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# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folio 51r, page id 00069349:0101
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Demonstratio pure Analytica
Quod in multiplicatione in  faciat +
sit quantitas X. = b.
multiplicanda in aliam X - C
fi ajo multiplicationem fieri hoc modo:
Manifesta autem est parssum multiplicationis
3
X = b X = cX. quaeritur solum ade
X b
b
an admitti possit - b in -c dare + bc. quod sic ostendo
Lonatur X a esse aequale ipsi b. patet fore X = b
eaderu
fortuma
aequ. nihilo. ac pocide idem autem prodibit multiplicando
X - b per X- c. Sive X sit aequate ipsi b sive non, qu
tantum e inter quia inter un cum literis generatiter calculumus
valores quoslibet literarum comprehendimus, semper ergo
eodem mudo prodibit X. b+ A +bC, quia
etsi
primum ponatur X aequ. b. se rel qec. ergo
etiam erit X + C aequa b+C. Ergo X + XC aequ. b X + CX
multiplicatis scilicet omniper omnibus per X.. Et po XC poncudo bc
(quia X aequ. b) fiet X + bc equ. bX + CX
fiet: X = b X + bc aequ. 0.
= C X
X = b per X - c. prollibit
X - b X + O. aequ.0
c X
+X
si v
jam si multiplicetur
+ X = b
+ X L C
 Cx +C
= b X
Nam si id quod nihilo aequale est mulliplices in  id quod etinmm
ni hoc loco X Ca) multiplices per quidvis productum etiam
L).
nihilo aequale erit. Hinc conferendo has duas aequationes invicem
necessario fit bc aequ.. adeoque - b in -c dedit O seu, bc
quod autem processit posito x aequ. b. ut procedet etiam
+
bc
B.