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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 10v, page id 00068204:0020
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affoctae. Sod duo alii sunt modi quibus idom porficio. Eorum unus
affinis est computationibus quibuo colligobum approximationos, sub
finom altoriuo Epistola. et intolligi potest per hoc dcomplum,
Proponatur aequalio ad ardam HyporbolaeX + LX   X +  xt
+ L x5c. Et partibus ojus multiplicatis in sd omdrgdt, 22 = XX + ~
+ 1t 24 + X5 sc. 23 = X3 + Z X4 + X3 8c. 2 = ∞4 + 2 ∞5 c 25
= x5 vc. Jam dd 2 aufer = 22 et rostat 2 = 122 = X - = X3 -
X4 = 1b X5 vc. hinc addo =23 et fit 2- =22 +  23 = X +  24 +
3
60(H
2a
30X5vc Auforo  24 et rostat 2- 222 +  23 - 2 24 = X -  X q
24= f
S12d X = Z - = 22 +  2 = 29 24 +  23 cvc.
Eoddm modo sorios de una indofinita quantitato in aliam trans forri
possint. Rudmadmodum si positor radio circuli. X sinu rocto ar–
= 3Xs
:cus 2. et X L X3
6YY
qorc. longitudind arcuo iotius; atque hanc
ivoriom d sinu rocto ad Fungentom villom transforro: quaero longi–
tudinom Tangantis
2V2 + 325
X3
3X5
X
vrr-  rdduco in in finitam soriam X+
erque +vc: 2ua dicta 7. colligo pohostatos djus +3 = X3 +
 c. 25 = ∞5+ qc. Ruforo jam 2. dd Z, et rdstat 2-2 = - =
345 - gc addo + 23 2t fit Z = 2 +  23 =  X5 + _ Au foro = 25
et rostat - 2+ = 23 - = 45 = 0 quam proximo Zuaro dst Z = 4-
23+=25 -c. Sod siquis in usus Trigonomotricos md jussissot
detuboro deprossionom arcus per Tarigoritom, dam non hoc cir–
citu sod dirocta mothodo quaesivissem.
Per hoc gonuo computi colliguntur etiam sorids ve duabus vol
pluribus indofinitis quantitatibus constanto: et radicos affocta
rem aequationum magna de parto detrahuntur, sdd ad hunc
postoriorem usum adhibdo potiuo mothodum in altora opistola
doscriptam tanquam condraliorum.  (. Rogulis pro dlisiono su:
porfluorum torminorum habitis) paulo magis depoditam. Pro
regrossiors vdro ab arois ad lindas roctas  similibus possunt
hujusmodi Thdoromata adhibdri.
Theorem s. Sit 2 = ay + byy + cy3+ dy 4+ 5y54c, et vicis:
:sim drit yy = = - b22 + 268- ac 23 + 5abc - 563 = acd  4 +3 a C2 - 21 a bbc
a3
as
+buabd +1 4bg- cd2 5+ . Ex or proponatur aequatio ad arvum Hporbo
ag
y
= 2 pro b. = pro c, =  pro, d. ot  pro Ex vicissom deungot y = 2+
222+833+ 2 24 + vC. Theoreni 2. sit 2 = ay + byd + Cy5+ dy
+ Ey2+ c, ot vicissim drit y = = - 62 + 3b6- ac 75+ Babe - aad-
a4
ay
a10
1263 27 + 55b9-55 abbe+ 100abd + 5aac - a c 79 + vC Ex gr. proponatur
a 13.
y5
aequatio ad arcum circulii. Z = y + Apr + 375
stitutis in Rogula 1. pro a
oridhir y = 2 -=
25 6rr pro 
6rr  120r4
23
quy4 X 57
+ uc. Et sub.
112Y6
112r6 pro d. vc
5040rc. Altorum modum
Progrodiondi ab ardis ad Cindas roctas colaro statui.
Vbi dixi omnia pono problomata solutilia deistoro volui do
iis praesortim intolligi circa quae mathomatici sd huclonus oc:
cuparunt vel saltom in quibus ratiocinia mathomatica locum
aliquom obtinoro possunt, nam alia sand addo porxloeia
conditi.
si usue hic fuisset
priore therremate
pro diisser series