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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 11r, page id 00068043:0021
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a
tu
se
insiilerari
in usum praesentem
e frutaur
Atbi Alibi ostendise oen aequationem diferentiarem, in, qua datur
ut res pred
icet perficiamatae posse reducitu ad quadcaturas.
Nam  AXly f gX horo si A vocetud Z fiet dZ = +7 x 4x dy
ye
seu d  dx F et d2 = + dy ) dx et 47
=
Zax X
edque dy+
Hinc video si generaliter sit dy -. = O posito ( componi ex , et  ex Z
tunorem pproceder
videtu an
tq
∞X
unde et Sa =+)du =S seu log. Z eu datur differentiae lignnchmum r erX K Hinc porro: +ax dx YX
a = () es pancitur C posse formani ex Z fiet (dZ ++
dZ +
aut formulam
ple Equib cum quadam exceptione
ordinate inter se seivant leges  omnel
psse
Hoc nunt Reassimemu
7
dX
quiq quaesibet srmula
sesuper res posset redum ad quaduturas
La
le
bb + bbcoco + eoco
aa F itaa
lbq
Nit
leu
neq
afaa
sitooquantitas
X = V: C, et Y = co: e, fici a4+ aa ee + vn
fiet.
c
a.
aacoco +aa vv + VV
bb ec + coco
et ponendo ee= coco+rn
t et X: y seu V: co existente Z.
seu Y X = V et y = c
Scocotvu coa
Unde equeretur quamvis formulam duarum vel
v sit verbi gralia 2aX -XX = yy. ponatur X.  = trocotur: v
seu 4 + sit jam vico = Z fiet = ele
quid si sic: X: a = ∞ co+ V : V y: a = co+ v: cd
dys
dx X
is
affevolialis. Ex dy
ex
a+y+
x- y +b
et ya = Scocotvn:eo
4 +1 = 12) 2+22+. 
E
et  v: c0 = Z
sed
(2+Z
juo ut aequatione res non proced.I
fieret enim i quempamoi
auferatur inde
X-y -G
extyxrx
 fieto
X
Xx-t BX
quod ut fiat scribatur
Xia scubatur X: a =L V+co: v et y: a = D + Co: C
firt () = 1+4 2. Z + c22 2-7  + b a b.Z + 1+ F
et qu pan
 y. X:: V. cd a Zta
A2: Z + 1. Z7 + 2 4 rZA 1. Z (+ b) + b. ZC _ - 1: Z) - b): (1+ (3. 2+ 1: 7Z (2) - 7 2 +b 4b. 
seu O = Z+2 ++2+b: Z +1. 73 F,:  -Z -1tb +1+b: Z + 1: Z
Cu O= 23+ 2ZZ +2+6Z +1 : - 23  + b- 1ZZ + 1+bZ + 1
Et Fet  (- 74 + b - 1 33 +1+67+y
Etsiet Xd=
Z3+ 277+ 2+6Z +1
a
d
=
at +
1Z61 -1
ZaxC
Ergo probiema redactum est ad
quadraturas  seu lineam cujus
cuiqs aequatio sit  du: dx = x+y+b,: X-y+B invenire possumus per quadraturam et quidem
rationatem quae semper prodine debet, quod notabilisimm est, si data aequatio sit rationalis.
patet si diversit modis assum sissemus valores X et y per e et eo, nomina numeratore V + co variato
valias aequationes rationales fuisse prodituras, quae tamen er ex se invicem pendereat
pro communibus aequationibus non proceddis hoc methrodus ex. ir
sit sit X = 14 es l:Z et y =7+ 1. fie 20 Z+2 + 1:Z = b. Sed hinc jam video
seu unadata dari et alterm posset
x+ y= a.
48.
etiam plurium literarum posse reduci ad aequationem
manius literae, sine sublatione incognitarum sin
sune ex una sola aquatione
per 2a AA(2I+I =  L + 2 +1 + Z7+ 27+1
ad quaevis egga
sen
ex. ponatur
bb +yy
fiet 2da reoco+nn: V - 4a10co:vn Scoco +vV. coco
s
5
relationem inter X et g.s
91 2 3. p sie gn  +)
1+Z
et