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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 29, page id 898203430:0221
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=221
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ORDIATARVM POTENTIVM LMIT. LAB. II.
P R O P OSITIO ALLLLLAI.
Oeus Ordinatarum potentium differentiam inter qua-
adratum superadditae, (5 summam quadratorum da-
tae, C5 additae, est ad concauum Parabola, cuius vertex
sit occursus data cum addita, avis ipsa addita, (5 se-
mirectum latus aequale datae.
Sto A B data, e A C quaelibet superaddica, per verricem verdB,
Lis cirea axem BC, cum lemiecto AB sic descripta Parabol2 BD. Dico
hatC esse Locum Propoluum, siue ordina-
tam CD posse ditterentiam inter quadra
tum superaddicae A C, ee summam qua-
drREOTI AB, BC datae, _ additx.
Piam differentia inter quadratum A C.
ee lummam quadratorum AB, B C aequa-
lis est duplo rectanguli ABC, cui aequa-
tur quadratum ordinata C D, co quod
AB ponatur semirectum Parabolae, ergo
CD porest praedictum differentiam: X hoc
de qualiber simili ordinata eC. Ouace concauum huius Parabolae est LoeuS
propolita Ordinationis. Ouod erat _c.
e
LEMMA. HI. P R O P. ZZXZV.
 datae rectae addita fuerit in directum quaecunque
D
Duadrata simul coadditarum aequantur quadrato
data, ona cum duplo rectanculi ex ipsis coadditis.
OTE data AB, e addica quaelibet BC. Dico duo simul quadrata cond.
1 dicarum AC, C B, quadrato AB datae, cum duplo rectansuli AC. B
coadditarum xqualia cAtc.
Nam, quum reCta A C sE vecunque le-
Eta in B, erie quadratum AC xquale duo-
bus simul quadeatis A B, BC cum duxlo
rectanguli ABC, his ergo communi ad
dito quadrato C B, crune duo sinul qua-
deata AC, C B, aequalia quadrato AB
cum duobus quadraris BC. & cum duo-
bus rectarigulis ABC, sed duo BC cum
duobus AB C aequunur duobus ACB, ergo et duo simul quacrata ca.
dem