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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 32
# Folio 6v, page id 00068245:0012
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Egoat. Ante omnia autem praedemonstro hoc lemma: bc = ad. Nam quia a-  ergo mu-
Aiplicando utrumque per d. erit ad = E Ergo multiplicando utrumque per b fiet ad - bc. Jam pergo
+ 3.X 2 = 1 erit ac a danteredes pibo. att
si a +c
en mo btd
dba +bc - ba + bc = 1
ab + ad
ab + bc.
X4 = 6a + bc Jam bc = ad per
ab + ad.
Intelligtur exultimo isto exemplo, propositionem hanc quintam inter Axiomata positam
aciliori
mondficiioris esse demonstrationis quam alias nonnullas, quae teorematis accensentur; exempli causa:
theorema est, si duae rationes sint aequales, etiam earum inversas esse aequales, ia ita demon
stratur facillime 4- E ajo b = D. Nam si ba  X2 = 1. erit = 3. Anteredens
probob  = bc = bC = 1. Num per temmadictum da = bc.
da
arbitior in exemplum.
Atque ista quadm sifficere