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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 46v, page id 00068197:0092
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It calculo generali fiat compendium specialis ponantur duae aequationesi
ad duas literas X et y, verb. gr. 1Lret  14 LX+ 19 Y + 15e xy+ quiy He=
et 24gY Y 29yy + 25py + 2g aX + 2 Bay +249aa 20 Explicetur y per X, faciendo
XXy13e a fient duae aequationes secundum X, quae debent esse coincidentes
vel _a= fi seu habere radicem communem. quae celtirebipe; si  Hae binae aequatiopes com
posit f = -63. 3a pendro expressae sunto (XX + amX + aan= o et exx + agx + aar v. Fiat
1 = m = R. E linabu Unde nascentur binae Aequationes
vilut li p = m: q et n: r = m: q, vel quo alio modo commodissime licebit
per quas determinabuntur ltere F et g. Quod si forte tollantur
 etoet
ambae, orietur relatio inter coefficientes 120, 102, etc.  220, 202, et
quod culaulus docebit. Id ub: generaliter praestiterimus utiliter adhibe-
bitur ad specialem casum, quem dat finis calculi  paginae
praecedentis. Generalis panon poterit etiam servire ad alios casus
et revera s solutio generalis hrarum trium aequatio, 1, et 2, 3
anon
Et atillter loco fet s, od hibebuntur 3, 303, 3Cd. Ita enim perpetuo
inter calculandum observari possunt
A Ita enim possunt
CA  observari permutationes ipsorum 1. et 2.
et permutationes ipsorum 2 et 3, sub quibus comprehenduntur
4 id est squadr. 2) et 19 id est quadr. 3,  At.5, id est A. (+ 3)
eol le a modes aequationetiam q et
dutu seu ex et o permutatis cebent mane
Ergo Calculus ise generalis est ergo pro eo casu, quo bres aequationes
modo
rent ses corum
quales 1, 2, 3.  reducuntur in effectu ad duas, ob coinci
dentiam radicum.
Ut caleuli (anonem is eni commedius inventumus, primum
aeqq. t et 2, reducamus secundum X quasi essent.
54XX F 59y. S2XX + 51aX + sCq et 6Z X X 16I aX + 60 aa - 0
ita eret E g9 et ponendo sepro 19, et Sr pro pro 159+ 12a, et
50aa pro 147y + 1ay + 10 aa.
Compendio ponendo 52 = i9 et 51a = 15G+ p a et se a a = 19y+ nay +1oaa
62 = 29 6ta - 25yt na e 60 aa- 24 gy +2 yt 20aa
ita ex equ tallendo X, fit aequatio per canonem dim generalem
4c
olim jam a me inventum 1(): 1 b = quadr. 150. 
=51. 60) L52. 60
Ubi explicandum 50, si, 52, et 60, 61, 62, habebitur aequatio secundum 
primum ergo in aequ. 1 et 2 tollatur H pr ponendo _=
Habebuntur binae aequationes se secundi gradus secundum ,Y
et 5
+8
rempe
et g- βc. 39) d