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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 33v, page id 00068197:0066
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Quaericur (dx LXx -bb, Xx- CC) fiat X- E +  compendio-
fiet Xx - bb = aa AA - bb n n, : M  et XX - cC = aa N - cc n M,:  e
ex ambo Et explicando numerat: es fiet aa b=
aa AA - bb n n =
+sstx anotu
=bB - bb pY
et aadA -cc pn = +sftv
et productum
+2afc0 AV =(compendio) ast +  tv
 2bb  Atv
+2afco stn = compendio) a 3 + 2) Av
2 ccrt stv
Ergo  xx - bb, XX- cc = aa 5B+ 4 27 t~ + 2a5Y stV,: n ubi nominator est extrohibils
ea aacgttort a ecocoto + a coa
+aa
a c = a et Btaacsts - bb P
aeu =agtr taacoco -cc 
au se Z = an egttant aco
dHo aui eroto -gafbboro
ascc Wyytr
+gaafscocotv
ote
arr mesio. aeff  itet 
=4afcc corp 1V
2aece tr 2 AtV
am = aet a9 +4aaH = aas - aabb + aaff - aacc + 4aaff - aats. aud)
a tag = 2f - dd aecc + agbb = fsec -bbec + Hbb -6c bb = f dd D 2lbec
+2afsis f _ co 2 tV
+4afCD + +bbc b
= 2c bb + c4) co 1 1 s 1
et erit aaeg = 2bbcc = aadd et baaff - add = 6bbcc n sedt et 6bocc- A dd = 6bbc - be dd
 as+ff. af s1 = 2bbec = bedd et ff do t libe  2
ta tandem pro be ponendo a, fiet et bb ponend
aaeutlvr +bauzaate t
quadd lv c
=aadd cocob rar
t renum sst estri
unsee a 
aneg - f lbb1c a sdd
en = aecc - agbb + 4bb6 = - ss cc + bbec - ffbb + ecbb +4bbcc = 6bbec - ff dd
Erxpotardum aaegllvB + bua ts) tvcoco + acd +
+6bbcc 1tvYY
otu
servabunt Legem jusitiae inter se
1t bocc et aF = bbcc
pra 10) st ~) raa tV
dadi qua  Bt V) modieiru qu. (. 3. .  v 
  los , - LL240
 +2AYZ
+ae Z + aY B
ant ae HZ + a AtZ +ap VoZ
raa -dd compendio ap
bracideam lua, 8a. +94 Mropendio a ita
(6a + dd
co)  raadd
+ 2a4Z YtV 1a222 - 4aco p. q aa 5 (1 2 aa dd
aa _ itam srrationalibus fit aa ANZ = apt v +2aa (coco +  Y) + co + 
sit at aZ = h, co+ V, fiet test n = ptv + Ea (Coc0 + p Y) 4 p Co . _ uut  = plv F aZZ H ) c
seu ah= a V + aazZ- dd co. Et coincrdentiando partes rationales, fit
ANA tZ +abnn v7Z  raepB + am toZZ-20g(0 2 + a Z - 4  co  Zax cocopiP
Trapco rapzc0
ubi  Z co et fint ahi M- 4ap tv taaquZe - dd coZ + dd coco.
colp Ze0 cocd Et q ga DA LZ +aa M VZ, ap HWB + amtbZZ 2a gtBZ( + 2q toco arutquun Z tap 7 Xo c0
 quaenequatio multiplicetur per d et tollatur dd col et prodibit
aa St VEZ tad nn Z = 2 to F am d tv2Z F, addgevah m - 8dd gtvaptv - 2 dd gtv a + ZZ + d1 4
sed fortate hac explicatione
+Haaddizalum _ Guaddz Zapto - aa ddz 2 42
ap achh Apin Fapi6 aapptuo + ap a  2 apah n aptr ap p2
 inaq2. fiat L = 10Z + 1a v = 2∞Z + 2ta, c0 = 30Z + 31a 1P = (2. h) Z - co =- (30 Z = 31a
ap- Z co  (a : h) Z= co corp = (a: h) ZCo -coeo = R.h) 30ZZ + (a: h) 31aZ
X = 30. 30Z7 - 2. 30 31 az - 31. 31aa
ce a41 55I aha M = 4 ah. 40. 50ZZ+ ah 40. 51a Z t atr. 41. 51 a a = 4 4a p: 10. 2027 + 4 a p 10. 1az. + 4 a p.1. aa
+00,00aaZZ 4ap. 11. 20 a7
=dd (: 1) 00, 2 hZ _ - a. h) dd0o. Vaz tet 3ddna
A = 40Z+41 a n = 502+E
quid si omiiso 2 rem reducamus ad solas  co et V. Nempe
+3d. 3631 aZ + 31. 9 au d0
aequ. 1. ex rrationilibus ert aptv + 2a a (Coco P()- aqco= aa An
et 0o oot = nOC + 101 P + 108a et 00V = 210co + 20,1p + 200 a A- Z10c+ 300a  = 450  1400a
00 V
veo t 1o t1FWa  00. 00V = ot 2c5 + 212p + 20a
natore  00. 00 raacoto + 00. 00 2da 1p Y1 = 00. 00 aqo 
30. t eo) aui oi to
400. 400
06i00 dn = 310. 47 Ba cito BB 21. eB. A. P  = 110. 201 aa cor est 
cust egratio ex utionulbus  Uvo Y a ntv Coco  ip) B adddtB col+C + 4)- agddcon W r  as
uuta smaplexo a let lolies toa 
tam pliau in aeet   +oo
pere lam ceipateilitm t, quam er e
e uteooissu im
ongaitu audda randon e