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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 46, page id 898203430:0238
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4c
VINCENTIL VIVIAM DE LOCIS SOLIDIS
Pter OR ordinata in Fyperbola PCO porest disterentiam inter rectangu.
lum ABO, e quadratum O A: & hoc de alia simili quacunque ordina-
ta ec. Ouare concauum huiulmodi Eyperbolx est Locus propoluae Ordi-
nacionis. Quod erat etc.
LEMMA VIIT. PRO P. LXVIII.
I recta linea secta fuerit bifariam, C5 non bisa-
riam, quadrata simul inequalium partium totius
aequantur quadrato ex datae dimidio; una cum triplo
quadrati ex interposito seemento, es cum rectaneule
earundem partium inaequalium.
CTT data recta AB secta bitariam in C, de non bitariam in D. Dico
Quadrata simul parrium inaequalium AD, D B equalia esse quadeato
ex A C corius dimidio, una cum criplo quadrati interiectae parris C D, e
cum rectangulo AD B iplarum partium inaqualium.
Sumatur C F, aequalis C D.
Ouoniam enim EB secta est vicunque in
D, Crunc duo quadrata partium F B, BD,
vel duo ipsis requalium AD, DB aequalia
duobus rectanoulis F B D cum quadrato
ED, vel cum quaruor quadratis CD; Sed vnum ex rectangulis E B D
cum vno ex quadraci CD aequale est quadrato CB, vel quadrato AC, er-
eo eadem duo quadrata AB, DB aequantur quadratO AC cum reliquo ren
cangulo EBD, vel ADB, et cum reliquis cribus quadratis CD, Ouod eci
P ROPOSITTO LXIZ.
Ocus Ordinatarum potentium differentiam inter sum
a mam quadratorum partium inteorantium datam, C9
rectanculum sub isdem partibus, est ad conuexum Fyn
perbolae, cuius contrum sit punctum bisecans datam,
axis vero transuersus sit eidem aequalis; sed sui recti
lareris triplus.
IE AB daca quae bitariam secetur in puncto C, ex quo ad ipsam AB CrI.
datur perpendicularis C F dimidio Forius A B aqualis, de cUI Cen
EO C, per verticem F describatur Hyperbola FF, cuius rectum lacus sub-
criplum s suo crantuerto. Dico hanc esse Locum proposirum; hoc est or-
dinatam