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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 30v, page id 00068194:0060
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9+2, ht6.
5912 +bsit
54g136ast
In: (sppo.
3et, 4
sit aequatio X + p X + qX + YX _ s. cujus aequa
 valor ipsius X per seriem infinitam inveniri potest sive per
curvam, X + p X + qX + YX  y. ponendo. Sesse unam ex,
ipsis y. vel per curvam X +pX + qX afZ X H Z
ponendo
esse sunam ex ipsis Z. et r unam ex ipsis fZ.
videndum postea iisdem nihilominus manetitibus numeris, ef
substituendo Y et s. in locum assumtarum idem prodeat valor
sit   X M. in B . = y + y- 5- y erc
sit rursus Xp1_
p3
2 2+ Z Z1 ouc. sed quia p
+
96
8
11y
1
fe
sed qui vel y H - 2 + 2 - 2 + Z p - 7+ Z- 2 + csc
2
ed quia a 1tyB Z 2. ert y. 7pa (  yp  - Y B - 1+ p+ Z
et y B 1 - 2Z- 223 + Z +2 + 2
ee
B3 -+ +22 46 2+3  38- 19 37 + 33+ 32 1- 37 -67 - 2 + 71371 07 12
( fiet X9, 1-y+y - y et per + 2Z5 +. Z- 27
-1 12Z -Z2+ 133 -224 4, 5 - 26+ 321
+1 - 3
3Z1322-67
Videndum an si pergamus necessie sit omnia evanescere, seu
quod demonstrari poterit, ostendendo quae am pro cgressio numerorum am
quolibet termino, et quae sit eorum summa
Imo d fieri necesse
est alioquin entrabendo. Odetur aequatio non identica. Determina
ipsam 2.
qu sit  XB L - 1, t-
seu
fict alia Xp, (D...... .. per curvam algetraicam
itau ut  duarum curvarum intersectione determinari intelligatur
quaerendum jam au possibile sit latem fingi ut fenitis quibusdum detracti
D, ut D r D exhibeat aequationem in qua vel
omnes termini destruuntur praeter paucos vel tota aequatio
dividi possit per finitam, quanquam si destiui possint reliqua
etiam omnia dividi possint per finitam Sumamus ergo
equationem generalem ad curvam analyticam atibualem
seu generalem radicem, (posito saltem X esse quantitatem
aequationis
Nationa radicem aequationis cujus Cunque, cuius altimus
terminus est F. quod si hoc modo res non procedit nunquam procedet
namposito aequationem esse: X+ px + qX p, pone
3.b2+ cBZT Imo video jam
arcum alium esse
potius generali opus sit aequatio ne + bZ +cDZ+ 6. posito
Tarcus et ob tangente: vedendum an possit analytice
inveniri alius arcus, qui sit ad suam tangentem secundum
hanc relationem.  N +p X + qX F. vel quamvis
arcum
eibe gratia dimidiat
quaerendo canm portionem etqus, et ad hua aliam, et rursus
aliam, easque per datas multiplicatas invicem addendo