius minore
eorum interrantium, quae datam dividunt secundum
extremam; (5 mediam rationem, (5 quadratum reli-
qui sermenti ex data, est Locus planus, seu conca
num Circuli peripheriae, cuius vertex sit ibsa divisio
secundum extremam, Co mediam, radius vero aequalis
sit ae creeato ex dimidio datae cum maiori seemento extre-
morum.
Sit
L C.
6. tuiu