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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
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in semnia hari schediorum
andem curra Conico est redusta
dationalem quadrraturam
avadraturarum promotio Im scheda (20 Maij. 169)
(1) Habetur C per alibi inventa
adeoque (3)
issarale,  hreg tiri-
c+ ec. = O. figt y = XX: a ee dy=
fi e fa. Znete a 2  bb S.  in E2g. 1. C  p 6-2 55
DOZ2 (aax S Xx+ bb. Quoe proinde quadratura etiam habetur.
4 et
a +bx. Ergo Falis
cae+ ee XY Quadratura habetur
Nrtus illud quaeritur an possit similiter haberi dmnmati qualis est
de  aciamus
Solys y2 Sagt bb: cgrtf C) sit y - 4Z fietdus d
 4 b  a  Euca3. GuZ. 5, st C = BC. s. 2i +  e bB. X . ff. du c. 14
potus sai sit fao se
ine y = Z, fiet 
it (do Ssuag
Batui so sit
et fiet 
+E San. q. s aX2 bb. XG
a biv i et S)2
= D fiol av = XX +X et fiet D a s. 1X +brida (Six t, nX 48
so da sncet re 
 1 siat daco =  xX r X tavEt P.
txx thmXLaKt
ixx+ ax suthexrante panto
quaxtapt u
eficiamus ut in 5q. 10 pariter et in aeq. 13 irrutionales som formulae sint eaeden
qvia igitur D et e sunt cognita, efficiamus, ut addendo, vel anferendo a se
fint y- ZC  dy
aetu (prius si hubet per cognitam multiplicando alteruorum)
scat (Xdx S:, ita ut res ad una tuntum quadraburae de inven
en ionem reducatur. Quae proinde erit inventa adeoque et altera. itaque
eopmis utdiu
Irrationalis
dubus ernt intentam 
armn aeq 6. eadem sit formula
vinculo  surditatis comprehensa nempe debent
am
Le
fit na af: r. et t( sm: nb = fmr: as = mr:a et pp = Hagg - nuW: a = rgg - Af mo: ar
rursus q= ah. Y et t= (hm: q- rm: att 2) mr: a et coincidunt 89. 10 et 14, quod felicitus
evenit, quanquam et si non evenisset redredium in promtu erat
et denique ss= aKk-aquW: a) KK = hvro, :r postremo
faciamqus r-a video autem licere ponere W02
0 et siet denique
aal
ita non assequinur destinatum nam aoferendo ita collendo fxdx s collemus
imo etsi relinquamque
et (de P contra intentum. Uno qualemcunque rebet
Y it determina lam, ut et 2,  tamen quia F. mi.a fiet 2L X + C = 2X + m
Itaque relinquamue Y indeterminatam ahuc et faciamus t Wo= O. itaque multi
plicemus  alterutram ex his 2X+m, et 2X X+ t per arbitrariam, ita, ut
deinde audendo ens nivicem seu 2XX + mx. per arbitrariam ut β, sa ut
additione decu facta possit destim X. et fiet: 2X + m + 2YBX + Bmr
verum ibi video infeliciter evenire, ut destruendo fiet B = -a: r, verum
ita destrnetur non lantum quod destruendum est sed et reliquam
 inclusige
ascicaenis tantum
omissis omnibus aequationibus inde a
Y -a, et fiet D+ Y - m Et dx bitoatn
iopX + 1X + 12
dxn sit s.
sit a X = 30 vy + 31 9 + 32, fiet
Aliter S. dx
S10xX + 11X 4
(3) ce
O-52.30y + 31
20X +2
20. 30yy +20. 3 y + 20. 34. 2
sit XZ yy. a fict C y ay
urse sopul tam
(1) qui
,fet posom
(i030 y 4 10. 2. 10 7 1 etc
0g rnayys tau2
seu 9e q S0t nayy quae proinde quadratura  datur
Zl3) 77: b fiet 5 e
( x+ 21Z+22. sit
 a latissime patent aequationes potuet, 2, 3 nam 
comprehendit sequentes. Sed est tamen ta adhuc genenlior expressio in usum
Htb dy Sy+. yruyeryt.7
nestrum: si ubia faciamqus 20 = 0 et, 21 = 1 habebitur
Hoc an verum teatemus. (dx SExX + 11X + 12 = C sit a X = 30yy + 39+32 et dx = ~ 3oy + 31 ay
per consequens: ( - [, dx. 2304 + 31 Y, 10. 36 p +2. 10. 311 et C. quae videtur compamtilis
viderturan et in eg. sequnda aeg. 6. sit x formula ipsius Z compambilsq enecali: ArX 1 dx Sux +51X + 52
60XX + SIX + 62
fiat +x gea. 2 41, _ fiet t = 41 n= S1: a4 Z fanimus W = 0 fiet 
q= 61: 9. 41 r = 60. a. 41 : 61.
ss = 62: aa. Hinc datur PX+b ax IDXX+ MX + nA
quaserigodatum et sil ex sds termet in
 sie ut sesx 
B
obs c
At artba:, c