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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 202v, page id 00068198:0404
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pportet ut progressio  replicata sit talis, ut in casu indefiniti, sc termira-
r.g. in progo Arithm. est 2(y) = y + (y) in Geometria Vy(y) = (y) et
in Harmonica 2bd= (y) = 2y(y) :, y +(y)
in antiharmonica (y) = yy = (73(y) _3:  y +y) 
Q vitendum qu sic si sit 2 (y) (y) = yy + (y)1(7)
quando in serre pb aliquid invenirigstans, ses est non parvi momenti ad
ravemiendcto melius progessione
y- (7) = (y) -(y))
sie in Arithmetica est
 = = - 1
in Harmonica Z e (yD
(y)
1s
(X (y): y = (y): y)
quid si y(y) = (7) (y) hioc non procedit, jam in terminatione fieret jus consa
in Gcometrica
ergo revera esset ad rectam axi parallelam.
:y constans.
Si (1) + e quid si (+ a,  (y) + a, : y constans = r fit yY - (y) = a
(y) + y 3 : 3)
14β et (y)C y + dy sit (d +) B ( 9 dy = a seu dy sed
gy (y) (y) - (9 ) = (9) (y) = yy. . Est series cujus termino
sed jam tum patet hinc non posse fieri lineam
(udas set 1
num quorum quadrati sunt progressionis authmeticae qui sunt scilicet sax =y
go yy _
(y) seu (y) +93 :y = constanti habet
quidem hoc ut ferminis lineae consentiat seu ut succedat aequatio, si y, (y), (sY
aequalio, (y) +4.: Y. = CyY +p
aequales. Sid non sucerat Uex differentialium seu 1d9) Y dus
eaum
C uode non p fieri dus infinite parva, un si cum
gy + (y) y) _: 2 y (y) =, X fiet (y y + yyrt rydy + dydy = (299 + 2ydy
y
umigordinatae  f 2y() = aa
y4 dy 4 a,=
fiet dudis =0. Erguu constans
yrydys + dy dy-gy fit 29 dy = rax. seu
et ergo hoc fldorema oq punctum curvam
S
y(y)= yy = rdx seu
cura noluquacrum series habet hoc ut si ut ex tribus componatur aliquid
constan aequalie nihulo non ex duob,s cum latera loscuplorum quadcati,
fiet yy = LYX
octanguli, ibguti sunt +E. A2 - M) H(2 - + (2 - +2)) etc. et lctum polygonam
+299 5 +da Ergo salle
=f+ df fit 25F4 255 + dfdf 2 af + aa
cirpumferentia suut A, B, C inveni et A: B = f, et B: C = g.
tam rationum datu sehies sit
quod hon licet applicare ad euibo
in curva rel nteriorem, ubi recomnis
escenditur abesse coa abscissa cum suns
tune liceret. Minuere
Numerum quarrando 
scissaru, tunquam novu termitum
reduco pt ad rabdals ordut 
b