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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 27, page id 898203430:0219
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DRDINATARYM POTENTINM LINIT. LIB. II.
draca parcium AC, CB, ergo duplum rectaronta ABC est ditterencia.
iner quadrat AB, _ disserenIAM GUIAdTAEOTUIM A C, C B, Sed dit- 2 2r. prim
plum rectanguli AB C aquacur 2 quacrato ordinatae C F C quum posi Conic.
ium sit AB esse dimidium recti lateris Parabolae BF,) ergo e huius CF
quadratum aequatur ditterencix inter quadracum datae AB, de disteren
EIAML GUadFAEOTUM parEiUM A C, C B: de hioc de lingulis similibus ordi-
natis ecc. Ouare concauum huius Parabolae eAt. Locus proposicae Ordinacio
nis. Ouod exat dc.
PR OPOSFTIO XXXXI.
la
Oeus Ordinatarum potentium differentiam inter qua
adratum, datae es differentiam quadratorum coaddica
rum, est ad concauum Parabola, cuius vertex sit occursus
datae cum addita, axis ipsa addita rectum verd latus
sit duplum datae.
CIT A B data, d quaeciinque addita B C, ac per verricem B, circa
axem BC, rectoque latere duxlo AB describatur Parabola BD. Dico hanc
eNC Locum propolicum: nempe ordinatum C D poste disterentiam inter
quadratum data AB, ec disserentiam quadratorum conddicarum AC. C B.
Ob Parabolam enim, ee semirectium
latus A B, est quadracum ordinatae CD
xquale b rectansulo sub duplo A B in
BC, vel duobus rectangulis ABC, sed
duo A B C constituunt differentiam inter
quadrarum AB, _ idem quadratM AB
cum duobus ABC; hoc aurem AB cum
duobus ABC est diferencia inter quadrata
AC, CB condditarum, ergo e quadea-
cm CD aquatur eidem disferentixe inter quadPaHIIM B, A Eequadraca cdad.
ditarum AC, CB: ee hoc de qualibet simili or dinaea eec. Ouare concauum
huius Parabolae est Locus propolica Ordinaienis. Ouod erat dc.
eRC10d++10a.
Ocus rathalaram polenium differentiam intor qua-
dratum parcis, es summam quadratorum datae, C
partis reliqua, est ad concauum Parabolae, cuius ver-
tex sit occursus datae cum reliqua, axis ipsa data, e
rectum latus sit duplum ejusdem datae.
b 1r. primi
COniC