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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 17v, page id 00068049:0034
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Ilud ad huc tentandum superest, ust
aliquid
tollamus simul
Utlimm terminum un nnulae numeratore e nominatore, revera
cum de formulis est agitur, quae habent nomnatores aut semper
res ad illas potest reruci.
O-
+99
um - ter 47. fiat y = P=
mm- yy
sum XX + 2mr X tum
fiet  Y.tipp.
X+Y.
2hp99. - ht9
= mm XX + EmmrX 4 mutu
= 2p44 . - 4
Et quidem in praesenti exemplo tollere simul utrobius et summum, et ultrum
non licet si tollamus ultimum numeratoris et primum nomina
tons vel contra sies quidem procedit, sed tunc idem est ac si in
ac si mulliplicalo prius Nameratore per neminatorem
ut nominator novus fat extrahibilis, voluissemu
in producto Sumetatore tollere terminum priamle utfium,
quod non gelevat
si et faceremus
Pum 78 = hh DD
fiet O=1
et
mm 44 - DD
tb p ee
FX Aa +  PX + q9X + r
de 15 sax +A XX + 5X + +
mtst- hh nm DD4Y + hh
mm 8Y- D)
Si. formuta aliqua aequatur Ito, semper binae
Unde aequaniiele lato:
quaevis radices debent aquari inter se
itaque  si esset m fingamus mn-layus in min-yy =0
eimul quatuor radices m+ hy m hy m+y m.y evel pro y
cnbendo Ay. eraaa fiet m + hex+haq. et radices novae erunt
Xr
 + m X + hgq
+MX 6 = k94
+ m X + 49 + mX   -9q
+ Ep X + mY y - hpX + n  + BX Y mY ) + pX
+ mY
ubi debent duae comnbinates ac duae quaedam equari inter
se
X +
ut et duae reliquae ita de verbi gratia si aequentur
- h4q+mt
hgq+ m et X +
in +hp
m-hp
vel debent squari
h9gtmr
m+hx
et X+ 2
etia aequabuntur X + 49 +nir et X + 99ima
in + p
ex quibus posterius est umpossibile
+ X lungs1
49+mr
m+p
hqqumt
im- hp
et X + = 99+mo
m + p
unde fit mhgu (+ mmo + phgus + part = mqqu + rm n + hpnir
seu p = m gu B ,- h: 11 F ehqq + -h
et rursus .hmqu (+nmD = - mqque (F mmV) + hgqB = h mY p
=ri94 + mer
in +p
et B = 1. n 14 Dm nhgy Y. higq- r
et p = 1 - h mgqe  n4q - mr :, h 49 = mr
valores duos aequando fit: mgq. 1 - h h99- nir = i h hm gg - h 99 hgq - mY
1 = h murgqu  - . -k mr hgque my
sit hag = mr = ao fei p = muqu. 1=h
trevitatis capesa hg9 + nir = 10 4q+nir. a =l94tmr =1 = 49+ mY = 13
ruasus fix. r ) Ergo fit 10- n h -   13h. D - 12 seu (h44 mr . hgot. bons -= ( hg qu hn, fugu 2n
et fit 1- h = h -1 quod est impossibile nisi sit h = 1
fit  10p + iom  uhp + 1 m. seu p = 1 - 10 m: 10 - 1h seu 1 - 10 = 1= h 99
P = 13- 12 m: 12 - 13fi sed 13 - 12 = 1 -h 99