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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 7, page id 898203430:0199
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=199
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ORDINATARVM POTENTINM LIMIS. LLI. L
XIT data AB, eique superaddita quaelibet AC; de producta BA, ita
2D VE A F SC aequalis AB, Per verticem F, circa axem EB, cum recto
requale dato AB delcribatur Parabola F. D. Dico hanc cHe LOcum PrO.
volicum: nempe ordinacam CD posse Tum-
mam ex rectangulo B A C lub data, d
superaddica vna cum quadrato datae AB.
Ouacracum enim CD aequale cst 2 FC.
etangulo sub CF in rectum lacus AB, vel
in F A ipsi aequalem; led rectansuum
CF A aequale CA rectanguIO F. AC, (1.
uc B A C vna cum quadrato FA, vel cum
quadrato A B, ergo CD poiclt spacia.
propotica, e hoc de qualibet ordinata ac.
Ouare concauum huiulmodi Parabola est Locus proposicae Ordinationis.
eR OPO51++O XI.
e
N FIrperbola. Ouadratum ex ea, quae orarhalut M
ter diametrum coniuratam, es Sectionem, ad qua-
dratum semidiametri transuersae, est ot. summa qua
dratorum, alterum nempe ex sermento coniucatae inter
ordinatam. (5 centrum, a terum ex secunda semidia-
metro coniueata, ad huius semidiametri quadratum.
IT Hyperbola AB, cuius centrum D, diamerer quaelibet cransuerla
CB, Secunda vero ipsi coniugata, de guancumlibet producta sL G F,
ad quam Ci quaecunque ordinata L A vlque ad Erperbolam in A. Dico
quadraum LA ad quadraum D C, esse yr quadraca simul ID, D C ad
quadracum idem DC.
Ducatur ex A ordinata AFI ad diame-
trum BII, quae ipsi ID aequidictabic. Kric
ergo rectangulum CHIB ad quadratum.
AHI, ve b cransuersum lacus ad rectum,
vel re quadratum eransuerlae ad quadratum
secundae diameri, rel sumpris horum sub-
Guadruplis, ve quadratum DB ad quadia-
cum DC, ee permutando rectangulum.
C HB ad quadratum D B erit ve quadea-
cum AII ad DC, vel ve quadratum ID
ad idem DC, ee componendo rectangulum CHB cum quadrato DB,
hoc est rnicum quadratum DII, vel quadratum PA ad quadratum DB
erit ve quadracum ID cum quadrato DC ad idem D C. Quod erat dc.
on
0-
b 21. primi
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