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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 24r, page id 00068197:0047
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 mo cedit iatius mndr sis
quaritur  Chytha, hy +. hb, hy +. hc) aessumatur Thyaha) L l.H + s. CZ t t CEy atib) L n D n t Z t Hipu 1c. A q  0t 
ntitu t + ff0G
(2) pmmoDtun DE
+hb EE - hb C
(2) pahh 42 +g9C4
L.he GG- hc04
+2hftur VOG nitres ipsius 2E+02+ 24 10 valores valores ita dven, ut primus 
= 2ha 2 10
+2mn D 1CG
+ 2h92, 102
=2 hc 8 10G
fiet: munndD qu (a -b) 43 + L (a. b) ma D
et mmunD D+ H qu cab) 4E + ahlc. b) mn D Z
et tertius item secundo; seu extremimedio; fiet ex  irrationalibus aequa
ht m
Ex rationalibus aequatis fiet
hthih+ A = m BDran Z = EE 4 4 +99 8G fb. ct 47
Et in his dluabus aequationibus explicando lonondim
ht et h2 per ag4. valores ex aegy. 3 et 4,
+5  O2 - ffmnO D - ss nn X) = 0
9+ c9 49mm C 3 99na 34 6
abest hic 00 et 88, 07, 48
non licet sunui eodem movo tactar
quodsi in aeq. 7. ponatur ff H(b -a) h 20, evarescet in ea Oe: quin evanescet etiam ZE, itaque residur
diviso per D, ex aeq. 7. fiet mannD + 2 Ca: b) hmnq-fmmO- fsnn E,  et explicando ff per aequ. habebitur
2 + 2 m 8 =mm C 
+ mmun DD + hhqul c - b) 4G
+ 99n (l. C)..
is valor substituatur in aeq. 8 fiet
+2h (C- b) mn D Q(= gmmOD)
iam (1D +gt
golb. dh a. D h
Haec aequatio 12, compendio et generaliter sic exprimatur
489b. chs 
12004Z + 1020D) + 100291 + 11083 + 1101 3( + 10113020
faciamus jam C) = (14) = 21C8 +01D + 200h,: 000, fet  10o Z4
(15) (000. cro. 1700 98 + 000. 000. 10203) + 000. 000. 1II0 ZD  2ro  AbL..
+80o oro. 1820DD +  H10SD
+P ret teonsx +2  pot. rerveo nortf
210. 210. 1602.  + 201. 201. 1002.. + 2. 210. 201. 1e02 - - + 2. 210. 200. 1002h8 + 2. 201. 200. 1002h7 + 200. 200. 1002 hh
000. 210. 1131-.. 40
+ 000. 2811101.. -+- 000. 200. 110Y
4000. 20l. 1011.- +000, 210. 101..
4000. 200. 1011r
siant sam cdeficientes termindum Y Z, 33, XD = b r savit b. 2. 20. . 1002 Z + 2 201 po. 100 tyt 4 200. 1eb 2 b
ob 77 fit pi 210 + 100. pe 210 4 voo 101 2 = 005. 1101-u0v. 1eobi1 200. hin 2ol  sceuri tromi Mer, 
seu 210 (NO- 4. 1209. 1002) -1101, 000: 41002 . 190
Eatem modo ex D) siet sublato
fiet 201  1 (101r- 4. 1020. 1002) = 101, 000. 7. . Capli est telli. ), in qua a unde fit aequatio, in
qua pro 210, 201, substituendo valores, fiet
3. ∞ob. 1110. 1002 + fL11 2- 4. 12v0. 1002, 10112- 4. 1020. 1002)uo  1) 101 F( 1 (1o1 2ete) 110, L ry. 1101. 1311)
X 1 (10n t) 1101)  = 1011. 101 + V (, poi h) 1BU uot II)
Seu sublantis Lllendis I( - 4. nov. 1002, 1011- 4. 1020. 1002)-
10OL. 1011 = 2- 1110. 1002
et quadrundo utrobique (APP2 1013 4. 101. 1020 (1002) - 4. 1011. 1200 (100716. od. 1020( (101. 102+ 4. 110. 120- 4. 101. 191. 1 sed
quam aequationem purgando et adinando firt tandem 4. 1200. 10d8. 1002 4. Hvt ry. 1110. 1101. 10,  y10. 100L
quae aequatio legem justitiae pulchre observat e a es nit   aitem t e
Exphlemus jam numerus hujus aequationis ex aequ. 12 vel 13, compendii autem causa a + h(t. c) vocemus tp, fiet
1200= tb c) lisitie 1020 minua Chtarb) = 99) t mmnnXq ( , 1002 = - tp gomn 89+h b -a vocemque h9
1D LD- 2mahp et 1101 = 2mgghip et 101 2= mm g p um 99 P
et exaeq. 20 fiet Ahtitpmmnuqueupugum, 4mttip myghp mmgop:
Dividitur hac aequatio per thpperta, et nultiplicetur per e, 3C
fiet =ek9 + 4 ep9g = = ahp ee + 4 e999 L Kpg9
ammontulitipoam heb. C) vocemus tik
 4 amoetitip pmmtriq
in hac aegpntione pronbisat pondatur multiplicata per h, loco tp, et h9 ponantur valores
fiet =AheK 99 = ahek hC) + 4 eg90e aegghK =. ( 4heegos- Ahoehk (+ 409999 t ci 19h0 + 99k99 +9G ht
Unde tandem fiet Kg+ + h k kgy = d
Sed K non potis
aliaqui in aeq. 12 omnes tegmini destruuntur, praeter equm sed hos
 iosers HG et fiA V =b 
ergo t
ibidem termini 1002, Hot, loi, seu termini continentes 
et pracepib simunter  D 24 F5  de 8
112DD + 1448Z + 114)8+ 123F+23O+23C)O =0. pro 3 sculatur V, et fiant
e monnt editraria quaed saedible
ntata compentiao
el 
hon hecse tatabitur tatu inter nisi etiam velimus
evanescere termunos DD, fY, YD quo non licet. quod si ratio datur inter Y et 8, ontato
et viter it ti et  sed
R fumatur aeg.
= 20V + 21H: C = 30 v + 3ch: 6ol 4= 40 v + 41h: deh, et fiec moovv
uet tollgatur ex invenictur 30, ut tollatur v, invenintur 31. et in aeqvotione
simparan ad tollendum hv, puperpunt 20, 21, 4C, 41. Endem faracnvo pro
9. facta ex 8 erit similis calcutus, x pro 20, 21 40, E1, nisi quod per
pro 11t et 14 ex. pontur 211, 24. + etC. quam duau auus a
tollatum 20 pos
2. 144. 40. 41 l.B + 144. 41 hh
obB + 144, 00. 4(hV
L. 00 2d 144 60. 21 p
es rdotio
s  p t
113. 00. 35VH + 113.00.9. hin
maju
qviis
NN van ns
ng..90+ he
requamb.