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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 175v, page id 00068199:0350
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quotres xX: aa, vel x3: a, etc. rationaliter sine p haberi
potest, emper poni Notest = vab is vator multi plicatus per dx
vel dy si placet, aequalis constanti, et torluntur simul X et a
sed si reperire oporteat, proveniat XX. X - (dg , 1) an
aa
tunc quoque licebit id multiplicare per dx, et ponere =0 constantiz
nec video quid sohibeat. Si tamen liceret, possemus praeparare
et
valorem. Exgr dy = dx Saa + bx + xx
.possumus saltem
invenire valor teminum in que absit xeta, seu qui
sit
occ + ex + Xx
x; 1) quem ponemus aequalem constanti, et procedemus
ut aute.
aydy: apdx dy.  X = aa + BXX, : , aa + CXX. Addatur utrobique - b.c etfiet
dydy dxdx (b.C) ) aa(t bxX = aabic (= b xX)
aa +CXX
aa ,1 - b: c sit = ae et b: c= β
et fiet dxdx
(4) a + CXX
dydus-dxl esica e aae
dudx ( (dy -Bd) a + (ay- BdX) CxX sit ja m clynoy  y Bax) cxX  deo
aa
aac
enstana
axax
dy+dx conc et fret differentianto aequationem S, fiet
(dy + BdX) Etx Ax B. dx Ax ddus _ dxdx ddx = (daq .  - (3 ddx ) qu (dy + dx B), a: e
2 dy axddX + 2 (3 AxAXdax = dx Ixady = dydy (a: C) ddy +d X dx (: C) ddy + 2d Xdys 2. C) ddy
seu omnia explicate scribendo
edxaxdax - ayuy (3 daxa: C - ( d xdoq ddx - 2 dx duy BBa: C) ddx
gdxdx ddx + 2F dydx ddx + gdus (Ba: C) dydys dux = f. d fx ddy + fa: C) dy a (iai e) dx dy ddy M a:. ) lyay illy
sit r  PBa: C = f. a2β- 1 + 3 = g. a, et fiet
seu ddy: dex  odxdx + 2f dydx + (3a: C) dydys,: fdxdx + 2 B1a: C) dxdy + (a. C) dys dy
a
sit  ipsi slu, dax, dx, dus proportionales sumamus dv, dz, Z V,
fiet du: dz ~ 927 + 2f42v + (B a : C) vV, :, f2Z + 2B: C) v + (a. C) vV, seu
(14 dt C
ad-
jam
dv: dy  9 tise + Ba vo R,:, f + 2B a + aa v2.
(_(v.Z): do - _. sit ~ = , fiet
et per 11 et 13, firt du: dz 9 + 2ft + B H,:, f + 2Bt +  Ergo erit
 a2
a de - t = ag + 2ftB + BH: e fD = 2βH _ - 1: e:  + 2B+ : eC
ae2
e
12
ea
=B
=   (per 3)  a + ac
quod per compendium vocetur R: aet fiet ex aequ. 14. fiet
Nac
a
ac
243, e
 ee
1Z.Z - Sat, f+ 2st. a + H. e,., ag + ft +At. a - t e
e