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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 259v, page id 00068194:0518
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111
n ini  mverti potest hoc 
seltaten siatiamus ls d et ad supplendam equationem panadumat legerm Honti
nun nectum in
Wos
redtue
erentiabium peramus
Sumamus Ax. Eude ipalet tatem aequatonem sempe
quadraturas. si y et (7) servarenti Dem Homogerectam e ut inve
Daotm 
conetzicae, sed opus est eliqua atrua
nata in in progression laedicixsim hac methrodi possimus conveter
d nsptu possi eat cate
ferentialem dunti
te3 lno in
au 
u
aliqu danto itile esse motest. nxautem poterim  pnere
bopolib atuassimi, ipsius cetam dx chilum
clationem ad 
eedt sed tunc in calculo iplicato constans diffirentialas exprimetur
Lb
ch
IbS
x b = (x) a = b
b = 4 + 16 +81+
 velci
C Assit = (7S =  quorito (2). en md e ) s duintuet
f+4 = 1. av ot
vel (3) = yy =n n
 Quariur sclicet aequatio exprimens relationem inter
C
et f. Et quidem si haec aequatio est
communis dico eam esse rationalem, nam nam p si ei altior tunc y habe vel (y) habebit
plares valores, ergo et (y) Luns habebit plares vacores ett at
u abel en seu m
habet tantum unum vatorem, ergo i ex unus tantum exquatbribus ipsiu
y Deu ipsiusy
prtiuet ad rem, isque erit iatioralis, quia alio qui rarsus fores rembiguo. d omissis igite
reliavis valoribu dabitur unus rationalis, int impossibilis erit
aequatione commun;
proserie infinita res procedit sine difficultate illarur vir uni
supees atirem in serie finita invenianm sed Transcendente. consideremus autem  nominatore
3. si sit y-
a + bf +c f c + 1) fagquam factur ex duobus, quae eodem modo se
i
abent ad X. id enim omnino necesse est, si possibile
est haberi serici sumii quia redurendo ad
vam si tit (9= ( et 34  per (3 y = h0) - () 0 ergo debit esse h (hi)= fr
debet HO) (5) C este = 1 seu quaerituo  relatio ad f eadem quae tad 514, ita
ut h() sit = f+41 -1 irrationulis valor ipsius h ex f ilerum est inutilis cb
Ensignitate rationalis in aegratione non mum est impossibilis debet esse in leger
ed rationalis valor integer in rasu prosent, in equ commum est ipossabalis
quaed.  pro fponiadto at fsit oegenerum
aliud quid non est possibile comminisci nam
quis ad huc ponat a f. in f.. potet
redgi rationalis antegia
eo tritur nim
D5+ (d f + ecc. + (5 +  F eF
Ad i (0)
f3 +h= 1075+ (105
= s10 5 7
 x 2i
C + (0 q (e 75 +C
d. sor  6007
Fec + sid Es rerc.
id est  ot
co
et itaplare Hecas lartoque et initat et n
sit 4 h= quHS, B peu + 4 a 20 fustus etd + 30. + 31 f  32s
eos
generitissimaformula nonscendens
15 t
rcnu
 Bc rexprimatur aliter loco X nohibendo sytfy G+
 hoc est s s aX+ + 1 4X + 2 - 1
 etpro axt-, fiets
ide
n d agnan u
y- fX= X = fyAg, ()  seu X+1 = 5(3+9 Ergo (y) = X+ 1 8 3+ X(y) y -:
vxx 9 et (st = 7 2F Rurtus  2XM= aty r4g +2 E EXtI -1 -Asytastr 1. 4 sy1 age2Y1
et debet 4fyt 49+2+1 esse = 450) + 49 + 2 - 1 est aen -  y+ 5.
Ergo 45y + 49 + 27 = 4 fy + 4Y 49 +2-1 quae est aequatio impossibilis
st  sist a grah. _ ax2LBXFC = y et (7) = ax + Eax+ a + bX + b +C e st L = 2aX + b 1 1t Vico
A16X +16A + 4 - 1 = Z aiba x + bax + 4a = a = aZ . Ergo X = aZ- 1693a + 16C, 17+ my In et X = H 22. p. 1cC. CX
=1baX - 166X ∞16C =∞ 1by
16a + 16b
hafumsou
9. 3 pro 1 ponende m
p-