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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 3
# Folio 7r, page id 00068205:0013
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Yq  a s 2) c eq 902  egao
dratiopalitate solu ed sic ut et equa sita tantum l’ascendat ad
l
y nm
y l-mm
1
fiet 2l = (nntgqp t 2m = (nn = 49) P era  S
Z= (Pp. 4) quennt qu) y = (pp: 4) qu (nn -94) urg Ly. 2) = npq
l
gainmLa  pp) quCan 4)a
C(B(antqq) (p. 2) = a (np9) = C (pn -49) p. 2)   = y  R - a) = yl y- a)
seu Cgqp - anpq = yY 2 a) - y sy- a) et quadrando utrobique fiet
ccqpp = 2459 np + aannpp4q DyyZ- a) + yy (y- a) = 29y 1(Zy - a Z + a4)
seu ccapp- racqup taannerqu--rgy Hy a r aa
a
=9y (9tZ- 24)
CPp - 4 C qnp + 2 aannp cc
pu.
29 ep gy (9+ Z. 2a) CC
4g
+4aa quinppec -qcerepoc
49244
se
 ae
=2yy 1 (2y -a (y) 4
4 4 aqnpysy (yt Z2a)c
qayetayaa
Et divisis omnibus per 49 fit
4C- 4anpqC + rannpu c ce
+2aanst.
=29pgy qu er. 19) ..
qaup a
ponatur y =Z seu g = 0. fiet  yy= quanup (1 at y+ Z. 2a =
seu y = a
sed hoc non lice
anp= l+m= 2t 25y sed y = Il son et  gy = (4 sed 1= niper
et H= npp. 4 et (- n p: 1b et sat pro gu = +aannpp (y a) fiet
N P: 16 4aannppn pp. 4 4npp
a
seu nupp +64a= 16aa n pp et determinatur relatio nter p
inter p et n, quae alia via determinata fuisset si Y et Z vel
l et tum fuissent quantitates diversae sed y= n pp: 4, ergo
habentur tam r quam p. per datam y. quae quodsi _ et Z
non fuissent eaedem sed diversae, seu q non = e, habuissemus
a P, et n ope aequ m nap, et l- m = pA9. ubi
I et n habentur per y et Z, quia 1 sq et m sy
itaque et cum Y- Z20 siu cumsmu p dita polygotilum definit incurvam tunc omnia
l
quadhatura evanescunt quia cum evanescentes
tiam evanescit C. summa qu terminorum progressionis Geometricae
sed auxilia simalidum
differenta ordinaturum maximarum sumalidum
videndum tamen an non hac methodo saltem utiles appropinqu
tiores obtineri possint, cum 4f y-Z est quantitas assignabis
quidem, sed valde parva. 
Haec ad Methodum quadraturarum dui de sch. ame descriptam ex
ippus Antographo ab ipso communicatae dresdae 22 decembir. 1704
ubi simul patet in hoc casu evanescere  auxilia quibus perveniri posset a
valorem ipsias C
atur
+
a upu
=Zaannppqqyy 1913
41.u  g
+ Sest
A+
oe
49
Axtust
C +anp q
raahapp
+ 1s re f.94
gapurus (yr)