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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 129v, page id 00068197:0258
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Rem nunc de in tegro resumemus
 orir ota o y
11 + 12 + 13 +4
21 + 22 + 234244y
31 +32 33 13y
Unde differenttati
H
Quadratrix quaesita
q. Naequ. 9, 00 X + 01X + o2X +03X+ X etc
y, 10X + LIX + C2X + 13X + 14X etc
9, 20X +2IX + 22X +23X + 24X et
17 30X +3IX + 32 X +33 X + 34X et
et
erC etc.
Ejus differentialis
Ho +LL. oi VAllosaX H IHe AaX et
L. n HII. praxt MF L IV. auX etc
 Ejus differentialis
NH, 60X 10LX +02X 10XX et
Naqu. 1. B, 10X + I IX +IX + 13X + 14X etC
Duy.V, 20X + 21X + 22X + 23X +2 X. etc.
1X P.V, 3OX +3IX +3IX + 33X + 3+X, etC
ese
er M
erit.
ett
l. II. III. _ sunt numeri ve
(0) (1) sunt doti
B. 1. sunt quaesiti 3 per
et differen tiale in compendiosissime exprimendo fiet vM + at aequ N.. seu vaequ 
do.y + di. y + dc. y et
 hunc Caleula
is veru haberta
0. y + 1. y + 2 y etc que coincidit cum aeq. 10.
s
stunoato jum o xgerallex halitur n possi absit 2 inbalitud adtus serul 1. que dum debentvincidere. Semper antem abest per ebrenm quod summatiax aoq
Loco Aequationis 7. assumatur alia inqua V assurgat altius quae ita scribetur
seu distincte Naq. V, CI. X 491X 46) 2N 4(0) 2X etc.
v, () OX +() 1X + Cy) 2X + (1) 3∞B et
et pro y substituendo valorem ex aeq. b. fiet:
V C) 6 6) 6)
(e) M  - (1). 11 ML + (2) L aequ. N. quae rursus coincidit cum aeq. 3
ut distincte explicetur, opere ipso perficiendum est
quod
sit jam aequatio data ad ordinatam V. et quidem simplex: (N aequ. V, (0) o X + B) 1X + C) CX + (I X etc
vel compendio Naequ (0) V + (1) V. substituendo valorem ipsius V. fiet: () M (1) Lq. N.
explicemus ergo aequ. 9nper aeq. 4) ut irdere appareat quomodo coincidat cum oqu. 4.
Aliter promredi
licet, tollendo
quia Y facul
Ergo coincidunt: + (1) F. 1 - (1) do (D 31. 2 - (1) d1 () II. 3- (1) d2
N d. (0) V + (9V + (2) V
+ 231 a X + II 32AX + H3 N + 1H3 ++ X et C
Compendio: Aequatio ad quadraticem erit Naequ oy +, Y + 2 Y +35 etc. concidit cum
ayido
= 1Dy. 1BIy 2tIVy: 3 etc seuto M
v, (1), oX +() 1 X + (1) 2X H) X etc
tollatur
Rationarile
nolixo
etc
e
+ I 21 a X + H 22 RX + IH23RA = 1V 4 fX
C
Aequatio differentialis N asqu fy do 4 ) der  d + )d3 etc sente L
(4
fer et loco ry. 9. fiet e + (0), + 4 2.1y.  + 1I. ~. y + I13. y. etc
Naeq.
+ y, + I. 01OX + LIg2XXF IlosAX + IIoTAX etc
y
quae aequatioq debet coincidere cum initio proposita 1 vel 3
Naq.) - (1)
sed quadra trix initio assumta
seu aeq. 3 erat:
altius assum
V N+Z 1 X + UI12 LX L MIBAX + W. +HX erc
V3
vero differentiallus Naq 
0)
1
seu compondio P.G  EG439+4G aequ. N.
Ejus diffecentialis
corne orxroixtog
nixatIl B3 KatB OX
+
+
 aequ. 3.