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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 32
# Folio 4r, page id 00068245:0007
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da
b+dX b
Nequa autem dubitatio restet ca - E o a ita probor probo:
Eb
DE a - c a.   ca. est auteum hoc loco tignum
multiplicationis
Pars - a s. def. 3.) a = Minus def: 3. )
quater
Duarto aequimultiplicia esseat simpla, vg. ut sunt trca ad A. itabistria adbis
quater. Cg = e Nam ca e  e
a
C
Ouinto si proportionalibus addantur demanturue proportionalia producta esse
proportionalia, Ut, cum ita sint 4 ad s. ut 3. ad 6. eliam 4 +3 seu 7
ad P+6. seu it eodem modo erit seusi  Ergo = arc
autem praedemonetro hoc lemma . bc = ad. Nam quia a
utrumque per d. erit ad-
H consequentia patet: (
jam pergo si a+c Y a
eudit
6+d   = 1 erit a+C a H S
Cergornultiplicando
a +6
antecedens probo b+dX batb
  (quiaha jam bc = a d per lemma praemissum. Ergo ba 4bc batbc
a +
cb
ab + ad ab +bc U
Dab t ad
ca-avi Intelligitur ex ultimo isto exemplo, propositionem hara quintam inter
b+ d
atc. D
Axiomata positam non facilioris esse de mon strationis quam alias nonnullas.
b+o a qua theorematis accensentur. Crempli causa: tleorema est, si duae rationes sint
atc t.
b+d 2 a
aequales, etiem carum inversas esse aequales; id ita demonstratur facillime
a
= ajo  - Namsi a X = - 1. erit 6 -d: Andecedens probob
d
6c
da
=bc - 1. Nam per temma dictum da - bc. Atque ista quidem sufficere
arbitror in exemplum observationis parum creditae, necessariae tamen. ad
stabiliendam contra Pyrrhonios, scientiarum severitatem
a+8 b
+o