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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 12, page id 826603459:0060
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De Manseartois
CAP. 3.
dri contenates ucut retu eller, non camem est CuHficiens
enumeracio, cum occurrane alix non pauca, quas esle r siort
lIguCE.
80. Tgicur verem coram dilucidius expediam, eres prxelee.
eim demonstracionum Machemacicarum lire medos, sire ore
dus, sive species Hatuo.
Prims quidem est illa demonstracio, quae per deductionem ad
absurdum, leu imposlibile, Procedic; érazooyn dicca: qua, rem ica
elle, demonstrar, eo quod sic impolsibile, vc secus sic. IIc siquis
demonstraturus, Reciarum circulo inscripearum, loncissimam illam esse
quae per centrum cranset; illudica ese alterac, quoniam impostibile
est aliam quamvis, per cenerum non crantcuncem, vel longion
rem esse, rel quidem aequalem. Supponatur enim, E heri Doltic,
recta AD actaucO, per cenerum non trantiens, diamcero
A. B, per ceverum C cranscunci, aequalis, rel etiam ipla lonei-
Or: BE duCatUE a CenErO C, recCA
C D. Dico rectam C D aequalem
ese recta C, B,. quoniam veraqi cs
recta a cenero ad circumterenciam
ejuldem circulis ideoq: A C D, (ex
duabus rectis AC, CD compoli-
1a,) eric aequalis diamerro AC. B,
quoniam si aegualibus aequalia.
addaneur, eota crune aequalies) si
isicur A D sic equalis ipsi AB, erie
etiam aequalis ipsS AC, C D. B.
mul Cumpcis, (nam quae cidem. ret
aequalibus rquantur, ccamincer PC aquantur;) si AD lonsiOE
siE ipCa AB, exic _ loneior, quam AC, C D, SinUI. CuNDLISS
qnibus ipta AB ~gualis cMt,) Achorum ucrumqi absurdum
est d impollibise. Cum enim AD. Cic recta, quxe inter data pun-
cta brevissima eAt, _ quidem unico; impossibile est uc rel longi-
Or sic, vel eciam aqualis, ip(IS AC, C D, Simul Cumpcisi, qua
non nisi per circuicum quendam a puncco a act punctum Ld
procedune. Non eMisicur recta AD, vel aequalis vel major
quam cA AB. Sed ec eaden omnino demonstrario procede-
rec, hubiris aliis recta non per cencrum dueca inseribaiur, pura
L F: si enIm P. P sic major vel segualis ipsI AB, eric proinde
major vel aequalis E C., C. F, simul lumpris; quoniam E C rar
diue