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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 40, page id 898203430:0232
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40
VINCENTII VIVTANI DE LOCIS SOLIDIS
ctangulum ODN, vel ACB. Larera isitur CD, C H polsune pradi-
ctas differentias: e hoc de lingulis similibus ordinatis eec. Ouare conne-
rum huiulmodi Erperbolae est Locus propoliae Ordinationis. Ouod ergt
dec.
CEMMA. VI. P R O P. LXII.
 recta linea secta fuerit otcunque, es alterum ex
sermentis similiter occunque: Differentia inter re
ctanculum sub tota, e5 seomento diviso, (5 rectaneu.
lum sub acoreeato ex indiuiso sermento cum interpo
sito in interpositum, aequatur rectangulo sub tota
cum eodem interposito in extremam partem diuist se
Menti.
OIF data AB vecunque secta in D, _ DB alteriim segMEntOruML V
cunque in C. Dico disferentiam inter rectangulum ABD, de recta
sulum AC D esse rectangulum sub AB cum GD in GB.
Producatur BA ad F, CUIatUTqUC AF
aequalis ipsi BD, _ AI ipA DC. Frie
ergo AB aequalis FD, Ob COIMUNEM AD
additam aequalibus AF, DB: quare, sum
Dea DB communi alcitudine, erie rectan-
gulum FDB aequale rectangulo ABD; sed rectangulum F D B aequale
a Lemm2z. est a duobus limul IDG, FC B, ergo de rectangulum ABD aequale eAt
duobus Tumut IDC, FO B nempe AO D cum rectangulo F C B; led 12.
tuS I C aequatur lateri IB, hoc vero constat ex IA cum AB, vel ex
DC cum AB, ergo rectangulum idem ABD aequale est rectangulo ACD
und cum rcctansulo ex DC cum AB in CB. Quod erae demonandum.
e
L L l
LMI
AcS iildem, super toram datam AB hac rectangulum ABD, quod
i A L, iungatus diameter D E et Commpleatur ligura. Lxit er80
metrum qudarala, quore differencia inter
rectangutum AF, _ AII erit eadem ac
inter rectangulum ABD, _ rectangulum
AC D. Led difterentia incer rectangula.
AE, AHI est rectangulum MF. CUIM KC-
ctangulo HIB, vel cum aequali supple
memo NL, et rectansula MF, NL. (.
Pap. in lib.
Conic.
VE quadratum de FHI, DH circa dia-