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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 11
# Folio 81r, page id 00068164:0161
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LLC: ()  A. (A) si BC (B) et CL H
LL )X CBI (BY
C( L2 : L3:: A2: A3 si B2 = B3
AA)) = (B)
L4: L5:: B4:B5 Si Aa=A5
Ergo L6: L7:: A6. B6: A7. B7. sit enim hoc falsum Ergo sumendo
AC: B A6. aeg = A7 (alsum etiam erit L6: LZ:: B6: B1. rontin hypo
sed hac non geludit, nisi u casu quo supponatur si semer cucyor sit ratio
et fit L. L7 semper major quam quaerendus modus  et conditio hoc
demonstrandi generatiter
d  ovemie d oplis
si curva sit rationalis integra, et elementam curor etiam latronile
integrum, tnum momentum erit ravate integium; tales curvas
quarm
XC  C Y = X et dy = e x dx. Ergo
fiet dx + ly =, de e. x   C X +)
Y = X + X  X M
ax + du = d5.
+
dy = C X  hX (m X ) et fier
+2hm Xh+m - 2)
L 2eh X  A2em XP +m -2
eth.r
2k. 25
+ th X
2m
(+ nomi X
fiat 1+2 eh X exhar = =  2eh X
seu 4eh XCth - 2 = - 1 debet esse Xet hor = 1 (9.  C+ h. 2 =0
seu e +h = 2 et 4 e h = - 1. Ergo sit C + h + 2et = 4 et = 4 +1
seu C - t = +15. Ergo e = 1 +  s5 et h = 1 - 15 et siet
(112 15) +
L15)
62 15)
et dy = 1F  X E.  + 1-  s5
et  Sdx atu =  S5X S + L s5 - 1 XCL s dato, ergo cirvo
X
Is +1 XC+ L5)
15+1
vertice
+ x. 15 - 1 X (1 L: 15)
7(+ S
 summabile, quia est Q 
et momentum ex axe est
(+ L55 - 1 X. + 215 +1. X) + L 15 - 1X
- 15)
x 15
rendeu videnum an eadem methodo an plures literas assumendo
X
tk -C
incidatur tande rationales, ut si ponatur 1 +. 2 eh X
- = - 2 Ct NC +h - 1 - 2 era Z. C + m - 21
etm - 2
+2emX + 2hm XEam- 2
2hm Xhem. veum
ub bi ebe ei. sed sic habentur quatuor aequades cum sint lantas tres titerae
inteum suffererit nos curvam habere  cujus dentur momenta et dimensio, sed
. as
Hanc curvam vere
quae nisi suppositis logarihmis describi non possit.
cun Mentono appelles Geometrice iphaavalem. Sid transcendente, ad huc sunt magis
seque eum isto est trauscendens. Omres transcendentes sunt Geometri ce irraoates
o contra firita esset quadratura circuli si esset rectacta ad Gpometrice
irrationales non trausceidentes
c possint alio rabates non intercae
sumi, quae sempe etiam analusticesputtractabiles, quam scilicet
mmnerator sit quadratur aut cubus smpli compositibes scilicet ex terminus
quorum numeratores sint quadrat, ved cubi erc nunrorum simplicium
ozbi gralia X + a X+ b erc., vg. y - X 1X + a FX+C erc
X+b
X +5
ubi lantu cavendum ne h vel n sit unitas. Et pulo ope horum solorum erminoum
infinitas haberi posse curvas ravales
P+h -2
quae quadrabiles quam areae quadrabiles
et ipsae curro mersurabiles, pariters et curvae momenta, Haream momcnta