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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 9v, page id 00068197:0018
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Hbc = qu (b.5) ( aequat sit C =  b -c et de K = n ( (b-c), fiet
et ca mb. at  c: b = m
p
ate
4bt 4b  b -c (2  qu (b. c) =  qu (b. C) ut st acb ML9-
aa
104
2
 at  lebo - b (er p , at 1a)
et 4b m =aa ( C) = bt (b-C) seu Atalm -aab talit: prei - nub nub m
seu 4 ab + 4 ab pie L aaba (= aab m + a abM) = elib a + tb m - l8 0t. 
et exa dividendo per ba, fit 4a + +um = da L  . seu atrm = Boat nn)
2aa CF  = - 2p + pp fiet la = pp - 2aa ip et a + 2p = +  p)
seu m = +  + pp + 2aa - 2pp - rap, : 2p, = 4 (f.. 2 p p 4 2a -2ap: 9
nun
fiet  b: C = 2a + (41 - E) pp + raa (rap,: rpa = atm,: m
et K =  (b -c) = d ac - Wmb = 1db. = pp -raa, b
a m
pat
pp- 2aa, b vel PP- 2aa,b
-pp-2aa,
=3pp + 2aa
at
(2a) + (+1-2) pp 4 raa (2ap)
4bc = quC b.c), posito b manere
et csieri  2apb., (+1-2) pp 4 2aa, seu C = -
est 
 vel
= pp- 2aa
rap b
31+2aa
si p sit negativa eligendum prius,  tC diversi signi a b, sxeundum
priorem expressiionem gir p sit affirmativa, et c diversi signispotest
utraque inservire ex pressio.
sit e sit data = Y fiet H 1- 2) pp + raa
2ap
seu apr = (+1 -2) pp = 2aa, et pp - rpr + rr = rr + 2aa
(+1-2)
544 154
et pr sen pp - 2rr (+ B rt traa (+1 22) si sit
5
4
et p = 2r+ Y(rY + 2a a (+ 1- 2)): + 1 - 2
Hinc si Y: a fit  D. C sit
si
F12
alioqui in imaginarias incidimus. Hac mefhodo dum reditur
quaesitum adrationalia, etiam habetur determinatio
sed recta 4bb 4bc = bb - 2bc + cc seu bbo  - b. bc + cC =0
b+ bb = 2. 3c b + 9cc = 9cc - cc = 9c, fit  b: c = 212:1
Cum vero patio C est minor, quam 1 ad 212, res ex impossibilis.
reditr ad imaginrias et ((4bc qu (b. C)) est imaginaria
dixx + lx tam X + (XX + ab, XXtaC) = AViXX t abi) + V A(XEtaC)
fit A qu (Zax +lx tam)  (X + ab xtac)
2X 2LXx. .)  (XX tab, xta C) fir 1
hPXX F Ex tan Y CX + ab XX + 40) = ZtCxC +
e
Rh XXF. . = 2V
 sit Au (hxY....) + (XX + ab, extaC)
aqu Z (XxA ab) + WV (Xx +ac)
An sic 62 + 10D = 210 + 1D si 669∞ + 0D F 2621 0D = 22 O F DrS + 2  10D
fil qu =89 et Z= R 28 et v - a
mt
Uibi solum C et D) sunt datae
. et  18640 + 0D = m66o + ac 44
ac
mmY
 sunt _ C et  quaestae variantes,, M quaesita non varians. 8 et Q dant
quatuor quaesitas non vartantes, et m est quinta, de er quae adhibendae pro
qunque asqrationibus identificatoris
si esset et + si B + D essen simelices foret _ d = a et Z= _ m teil t dG +BD rmnaC + au 9y D
 et f ubi non  non habet locum successs, sed sidendum an non in retento t
posito B, tD
limas