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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 111, page id 898203430:0303
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ADDENDA LIBROLLATIO.
tur duplo quadrati IC, cum du-
Dlo quadraci ID: ergo quatuor (I-
nul quadrata AB, BC, C D, DA,
aequantur duplo quadratorum lA,
IB, IC, ID; sedtam duo quadra
ca IA, IC, quam duo IB, ID:
incer se lunt aequalia; ergo quatuor
quadrata laterum AB, BC, C D,
D a aequantur quadruplo quadra-
ei Ia, cum quadruplo quadrari lB: Sire aequancur duobus simul qua-
dratis diameErOruI AC, BD. Ouod CraE, AC.
SCHOLIV M III.
N parallelogrammis ABCD, F FGFT, equalia lacera lingulum
A. sinigulo habencibus; sed quae dirersos ansulos inter se constiruant,
adeoque, et direclas diametrorum lonsicudines; par tamen quadra.
eorum luper diametros RC, BD unius aequacur pari quadracorum su-
ver diamerros L. CF, PHI alterius. Nam urrique ex his paribus aequa-
cur summa quadratorum quaruor larerum proprii parallelogrammi: led
hae Cummae quadracorum incer le lune aequales, quod unumquodque
lacus, unicuique lateri lingulum linsulo aequale sic; erso de paria qua-
dFAEOIEUM AC, BD; F CE, PII lune equalia.
Ad pac. 85. Ouartum Lemma, es Propos. 33. sic aliter
clarius est exponenda super hac fieura, ac de-
monstranda, cum additione sequentium
Scholiorum.
Tfuerit quaevis Paraiola porrio ABC, cujus sit basis AC
D diameter BD, ac trianculum inseriprum ABC, alierum
vero larerum, ut AB sit quancumlibet productum ver (uS L
sitque diamerro BD, inter D, 8 C, ducta quavis aequi-
distans PF productam AB secans in F, curvam BC Para-
bolae in HI, e reliquum latus BC in G. DicO, FII inter
curvam, e basim esse mediam harmonicam inter rectas PF,
FC.
PDer punetum B ducatur BM Parallela ipliD C, quae cansat parabo
lam 3aB, e per C. ipsi D B parallela C. M, quae producacue ulg; ac
BF, ii FI.