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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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De Propressione Ceometricdo
C A l.33
Dollent omnes illae propoliciones ubi illam adhibet Fuclidess
quod itaque non incommode oro illa Duclidis detinicione lub
Ricui pocerie.
Elis pramonitis, Propolitiones ageredior: poltquam monven
ron quod, pro Maeniindinibus (de quibus Polis aeie Fuclides)
nos simplicicer Duantitares ubiqi substicuimus. Ouspre de quan-
cicacibus aliis non minus procedunerum proxoliciones cum de-
monstrationes quam de magnieudinibus.
 Si fuerint quotcunque quantitales, quorcunq quantitarum sieillatim
aque multiplae; quorupla est una unius, rotupla erunt es omnes omnium.
PACa B A =- Ma, B = MB,
C = M 3, _c. FrunEA + BF C.
_C. = (Ma F M B + M y _C.
M in a FB F g _c, uc mulci.
Plicando parebit. Idem igitur
a +B + 3
M a F MB + M y
est communis musciplicator M, quod erac probandum. Hic
idem demonstratur univertalicer pr. 12. deratione qualibet.
non minus quam mulciplici.
2. Siprima secundae aeque mulsipla fuerit, ex terria quariae, (A --M _
B = M B, ) sitqe quinia secundae aequemulripla ac semta quartae; (C =10-
D = NVB:) erunt item prima es quinta simul, secundae; atque terti a e
fexta simul, quarrae, ae que mulriplices. Nempe A L C = M a F Na,
=M F NI: in a. e B FD = -M BFNB = M + NV: in B COm-
munis icaque verobique malciplicacor, M + II. Idem ostendi
tur in quacunque racione, uruc non mulciplici. PrOD. 24.
3. Si fuerit prima secunda aequemultipla aique terria quartaeque
CA =M a B = M B,) e sumantur ae que multiplices primae es ter-
riae (NA, NB; hoc CANMa, NMB,) erunt e aeque multipli-
ces, illa secundae, alque haec quartae. Ouippe vrrobique est NM com-
munis mulciplicacor. EAque haec una Species argumentacionis
ex aequo, tive ex aequali, Si 10v.
4. Siprima ad secundam, eandem habearrationem, atque terria a
gnariam, (R . a: : B. B.) P andemirem rationem habebunt a que mul
siplices primae es terriae ad ae quemultiplices secundae e quariae, juxia
quamliber mulciplicarionem, respective sumplae. PuTa AM. at: :
B M. Bp. A, a:: B, B. hoc eA àB; erit, aequaticer 
erinq