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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 66r, page id 00068201:0131
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schediasmadeR adiilus Cubdis Octitr. 674
e
a
ine
  Z11 q ++ Z1 p0
fict: Z (12)-. 2
Sunta ergo aequatione: Z + 2 pZ - aZ - 2 aY f0. Ponaimus scilicet ut numeros literis velus in eparenthesi
g12.
per2.
adscriptos, ut intelli garuu, aequivalere, et P 1 2, et a 1. et arp, a, quisiesset  (2) B  (d) aqZ (2) ar
Poronis 
nicties
X,  3129 Z + 49
a
Et divisis omnibus per a fier:
84
Aequatio puram hhabens potestatem
summam:
XZ f
po
3
sq.   rep pa por  dpeunt
a3
a
R A 8qu
2pZ H
- an Z 7.
- 2ar
24
X3
e
Sed antequam pergam, rectius, arbitor caleuli facilioris reddent causa, aliud
is f eligi exemplum tractabilius. Nimirum:
+1 27, 2  Z13⊓0 fiet . Z + +Z ∞ 2,  Z+37
1)
Ulnde um facemus. 23 46fZ + n ag Z + 6aeh p0.
ponendo fr6. A9B1. B 6, perinde ac si scriptum esset.
43Z + (6) fgN + (1) agZ + (6) arh 70, literas ergo modo un istas, f. Et emodo tnitati, 
18, ad aequationis totius comprobandam veritatem, modo, literis  numeris adscriptis ad examinandam
2ibo 
2
144 veritatem quantitaris cujus libet aequationem componentis modocuilibet alteri quantitati,
36 applicandis ad alia quoque exempla faciendae causa, aequivalere intelligemus. t
216 ponamus Z   X a- 6f.  ascribendo literam, l. numeris essentialibus, qui scilicet a
88 potestatum ipsamm natura et exponentibus oriuntur: erit X p, 3l 29Z t 1 9 dnet g  as
76
2
2
65
2
11a97
N.
+6aeh p
. a X (- 3a f X) idat x  216fd
Aequationis ergu (6)
huju otae possumus
54
2quo
+ 3a f s.
d
314 18
791
EL2 + 42
-
+ 4 0
 
vel dividendo omnia per minre -6 + 4 p.2
=ublis _ + 2Hs3 po tir X X +
3l 
..- + 1243.. -664(9
29
= +6ah,
X 3645 X s+ 26f
244 ola
+11 Aga.. a - 18 asg
J0
3la
3a
Huic aequationi jam similem per omnia et aequalem aliam ex ipsis radicibus excitemus, nimirum, ob aeq. 5. fint:
esse securi.
06
(+6~R
X +um X - 2n Xarmtan o. Unde: X + 1HX - qma  Xa Em+ In 10, undete 
unde den rursus X (+ Em X) - AMAX +8nin
188. Aeq (2)
el
-2n.
in.. -ane .. omn  p0. sive Aeq (7.)
2m..) +omn..
= 8 m
de ni Cs
X A gn
0 Conferendo Jam aequationem 7 mam et btam
+21 an
-s2
4
ramn qui-qn
fient aequationes collatitiae duae, et quidem ex cillations terminorum penultimiui, fier: (8)  H  T3sp L 1ag
fiet dmn m
20
en -smd
min -ema
acu il neso. sEasg rbaesius ara. t quibus valaibus collatis
earex  nague, et facet multus
a nixs 1mne s  gmen- Bmn voculimus  a B et  lF etc. vocabim
et 36F + Hag, vocabimus = il  a C et amnam aui demque appellabimus  4 a et fier:
d2
(11) 2 L aDO ac proinde 44 4l d6 quam valorem aequationi 8 inserendo, fiet.  
(5al a 18
2
a A
Y 2
44  +564la8
aO
uo ero ealeo n dea r. e.  utu piue
f + (13
20istae H- 4la 8
Ja
49
+qu
intervenientis fier quae nec
us p
3la 4p2 (d
3 Fmoerqde9 SeyB
ila f, dp
icrq d
an L rans
er
1 B
+6 H p  13
11 46
d
(26s
0.
+ 4412
a
11.
66atd
6ah
Rr6 0
iqu
(214+ qu