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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 15v, page id 00068072:0030
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Repeto novissiuu.
H ia = ∞ do: deo
X: a = dz: deo dy: dx = ddv: dd. sit ja
dy: dx = XX F yy, :aa fiet ddv: ddz = (dZd Z: deodeo) + (vd videot
seu ddv: ddzue = dZ d2 + dvdv 3: deo deo. sit avaso = Ardo
sit dadco = dzdz dav: ddz. quod est in potestate nempe
ab haec quantitas sit constans. Ergo resumamus sit
e
dv. d ZVddv: ddZ) et X: a = dZ: 
sdavidaz
mox valabut quod vetet)
ponendo dZ Rddx: ddzue) esse constantem, quis enim vetet
a
2
 a
fiet dy:dx = adv: ddZ. Jam habuimtus dyidx=Xt:aa
: dzdz (ddo: a
4
fiet dav: daz = dv dv F dZ d2
seu ddvddv: dd Z ddZ = dodv F dZdZ,: dZ d7
(dodo +1) et fint add
fitddv. dZ =
azar
dz
d(dv: dz
s(avdv + 1)
lae
Nam si sit dEx regula quod si detur de
a du d
ad
dis = ae nat u Qid
CB a (0:
au
dZ
 vel v: V)
sit ad. =. 
: 3 rel (20: 18) - (W: ) ntdo antum hic
pro 2 pone de, et pro W, pono Av. Datur ergo log. dz ex doid
intervenientibus quadraturis. Ergo datur elatio etiam inter
X et y. Neque enim vero opus inveniri v et Z. neque enim assumq
simus nisi do et do. sed ob rei magnitudinem vix andeo adhibere
ta et diex ddqe
sidem alu sit doid
sit H + aa2) H +  t+ et fiat st +aa)-
Digd= (a a 8() 40. 28D. Ergo fiet
ua logi=99F aa d8:3) seu alogs(P: 1p)= loq- a: ): 2
aa88, :28F et 
seu ta logi 24l0g B. e 2a log = log  ap: 294 sey
aa: 2cc7 log +2log. 1
seu aa: 2 = log. EB + log.
s
lon jam log2 lagdz et
du: d2 ( seu t: a (per 15.15) = aa58: 2a
yytxx ydixe jam per 2 est
X: a 5 Sidaz: ddv) porro duo afdvicZ (adZ: d2) (dB A15)- qu: d2
v.x. Ergo per 14 est 
ergo per _7 et 25. fiet XX: aa = (26) 99+ XX, : XX, quod lubsurdum
(27
X
unde jam in ag.7. praevideri poterat, rem. non prochi
Aaliter: y. a = dv. d ) dv: (aZ Z. V) sab. Ep. = d2
A2. L
dy: dx = ddv: ddZ  et quia dZ (Z. V) constans
sy.D
v) ddz +  (VcdZ Zddv: VD) et quia dqe selze il
site = doid
sit (
qa sed quia
et sadque
s nd  :Z + ddz (du.Z 0 et quia
az Tad: dz est constans fiet daqu + daz (ddz.
e
istans quod non licet. sed si v.a duid, sadodat
constansn fi
a
e
consaas
 sed idem
20
az: de Idd o: dz et d2 adx B a7 sans fis ap+ Raqs
a= dc: de. x. = sad B: d
e dcodz dodo
a aoavidoao  axiaeie fis tpte d
L
vitur
anti