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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 2v, page id 00068049:0004
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ym sit
yy - nn
yyc 80r0X + 12
et fiet
a(dx
et valor 4 videtur pvalore 1. simplreior
f1x + 1
2 SIXFI AXL 12
1
ueruum
Aliam rationem trans formandi ex cogito. In omni irationali sumplice y
Cuique quadatum  est rationale, (etiam ydu est cu seu cujus quadratum
eham ydy est rationale et yddus
jis est rationale, (it  G = Sex  nm
vel et dy sau etc. et au, et daque, et generaliter ubi numerus dimensior
est par secus si impar. sit ∞ Y  vy m,: 1099+22, fiet
d+C = O: D sit ded = DaB - OdD, : DD fit da Broriu
12. 1o s 3+ C2OGy+ 2102y + A2
d0 = 1 317 + 11 dy dD = 220y dy et fit ded d
et fit da =  20y  in v sit C0 = 1 3+ nyE+ 1 y + 13
10gy+ 22
fit _ d0 = dy3. 109y + 2. 11y + 12 et dD = 1, 2. 20yB.
ergo ded = d
F3.10. 29+ 2. 11. 20y + 12. 20 yy
F3.1022.. + 2. 11. 22y + 12. 227: 12 (20y9+ 22
-2. 10. 20 = 2, 11. 20 2. 12. 20.. =2. 120y
od video qui ubi tollendi sunt termini pares.
Sed video quemcunque assumam
alorem ipsius ce rationalem, si  y simplex sit in nominatore, non posse tolli ibi;
quandando; sed in numeratore video non posse tolli s.
 Cd = ir y + 12: 20y+ 21. fit deo =dfl. 201 + 1. 21 -
11. 20. = 12, 20)
n
seu deo =H. 10
deo= pa run de: vv
Sit C = 119+12: 20y fit, dco  11201
sit jam y= s un fit dy d sa mm
an
orgo datur Cdx C2 tum
sit deo - dyy8: 99+ ab
(2(20y+21
jam  ax-nun +2x 2an X Et
x-naxd +cum.  ( (Xx. n
Et ita innumerae alia habentur
quatraturae
datur relatio inter co et y ex suppositis quadraturis
 erit du yu rationalis et dy y etiam rationalis
sit deo = ydgs. a ofiet a= quaeritur sydx vel sxdue datur sydx
vel (y’ix vel gy dy Cydy
sit C0 = sex + 2y + 309:, 40X+ 517 460 d. fit deo-
sit C0 = 18X + M 9 X + 0Xyt 11 X y L 12XG ratie Ca o ay. 1Gax LXay  Hgy
Est auteum ex aeg. data yu = xx mn:, x nn seu Xxyy - nngus = xx- nim
seu X bet AxXydy +aB Xyydx. = 2X AxtnnyA Cg. 2. multiplicebur pere
per 20 X + 30y +, 31
Cd =  + 11X + 21 y + 10X + 20y + g0_Xy sit dco = 1et 2idy + 210XdX + 2. 20 y dy + 30 Xdytseydu
ducatur dec in X aY  fit W. VX _. deo in 40X + 50y +41, fiet
Ugu Xdx +21. 40 xdy + 210ff0 Xx dx + 2. 20. +0 pydy + 30. 4oxx dy + 2040 xydy.
4.p0 21 xdu
collamus neque et rylus etga et xtx et
deberent tolli Xdy xyax Xdy ydys
sit 50 = 0 evanescent Xyax et y d
Xay potust tolli,
ergo; restat Aodun Tollend  Xxdr ; vel si colli non pt
datur simul (XX dy et syax seu mo dato datur alterum ex casu praecedent
a in casu y exi lentis simpliciter irrrtionalis per X sed generalitr. ex
Ergo ex se linvidem eantur)Vdx et sxydo
e invicem cintur XXdus et Xydx.
. Sed (X y ex datur in casu prosenti. ec itaque  haberetur quaesilum remm
I potest oontti et 10.
reassumamus 30 et g1 debent manehe, item 21 et 40
itaque fiat Co = 21y + 20)+ 30 Xy fit deo = =1 dy 1,20ydy + 30x dy + 30y dx
et LCo = 21) + 2 u 10y + 2. 21 1oryy- Et Zlo= 2t u sh  ntys
282. y7 + 2. 20. 30 X y2 + 30. 30 XXyy
additus Agtu ydyt quistu igato
fit XX X y dy +Z Xyydy = fnn y dy = fx dx
Fhop. 3o xydus X31. 30gyax.) 4eo y y
320. 30 92 X 620. 30. y X ax (36. ∞2y dy. 2(30 X x
gX y dx gxyd y
=2unxy dx
nhut ni discormus qua
ocris aota namloter
Hicis demanteatur dari sxytusa essum
mndlliplicetur per y, et XX yy dy + Xy dx = nagy dy +∞y dx. Ergo Xdu et xydx pendent aje
luvicem, E seid X sxy ex pendet ex Exxyydus quaedatur ergo et sxydx datur
imulliplices per
xytit xx xytdus + Xy dx = naxudu = X ydx. sed sx yd dx pendete aya
sta set pis ayt, fq. e iest sumatitis absiure nm sum r pe h est et pogcus psetts a siam set
Xy ax pendet et
16. Su 4