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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 48, page id 898203430:0240
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VINCENTI VIVTANI DE LOCIS SOLIDIS
eROPOSITIOLMMI
Ocus Ordinatarum potentium differentiam inter sum-
mam quadratorum coadditarum datae; (5 rectanou
lum sub coaddiris, est ad convexum Fyperbolae aequin
laterae, cujus contrum sot punctum bisecans datam,
vertex vero ab eodem distet per semitransuersum avem
potentem triplum quadrati ex semisse date.
TT AB data linea, guaxe bisecetur in puncto C, ex quo erigatur peru
 Pendicularis CD pocens triplum quadrati A C, _E CIII CCHETO C, d
Temiaxe transuerso CD describatur Eyperbola aequilatera DF. Dico hane
ese Locum provolicum; hoc eA. Si in producta A B sumpeum si quodli-
Dec punctum F pro occursu coadditarum AF, FB,
ordinacam FF posse ditserentiam incer lummam qud-
drATOrUM AF, FB, _ rectangulum AFB.  
DUCAEUT Ex CEHEIO C A(YIPEOTOS C CI, Qua (quU
EIyperbola sic aequilarera) rectum angulum D CF
bitariam secabit, adeoque in criangulo rectangulo
CF C anguli ad C, C semirecti, nempe aequale.
erune, adeoque latus C F lateri F C aequale, et
quadratum quadrato. Descripra autem ad alteram
Partem alia sectione HII ip(I DF Opposica, _ prO
N. secun. dUCEA F. F ad P, eric rectangulum LO F aequale 2
liComc. Quadrato lemidiametri cransuerlae CD, er80 qua
deacum FC vna cum recrangulo IG F, nempe qua-
dEaEm F F aquale est duobus simul quadratis C L.
C D, sed CD C ex Fypothes) criplum est quadrari
CA, ergo quadratum F L aequale eAt quadratO C F.
cum rribus C A, Sed disserentia inter quadrata AF, FB condditarum; de
recrangulum carundem A F B aequalis eAt quadrato C F cum tribus C A
(per Lemma praecedens) ergo de quadratum J.F. eidem disserentiae inter,
quadraca condditarum, ee rectansulum carundem aequale erit: et hoc des
linculis similibus ordinatis ecc. Ouare convexum huiulmodi Eyperbola.
DF. eA Locus propolix Ordinationis. Ouod sit laus DCO, 2C
esde L
LEBRL SFCYND.
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