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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 218r, page id 00068196:0431
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ules reper
in aequa
formula
X 4etc
Endo rqua vel xxtete
i Novam tandrem Analysin inveni, per quam omnes quadraturae
revocantur ad qRationales, et quod hinc sequitur ab infinitalibus ad
Exponentiales Expressiones. Id obtinui singulari quadam ratione explicando
literas, ejusve explicationis ope tollendi terminos. Incipiamus a simploco
quantitate irrationali sub vinculo per rationalem utcunque multiplicata
apim habeo modum deprimendi quod sub vinculo est cecciiaat
donec fiat simplex quo facto res ad quadraturum rntionalem
reducta est. N Incipiaruns a radice quadratica
y = Y(XX +C;) e sit X = 1Z + 1, :, 202+ 21 et substituendo e  x tollend
arbitmriasque (0: 20 et HZ21, ita explicando, ut tollantur in numeratore L
+ e fiet y = VX  20Z+2) sit g = . (X+.) faciendo x ut ante
 10Z +H9: 202+21. fll el tollendo duos summos numerutoris terminos, fit
 fAC. :202+ 21) Lm.  q 0 2) X(. 22+..)
vel erit = Y(X +.) Et sibo = 110Z7 1a p20Z+ 21, fiet substituendo
et destruendo y- YC. X +. V 9, _ etro2+ 21) Vel erit y = Y(. Xe .)
Generaliter
et fietattso
ut anto fiela  =  3( X2C- P  0Z+21)): () (20Z+ 21) seu
2+.):  (203+2t Utroque initur
inferiorem Atque adeo ns
sub vinculo ad formulam paris quadus proxume hac quia
des firrationalis quadrat qidix qu
ad intirnalem hac via
giasicao semper revocari potest
nmin
eem vide sumedere et drcablica Radice. sit enim e 
 formula Y.(3 (X +.4)-firt faciendo  ut ante fiet y-.  + .); : (202+ 29
it rep sugdit itedgit y = (XdE raifint = 2(A2
  ane vila 
 vulms
erim sot
,5) 20X 21): ((202 + 2)
(. 21+.. o ( Vet) 202a) sed ita nit luciamuo
idsanus= 2(X) ex +. firttC
di d (9bZ + _) An  B. ent  .)
ni
Eodem modo
aso , Z +.): D2
jetit ii preet ubi voearever
Vidcontampu remedium pro i= 3
erenhem
 lu nempe, fatiendo, x ut anti explicando perZu fet
aut a mobtinetur depressue
 ariam ergo haec via nonest deneratis aliam
 ., , oz): tet
cogitavi; quoe sem
Xe + usuit X = lZ:, Z+ M, et fir
At dividendo, in vinculo, et utic epl tando 20 et 21, ut fiat divisibili
videtuo succedene sit 
Atar habemus  L 3)( 23 + 1): (2) (207 F 21) ura jam habatur deprassio. Dem
enim vero hoc remedium non est in potestate num quia divisio fieri debet per Zam
semporest cum potestate videtmus tamen in exemplo utive =1 fiet utique
barcx
X= lZ: ,Zr m, fidt (+ 1C
fiet 1
 YloX + IX F1ZXX +X3X + 14) = y, et faciendo
H.+B nim PZB  id
+12 lZ_ + uUm ZS Fiam .
m+ 14
visibilis per latus denominatoris
 obigu. Z+m
in indefinitis, seu pertam. sed apparet befier inem posse, nam Numeralor
ubi id agitur ut Namerator sit
constat ex quatud liteis ix quibus tres posteriores, seu omnes
mo ergo nisi prima sit per
 sit divisibibis peridem, non potest totum pe, 1d
praeter primam sunt divistdi per
nempe 10
esse divisibile. Sod   10lZ per
q+m ind indofinitis dividi non potest
Remediurum hoc non suctedit
centemus aliud, quodem eo consistit, ut in ipso vinculo faciamus
Ergo
esse fractionem antequam perveniatur ad explicationem, ita numeritor
enominator futionem potentiam a genominatore valoris ipsius X
pro bona parte mutua actione destruendo tollent. tente
virtat
finis huius
plagalae
fuduos summo
nsta