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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 41r, page id 00068051:0081
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 erdx tagdus = xydx seu redigendo ad  rationes sive
numeros, e ly: AX = X: a = X: yX: a et quia X: g = X. a: y. a fint eg. du =  a - XX. a a. a. 
siet X: a Z coiZ et  g. d Sdz:p. fiet E est aq 2 fiet et dy: a = dz: p et dx: a E Zelo - 0 dz : 23
Ergo ex 2 fiet 22dX:, pZdc0 - pco dzue = co. Z - coco: 22: sAz. p Sed sic locere tollere duo
divellendo nam oportetet facere co: Z- cdeo. 2: A: p = 0 seu X: a - X: a: y. a quod
abscndum foret. Ergo loco aeg. 4 sit g: a=  + saz: p + Z. c0. fietque
4)
dy: a = dz: p + Zdcd- codz, :coco et ax: a = Zdco- codz: Z2, et P 3, 4, 5, 6 fier exe
dZ dque coco + P Zdeo = p codZ,: pcoco y: Zdeo = Codz.. Z
= co: Z = coco: 3Z: SaZ. p + Z. 10
fiet ZE debet poni AZ lcd): coco _ = Z (deo) co: Z - coco . 22: SZ. p + Z: co = 0
seu Z c soz: p FZ = Wd Z Z co sazip + Z - c0co Lb
(2) aco sZ: p + aZ:c0
XXdx, + aydy = Xydx siat X = aco: Z et y = a faz p + aZc0. fiet
(1
dx = a Zdco = aco dZe, : Z2 dy = adz: p + a o dZ - a Zdco, : coco, = a cocod q acopdz- ax polo
 XX dxd = B aa coc Zdco = aa coc ac0 dZ; Z
Xy = aacoco sdz: p + a4ZC0,: coZ
+ aydy - aco sZ: p aco codque t a ed saripacopdZ- a co sazip az plco + a Z acocodz + a z a co psz- a za zpdeo; c0 p
=X ydx P = (a acoc Saz.p a7dio + aa coco sa p aco dque  aa Z0 a z dco  a a 20 aco dZ,: c073
Hanc aeq.5 seu explicatam 1. divellamus in duas evan escentee differentiales et fiet (con)
coopus
12
opaaocoazaco - Z aco SAZ:p aZ Pde
cocop2
aea cattao Chopacoeoun spaz pates - Z a za2 pdeo paaoco suq. paraeo 
seu 1o4-  co 2 B a s: p - 7 des = c0 Z sai p ao = co Z H =  et habetur co: qe per sicip
ergo habetitur X per y. quod absurdum. Non ergo licet sic divellere, si liceret
solutum esset problema, nam tollendo co, et differentiando aeq. sine ed, haberetur relatio
inter ZA2, P dp. verim cvanescentia psius p. oia tuibat.
An sis:
X = co: p et es y a = (dZ: p et fiet da = pdco -codp: pp
etAG= de: P et dy. dx =  dZ P: pec- codp. Hi valores substituantur  aequ. formatas ex kia, yta loit
lite fiat divulsio,  et in una aeq   absit dae, in altera absit dexelt ds
adsitque L ap in altera B) adsit deo, ap, de in aeq. 6 erit co, p, deo, dp. adeoque datur
relitio inter co et p, sed in aeg. 7 erit co, p, des, dp, dZ Sdz: p. ubi tollendo saz.p
per differentiationem, f habe bitur  Wo, p, deo, Ap, daco, ddp, d2 atque. est ex org. 8
diferentianda dabitur idens co), , deo, ap, ddco, ddp, quarum ope tollendo C0, et P,
fiet aequ: Ope 6, 8, 9 tollatur co, et p, restabit aequatio; in qua erunt
 deo, dp ddp, ddeo, dZ, ddZ
Faciamus ddzue  0, et et tollendo x eum sins
effectionibus per B aque ope aeq. 6, habebitur postremo dque per solas de, dap, a adeoque
seu pos de pocendo a
()
Excmplum sit
X: a = co : p y: a = sdZ. p fiet dx = pdeo - codp,  pp et dy = dz: p et
CMa.
dy: dx = dzp:, pdco-codp   dy: dx = x  9 :ya ergo fiet
+Cd p: PP,
dZp: pdco -codp = (aa) coc: pp (: saz. p aa et veducta aequatione fit
dZ ps = jodat dq p saZ. p = (x coco deo = p co deo - co p- ( pdco)
feit  co dp - p co dco 2 0 ergo dze p sdz: p = - 2c0 ap
et differentando bt saZ. p = 208 dp: p dq eti B. p L -p d2 2c0 da p + co sptes + 20 p p ta (t pli 1
ubi in 5g. 12. fial ddZ =0 ex 5q. 9. different rendo, fiet. P
(d ddp + 3co deo dp - p co dda - p ded - co deo 2pdp 0 ope 9 12, 14 inveniatur eg.
in qua absint  p et co, habetitur aq. ystans (15) constans ex deo, dp, ddeo, dd p, d Z
jam e ope aq.)4 tollatur vis uffectio c0, per p. quia ex aeque. ∞ datur co ex p
per quadraturns ergo et  deo, et ddco, per dp, et dep; fiet habebitur dq per
dp, dap, d et a adeoque res erit reducta ad quadraturas Quod
accuratius e exerminandum firet eum magni momenti. Ver t
Nam  pro de ponas dZN: a et  adeo pro dap, dz drr: a
 habelitur aeq. in qua extabit dZ II, I, a
adeoque dabitur Z per X, ergo et dp per Z
sed dubito an post subtatas eo, et p, tolli ad huc possit
deoris eo, qua parto deo et ddeo, quin rarsus cedeat p.
So Hinc video non fuisse opus liz eo. sit
ex dy. fat y =4
aqu. (1 nc
sdZ: X et tub ex 1 et 2 sublati s fia
aey. 2.  unde tollendo fdz: X, hebe.
bitur aeq. 4, in qua X, 1Z, 3dque, a
lui an