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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 26v, page id 00068197:0052
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fidt hu, i (Et 1eG) = Hb. Lt 1 f5 04- an  alie 4 e 
= ma CD +unD - bh g- blq + m D L0
 2bh:
= hl 24 + 99C 4 - ch4q- chez 4 rtue  1B
ob rmtionalos fiat th lih P ali4Z HH. abi) 0q . 
Aequitur medius valor,  prico quam
lentio; et ob irrationales fret
ee GC ph (a. b) Y+mn D; hf
1b 
pee bhC G- bh 712 lli 2 1 G. cli 44 + Bg- si  4
t.
ut ex aeq. 3 explicando si, Kofilqu Ca. b) 8Y + mnumi 3D + 2 (a B) trn QD
siet ( ah +5 74
= h (C b) Q + mnD,: h9
oberrationales fine
e
c
fas G ul qule. Gylx  t nuna DB +ih E. b) an 4B Aga (9gt b. e hq = mingus et ungude
(t epaega explicano 3
s in aeg. 5 si facias ff +(ba a h = o, sem f = (a- b) h, ermescant in ea co et 4, et rebidnisdiates per D, 
cb c)h 99 8
siet m  mnun D + 2h (a- b) m xQ nmfs0 + nutt G, vel mmt 3 + vnd z -mm  = E
Eodem modo in aeg. 6, si facias g9 + (b. c =0 evanescent in ea cQ et YL, et residuis divisis pls D
tiet mmnnpA + 2h (c- b) mn q LtumggC + nnggE
Et opi aeqq. 8 et 10 tollendo mmnn D, fiet - 2h (a - 1) mn Z + mn hh. 1) 0 + nn (a - b) G = - 2 h (c. 1) ma tmml . b) ex ul. 1)8
et tirt -2mn G + mnC + un C =0, quod dectu in a = b + b. c, seu in a - c producit aeq. 11 sed di splicat
quod il non inveniuntur.  C) et Q et e intervendentibus  t a, b, c..diiCi.
Itaque praestabit redire ad aegus. 5 et b. et explicae caetera per D. purg. sit X 8 - 30DY2 et C = RCDF 4 et G - 30D +1
lita opus est aeqq. 6. ad tolla ad AA, X, et  D, _D, et s in utraque aequatione, habemus autem in eam rem
hibitrarias 10, 11, 20, 21, 30, 3, F, 9 m. n. Tentemus tamen prius viam conpendiosiorem, et valorem ipsius e inventum 18
Licerit
Substituamus in coqu. 5, pat hhguscabi sq + mmani DB + 2h (c. b) ma 4  mmgu C) At gu (99 b.) ) 2m BC . gy lgge (b. esu mm Cd C o
(1. C)t c9 ..aggnim D apragin YD
3
+ mn vg (gu Xb. 9) t) 9)
h
Comprndii sit . 1200 GL. + 1O7BH 10B2SCL IIO ZP +140,8+ 101D6=20 (tmnungu B)
sint 3240+Zh et () = 304 + 3ih, Et ex 4eg. 13 fict 120078. + 1020. 20. 2098 17 1020, 2d. 21hG + 1020. 21. ahh 4
Ubi H aequando nihilo coefficientes ipsorum
e
L
+∞2 3030..2. 1002. 30.31 ... + 1002.31. 31 th
+1110. 20. 1 21110. 21.
IIN 30 , +1101. 31
1011 20. 30,-1011. 20.31 .. +1011. 21. 31hh
1011. 21. 30 1
Sed quia is calculus paulo prolixior ideo redeundo ad aeq. 13, faciamus O = 210 4 + 201 D + 200h,: 000
0f.8) -7 210 - 1002. - + 20, 2. 1002D7+ 2. 20. 201 1002 - . + 2. 40 2001002. (  + 2. 201. 2902 D h, 200 L 602 it
et ex aeq. 13 firt 000: 12008 + 800. 1020D7 + 9002. 111087
O4 20. 1101 ..
000. 201 .1101. 300, 200. 110. 1
+000. 200. 1011Jh
uti tollere spaptet tres ter minos summos. fit ob X4 210 4 00e. 101, 210. + 0002. 1105 = 0015. 1101 - 4, 1200. 100Z. OV0
l s
800. 241. 1011 DP +000210.1011..
1002
4. 10021∞o fiss 4. 1002
adeaque 210 - ( (1101 - 4. 1200. 1002)  110I, 00b et eodem nodo (20  (10112 - 4. 1020. 1002) F 1041,   1 002
superest ZD et fit 201 = 000. 210. 101 + 000= 11107:, 2. 20. 1002 + 000. 1101
seu =2 L 000. 1011 (+ (1101- 4. 1200. 102)  1101) + 0c 0. 1110
(2, 2. 1002
201 =
O (105 - 4. 1200. 1002) - RCoc. 101 + 960- 1101
vuo
(25)
(2d L (101, - 4. 1020. 1uo2)  1981 7 2.1002
1011 +(110 - 4. 1200. 1002) f 1011 . 101 - + 2. 1002. 1110 == L (1C11- 4. 1020. 1002) 1V11, V1101- 4. 1200. 1002)
Emotandem 1aH H (ctO H02).
et firt - 1011. 1101 + 2. 1002. 1110=- 1(1012= 4 r1020. 1002, 1101 - 4. 1200. 1002)
quae aequatio explicatis significatio nobus pumerorum patiticorum, praestanda est ope residuarum, arbitrariarum m n, g
et ex aeq. 18 sublatis 2Z, DD, 4) sperest 2. 20. 200. 1092 CB + 2. 20: 1002Y + 200. 1002 h0
000. 700 H1C1I 
undem redacta sunt ad  per valores simplicissimos
en
(1611. n. 1101.  + 4, 1002. 110  4, Per. 1101. 11O (122) = (1011. 1491) - A. 1020 (1002) 101 - 4. 1200 (002) 1011 +16. guor 1200. lest
iaque superest explicatio numeroum fictitiorum
Seu A, 1002. 111O _ 18H. 1101. 1110 = 4. 1200. 1020. 1602 quae aequatio servat leges justitice et potest inservire pro lanone
 1020. 1101
e 1200. 10112
astenus vene nor culculi
ll
se nerali, aequationis trium literadum legis homogineorum inter se servantium
reducendae per mtires simpli seu reddenda identicae per valoces simplicissi
5
duarum ex his ex tertia 
1200 = heb. 9 (hb. 9 +a0) 1020 = mump C h Ca b). B) toot  mngs (9or hsb - c)
h (a- b
quia g9 +. (b- C) h. tam saepe occurit
111O = 2ma (9gth cb. c)) HIOC =mng Cgatib. Gh) _ 1011 = umgque (gg + b. d6)
ideo compenvia vecetur hp et Hba
(29)
ha. 6)h
Et exaeq. 28 fiet: ahm sipinta  ahemingu hxmmnntilipp hCa.b)
munt esthe man hegomnunaF ahena muhe mngghemmgglp = ahenn tb. c hpmnanche go) napetip
(bnc)
Mhib. e)hp mgh
vil alegninp + h ccg aen p - ke genenpp +
(et divisrs onnibus per nggm n pp, sic et mtu tistu
Thecgsque porco pro hp - is(b. C) reponento g sit - a
et  contrari, fietque -3nee + egg - 2he ( 4+
 htegp=-gheegmn p aie(.  ma pp
s eheegu -eg + h( b. cg ep L rt eg ep = - 4thev (-c) + 4he (b.) 99
)u +2egt = 2 helt- 1)gg = 0 quae divivi potstael g
et explicande e per a- l, fiet
hra + 6hab - 3hbb + agque - bg9 t B ∞ gb C Et c eticb B lb + hcc = 2hbc = 0
gg: h = +  ua + 3a
unde tandem fiet
ct 40b 108+ aub.  sed clculus resumendus
2eng99F 2eggti(b d
acogtsb 
siet
= 17) =0