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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 31r, page id 00068201:0061
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entamentum duas crrationales
si sed deprehensum est naturam obstared ucendi ad uemetu
M X+b, XtC + B VX+C,X+ d = y
siit inm, X+b. XFC + 2mn X +C Vx+ b. X+dC
nn. X+6. X+C
p. X+ C + 91 x+ b. X+d= Wd
fit + pp X+C
+99 Xtb. x +d
pg mn
sit cdc0  ~ yy. peret O
p9 = mn seu q= mn: p
Mm XX + nm b X + mmbe
un Xx + nnox +un de
C
pP XX + 2pp CX + ppCC
mnan XX + mmnn, b2X + mmunbo
pp
Ha
pp 5d)
pp
ram = mmppmmnn+d) =, 2pC 0O = napp(d + C)
sit nm= 2pC -npP Cd + C), :, pp(b. + C) - nn (b+ d)
m  P = nnpp,: pp = na = pp. nisi pp nn
2
ubi reset
Mm = DCC= nappdE :, ppbc = un bd sed nonnecesse
aquando valores 2 et 2, iter 3 et 2 habetur
nn- p, bis, nam ex 1 e 2 fiel
2Cp 2C = nn (d+ C), : fb+c - na b+d) = 1 -nn : 1 - nn = 1
P
PP
et
pH
Ergo (DC nnd) = nac = b (+9 - na b (= un d). Ergo
 pP
nn c- b = 1 seu nn = pp
pp
c- b
Ex 3 et 2 fit eode modo cc = un dC = bc - nn bd. seu
cc-bc, Dc. nn  cc-dc = C nisi cum
Pp
ubi res etia
voc-db 0, sed tamen
sed quia u necessaro fit 1. ideo vel C = 1 seu C = d) non necessaria
succediti
vel C = b utroque modo alterntra irrationalum una
perit. Itaque propositum consequi non licet
d