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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 186r, page id 00068199:0371
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  suX dx VCM +HXX:, p+ EXX = Cd pendet ex Conicis
quadraturis posito e esse numerum vatu deve gam rationatem
integrum quemcunque, nam si posito XX = Y et XdX = dy : 2
et  g ay fiet Cd = (in Ly dy S, MtMA:, pagy, quae
patet ex quadratura ex Conicis quadraturis habetur.
Imo generalius si sit
( = ( XdX. XX V, M + RXK,.3
AXX
posite sid
M
 ed per Conicam quadraturam
ficare relationem rationalem habetur quae
sit 10rab + 1 Sac + 12 Bb = X. fiet XX = 210. 11 a. HC P. 10. 1b Vac
2. 1. 12 CY ab + 10. 10 aD + 11. 11. ac + 12. 12 bc. debet ja m + nXX A
equari quadrato a 20+ ab + 21 ac + 22 V bc, quod est
similiter p+ gXK = quad. a 30 Vab On +31VACF,
3
ergo fiet
Lr) ab en pN. n1O. 11 = _. 20. 21 n 10. 12 = (4. 20. 2 n. 11. 12 = 4. 21. 2E
2. 20. 21 a 1bc + et
9. 10. 11 = 1. 30, 31 9. 10. 12 = 4.30. 32 441 12 . 31. 32
1300
t ni2oo C pes sed superest
q
e, 30+n. 10 ab + n H ac + n12. 12BC + M= O
 a 22,22
a 2020.. = 21, 2)
et +a 10. 10 ab + 9. 112 ac + 9. 12. bc  p-
0
O
quae duae ultimae aequaves ut resolventur pro a, b, c, ponenda
30.30.. = 31. 31  = 32. 32.
40X + 41 GOX +51 60X +6) et ex duabus ultimis aeqq. t fiunt sex
a
ut tollantur XX, L, et X; ad quae
se eet nempe ex qualibet
afficientes esse artitrarius manifestum est
X