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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)
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dversus M. Meibomi
bomioretragrante:) Non itaque aequales lunerationes  et L3
quod vulcMeibomius. ILem quarcO. Si aequalibus inaqualia
addantur tora erumt inequalia; (per 4 aX. Y) e quidem illud ma-
jus, ubi majus additur: C quod, crcdo, nec Meibomius negabic.)
AC, Eracionibus = XZ addancur inxqualia; illic = = 25, hic
Bt, 2EBregaCa erunE aequalia, nempe utrobique 28 - = =-
2X E. Non icaque aequales lunc raciones = _ 2, quod rulo
Meibomius. Irem, E racionibus aequalibus =, 2, addaneur
Meibomii sen (u) raciones Fe 7; 28gresatum illud ubi dadi.
CurZ, (nempe 3Z = =X3,) majus erit eo ubi addirur 23
(nempC == =8 X4:) racio icaque 8 major eA quam ratio Z3
non aucem minor, quod rultMcibomius. Icem quinco. Si ab
aequalibus aequalia adimantur, residua erunt aequalia; PeF Z aZ. F.
Acharationibus =, Z, auferantur aequalia, (puta ucrobi-
que ratio 23) retidua non crunt aequalia (Ccd illic = leu
e
Meibomii lentu.) Non isitur aquales lunt expolicae rationes
5,23 quod rule Mcibomius. Tandem (exto. Si ab aegnalibus
inaequalia auferantur, residua erunt inaequalia; (Per 5. aX 1.) de
quidem illud minus, ubi majus onfertur; (quod nec infrciabitue,
credo, Mcibomius. ) Aeha rarionibus =_ Z, auterantur in-
aequalia, illie quidem racio 2S, hic aucem ratio Z; re-
lidua erunt xqualia; nempe ucrobique racio 5, (mami 28) 4
35. 5acq; ccia 3) 2 25 =E, uEPatet. )Non isicur a quales Cune
rationes F X Z, quod ruleMcibomius. Icem, li ab xqua libus rari.
onibus =, E, auterantur (irem Meibomii sentu,) rationes 3
3: reliduum illie minus exit, hie majus (quippe 8) = (+2=
3 ac E
2(28 = 2E; UE PaTCT. ) ErgO, quae illic auterrur
ratios, major est quam quae hic autereurs: Non aurem mi-
nor, quod vule Meibomius. Ec quidem, nisi haec abunde (u-
cerene, addi pollene iltis alia intiniea quibus constaret, quam
absurde dictum AC, rationes Z, Z, itcm Z,2, _c. invicem
aequales; auc etiam rationem = majorem ese quam Z; &t qua
his Cimilia.
20. Cum itaque quxe advertus prov 8 e5 Fuclidis (aliaq; qua
ab hac dependenc) adducit Mcibomius, 2 P. 126. ad P. 136.
inclusive; huuic nicantur omnio, quod racio = major sic quam
ratio = (Hc enim iple ait D. 136. l. 3. Caererum omnis haec rali-
oeinario, qua Euclidei Theorematis fassicarem demonstramus, Paucis
verbis