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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 324, page id 826603459:0370
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B +
Elemensi quinti P uclidis declaratio.
EC AP. 35
B 3 ideogi A + a. a:: BFB. B. vel AC; SI A à, erie
(X + T = ∞ 4 E, hoc eAt
A + 2 = a f 2, AVC
4 R
A
C + 2A
A
 F 
a. Imo vero, e
7 + 2 a
a. Et quidem uni-
vertim. Si siE R a, exie etiam A L. M = a L M, Eive
P  N A
2  Mae
a Ouomodocum haec, cum praecedens
junctim ee unirersalicer demonRraneur. Sed ee per L. emmano-
Arum, haec junctim cum praecedence. sic demonstratur; Si
A ea. a:: B + B. B; eriE (AB  aB = a B  a B, _ AB
=aB, ideoque) A. a:: B. B.
Detinicur hic argumentandi modus, praelence propositione
demonstracus, ab Fuclide 24d5. Compossiio rarionis Coui
idcors aby s) est sumprio ontecedentis cum consequente ranquam unius, au
ipsam consequentem.
Acg: hic eriam Clavius duas alias Rationis compositiones ad
junsic. Primum appelIaE Compositionis rarionem conversam; quan-
de sumitur antecedens es consequens veluti una, quae cum onrecedente con-
feratur. PuTa E A. a :: B. B. erit AFa. A:: B + B. B. DAX
duas involrit Fuclidis operaciones. Nam invercendo, erie
_. A:: B. B. _ componendo a F A. A:: BF B. B. vel A+ a.
a:: B+ B. B. Vel BC; AA. a :: B. B. erit (AB = aB, et,
AB + aB = aB + a B, hoc CHt, A + a in B = a in B F B, adc093)
A F ∞. a:: B + B- B.
AIEeTAM VOCaE. Compositionem rationis contrariam; quando refer-
tur eadem antecedens ad antecedentem es consequenem ceu ad unam. Pu
ca (I A. a: : B. B. exic A. A + a:: B. B + B. EAGUCHRC PTR.
cedencis inverto; e cres Puclidis operationes conjungie. Nam
invertenido erie a. A:: B. B. _ componendo A F a. A:: B
B. B. icerumq inverrendo A. A + a :sB. B. F B. Vel etiam per L em
ma noctrum; Si A. a:: B. B. CrIE (AB = a. B, 2d eoque AB L
AB = ABF aB, hOC cA. A in B F B = A + a in B, idcogue)
Ad. l ta:: B. B F B.
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