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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 47v, page id 00068197:0094
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B= v0 10 octi . ed. l  
C F 31 16 1321+ 
poAB - auB r P0o a 102+ ac. 109+ e0oi
- 00. 31C
()=AAC = 1. 310
sed hic iluae incommoddea F
occurit: DC  m
rc supersunt literae ad follendu F
00. 31 108
e 3 oq
00. 13∞  =1
yo. 3219
te 8
V1. 32 e sutnuris aufsir tes, t Catsuosima p. A. 32  Sit
IV22. 3( +gia 1b
 uor
(103 +5(  13. 32
quoo quduli asuoa pediade pondiscet q
nisi ipsae L m n datae adhibenaturr:
1 p) )
su irratohalitu
sed supederit in rasionalibu. Ut autem ABC, t non otineat 1000 sin rationalisc 
is tiat  pro 6 D Y. poritur G 
in AC = 0 seu 1. 31BL. + 12, 3291 + 13.3 =0, seu nB1O + 12. 327 + 13. 338 = 0
es non continebit
quia ex assumto 31 = 2. 11 +00 C fi t o+ 1- 31 = -
tis positis eun HC, contincat 0gd.tesimiles, ideo B
 CD et similus et YBDOL
XEA = t +, 0 + ut D AB - h B + 00. 11 1ON
80. HO 00. 12
et  =2.43 et -00 + 1+ 31 =
fit 32: 31 = - 1: 3 et  seu 32= - 2 11 -00,:3
et 12 = 11 + 2.00,:3
An tia d - fi1 NOB + 12 C AB 10. 188 + 0.  sO (Ex mationad  (1i2) = 1GHL A = ve C311
+ M. 3
B = 4 +00 VC +001D
 F 6= 311+3250
pt. B 500 +OG + o0 9C intC. 3. . 3 
 CF 131 +CG + 32 13G +nC- 400u e
lt ne uo ux  re ns
12 = H. 32 00.11 - 90. 31 400. 32- Il. 3 73
tit (23st.   00. 1 3, 400. sit 3
00. 3= 00. 31 5 ( 11. 3131
M fit 31 = 33CF 1. 3 - 00 31
12 = 1.31-, (.3(-00. lB - av. 00. 114 a0. 1. 31
00t qu (00 -31)
00. fl. 31 (- I13L. 32) ~ 00. H. 3l 00 H. 32 (- 11. 31. 3d = 0e ev 31 7 ee 00, 32 4 00. 11. 32
hlb 
fit (32=
Dip. 00. 1531B0 q u - ∞3. H -00. 1 3(. ,. 13 1100. 11. 31
80. H. 31 +00. 01. 31 = 00. 31. 31. Ergo 12 =
sseu 12 -0b. 11, I1 400 +31
00. 31 4 0d. I1-00.00
=. 3E 12 = 1I - an potuus 31 411 = 0V
Y700. l1 = 2. 00. 32
32 = (11 + 12 =31 = 00. 11400. 12 =18. 31 5 i 1Y
11. 12 472 12- 3412 = g0. 1L +00. 12 - (. 31
erto 11a 1412= 31,  H23t
11. (I1 + 1L. 124 1. 31 = 00. 11 400112 - 12. 31
31+I, 12+11 = 31+131+32
D Ea n F 31. 12(+3 1.s)  1. 12 + 1. HI = 31. 3 + 31 32(F 11. 31X 11. 32
60: 114 00. 12 = (11. 9d - 1. 11
00. 11400. 1 = 11 32 F ( 12. 0d - 12. 11
fit 1(2 = 00 t  See (a0 + 31 - 11) 11, =, 11 = 00 + 31
b0 -+ 12 = 4.4 et 12 = 32 -00 = - 11.1
Ergo 12 = = II. et qua AF - 0 fit 32=  31 sed ita A et C habersat cavrcem ratione constante
Ergo faciam, 0c fit 32 = 1  H(00. ) + 3111 F u. 11 4 11. 11 = U. 00 (E l1. 31 = 31. 1100. 3] = 31. 3)
32 = 00 - 31 + 11, 31 ut 12 = 00+31-, 2n 11 = 00, =+ 311
=90 + 11- 31 11+ 31-00
-00 +11+ 31
12 = +00 - H + 31
-00 +H + 31
mon
sit l - n = V
et R- M = A et l - n = n
(90. 31 - 11. 39O + (00. 32-12 32)
 (00. 4 - 1. 3) D H00. 2 - 12. 39)D
 00. 00 Y
00 - 11) 31YC + (00-11) 32fVD = 60-3)1 AO + (00-32) 122D on
sx rstionalibus
debent desrin O et D, fietque (00 -11) 3IV  = (∞ - 31) 11 A ~ et (00 - 11) 32V -(00- 32)121
in posteriore pro 12 et 32 substituantur vatores inventi
ita prodibunt tandem aequ. binae, in quibus solae supererunt
I1 et 31, quae si solvi possunt habetur quaesitum
fin 3C  laor
32 = 00. 12X :, 0OV - IIV + I2X = 00 + 11- 31, 31G :, - 00 +11 4 5, fi 80, 12 A (200 +IIEZ 1) = (00r- AV H LD) (ooru-
D  1A  u e C- v ev 4 00. 11 (+ o8. 31 00 31, n. 31 l31.31) (00-)r (00 ru. 39. H
12 (-00 + 11+ 31) = 11 (+00 - 11 + 31) et fint re X 11 (00 = 11 +31) = (00Y - 11V) (00 + H1- 3931 + 12X (30 + u. 3s)
tit 12 = voX voID A (00- 1 +31) + (11 = 00)Y (0DFU -31) H,: (00 +U-31)BLN. (3 (vv- ut 31): uov FuIL 3)
fit n. 31A (00. 00 = qu (11 - 31) =, 00. 11X (31.31 = qu (00 - 1) )+ (N - 00) (11. 41 - qu (00 - 31))
esset 00 -31 =f 0 sen 31 =00 firit 00(1A (200n 11) +1 - 00) 1 (11) 31, . (11. 71X = (D (2. 00 - 11) : (11)
Jeu 00X (2.00 -11) + 10 (3V (11 - 00) = 8 (200 - 11) sid hoc non licet
 si esset A Nec lient facere 11 = 0D, nam eonnescenst V in Calculo. Nec licet facere H = 3I, nam fircet 32: 31 = 12: 11
(sit 11+ 31 = d seu  31 2 = 11. firet 00 (iA (00 -2. 11) 4 (11 = 00) V (00 4 212)( : (90 + 2. 11.)(1) = - 11 (00 - 2.11):00
Si esset 00. - 11 + 31 = 0 fieret 12 = 0, et  sed hoc qua
Si esset H- 00== 11
si sit 30+11 = 0 parum lucramur, ut et faciendo 00 +31 =0
EZsR.d ita ascenditur ad _ quod nolim.
non licet quia fieret 1-00
1 = 00. et ubique depressio fiet per Mr, lasleed ete 11 et 31
contrahetur calculus tamen haberetui repro si fint H
habetur depressio et fiet 211 =
ascendetque calulus non nisi ad gradum secundum  dutque  31 = 21+ 00 et fint -00 A (2. 00 +11) + (11-
andes casus impossibiles a
firra ut et tint
Ct 00 + 11 = 311
ot Zandem habebimus: -6.00. 00 X - 3v0. 1X + C. 11. 1V FocinY A. 00.4Y =c. voV = 2. II. IIX + +. 00. 11 +00.11X 200.00X
sea (2A = 51) 11. 1 + (Z, 00 X = 3. 00Y) 1 f +: 8. 00. 00X + 3, 000oY  0. et fiet a  2~) Hc-∞) L ( 1to
Sed non video quomodo potuisset deprissioe obtineri usque ad gradum infimum Li posset amen ad huc tenturi fingendo
sdae in intoris t  a piict iberum Encdi in casus impossibiles. Plud tanen adiue habemns
possunt esse affirmativae vulnegativae pro arbitrio
medium contra imposibilitates l valore ipsus i1, quod s ad huc linasuptias iquptio, et id co 3 assumere
VO +is
quod in ABC