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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 58r, page id 00068197:0115
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si omissa hypothesi quae aequationem tuctabilibrem reddere conati sumus, cogitemus de m: hfficiendi ut
etiam 50 fiat 0, seu ut V exteminetur ex valore ipsius X, (.) et relaquendo v in vilore
ipsius D, evitando tantum us fiat 20: 60 = 12:56, alioqui C firet consans; cipi sane hoc modo
ita incipiemus ab aequatione fecunda per quam detem
minabitur relatio inter 40 et 20, et ex aeq. 2. firt 20. 20 - 2. 20. 40, aa = 60. 60 ab = 60 169βB
Unde fit 60.60β3+ 20. 20aa = (. 2040 a a seu 20. 20aa - 2. 2040aa + 40 40aa = 40. 4ua a 608
seu 20= 40 = 1(40. 40+a - 60. soβ3) Tubi posito 20 = 40 firret 40a = 60β = 20a
Et posset feri 20 = 40 = Et posset fieri 60 = a et 20 = β = 40. d video hoc non + licere nam  ob
 Valorem ipsius 60. 60. hac aequatione repertum, substituamus in aequ. 1
(40. 40 B(3(= 20,403(3) - (2)40. 403β (- 20.  β() - 2. 20. 477 + 20 20y. ende tandem, fiet
digmeni inter q
1oV, sequalisminao
2. 40. 20)B ir. 20do)(
seu 40 - 20γ. β = 2(207: B8) (V . BB)
seu 40 = 40  :20 = VC VBCt + y (V BB): BB
ita pro d sumetur quae est major.  ponamus 20 = ββ:)
et, 2.qu  20 foret 2() + 2 (W - BB)  PB, : 7 sed
hinc deveret posse extrodicadi ut 60 fieret rationalis
ho non ficta duulsione aeliquamus ronem 40 = 20) GStiss
sia o bo B B A 2. 40 -20 = 20   (  1)= ws  B et = BC)) -1
n casuparceu an
28+ 92 + 89 = 3 8
Et ficiendo 60 = 20) fiet s) 2 = 2) (B + sC 1Y - pB) =
ut quod videtur coremedissimum D = na aa BB
fier 20 (V ((t SY. 18)- 1 eto 0 a: 
Tentem, aliquid amplius nempe videamus an liccat
fucere simul 50= et 5b =0 quil aa ita extribus
agrationibus 1, 2, 3, poteriuus invenire non
sulum 6020, sad vitasse etiam vatorem
ipsius a quiest adhuc ratitiar. Et 2c 60  opus
Ex aequa, un 50= sit eo ol- 9 - 3
60. 60 ab = 20a4 (20 -240) Cx aeg. 2. ubi 5
690 aC = 40 a4 (40 -2. 20) ex s p. 3
fi jam ab = -BB et ac = - 7)
20Y (20 - 2. 40) = 405β (40 -2. 20) Uende het
X -2. 25. 40 βB
20.20)) = 2. 20. 40)7 = 40. 40 B 1 . - B3(2
seu 20. 20)7 -40. 40 ββ-= 2. 20.40
siu Z  =g (3 + 1)
et 5 = 215E:, 8-5
30 = E, 25, 5. 4: 3 - 125. 81 3) = 100.
2.4020): βB + 20267 (20 10
fint 40 = β+ (9X (() Etato lo torete
a W co -88t 5 y fit 30 = 2, 4 E
2H et 99- 55, H X 
 guE, t218
ee
aequifieret b =c
3t 75. S1. SGA  3 Z, qu ( +5)
sin 3
fint 60. 60 = (20) 40 (10 - 20) aa ; quBβ - 2077 = (20(a, 240 - 20, :BB unde tandem fiet
Er, qu  ts) .00
magnem in caleudo stragem dabimus.
I= YH. nstace t 1. (rad Pa r fudi
B 2. 10. 40 + 4040 = 2
et 2ond 82 2040 (7) () +gosatulY. PC)
seu 20 207) 1 2020)
se prastat abstiere ab hypulles
=4090+ 40. 4e qu (pr - 16)
= 40,40,  ( + t + 1 a sip eV
et 20 20 =2.40 = 40 (  V- BBYB):
2e - H(VE 1Y)) + 277
20. 20 B-. 1 L. 20. 40 V BC + 40. deq u Y. A(B) = 40. u q u (B7. 11) 1 40. 4088 =
1 = 40 1(+  - Vee
preniter fici t 50 =d
  - B2 + s ( 4 yiBB 68)
38. 71 + e. 1 
1-γ1) = 2020 qu (8P. 17) = 20 2e p. (2. 7)) + 2020Y
quaesissemus prodisset calculus talisa
duc holop  tin 40 = 20 BB  =  20  rya- CY + () ber 1
il fit sCB. pppy + G 4) = 2   s X eB a0 ∞B - no BP+ 20)) Ll7o)1. ros 1 190 
40. 10 P1. 40. 29 (B
fit ev. 40 ββ - 20. 40 ββ +20. 40 6) = 20. 20)7 - 20. 4017) +20.40 BB
pV LY+ seri, Besto. (B. (Y B in 40. 40 (B - 2. 20, 40β3(3 = 20. 20γ7 - 2. 20. 40)) out ante.
. qap
=(1 ay. 2) 20 aa (2 40 - 20): B( = (ex a9. 3) quaa (2. 40. 40): . Ex (est (40. 10 20. 40  B(
nunc etiam aequationem cum 2da vel tertia conjungamus. Ex
a y H ed CC Y  = (2, 40. 40 (353 4291207Y  20. 40 (3 - 2. 20. 40)). Er ex 1 et 3tio valorefer
2. 20. 403β3= (2) 20. 20)) - 40. 40β( ( 20. 40)) ita quas duas aecpation
(6. 40Y) 20 20 uninagendo sit
icafem ien fieret BB = V)
pncrione ipsins 50. sa ex
1e 60
c:
baa (40020) ; (B = 20Y, et ceq. 40. 40 BB + 10. 1) 1 7
59 et c6 simal destracre
r. 
e
i
12 = 2, 25, 5. 3, : 4 = 125. 3: 2 = 325
(1 20.46+40. 40a 460. 20)
=2. 125) sungsia eq. ds o est
aJ. 2. 50b0 7 2o) Hari jure si 2
Rpostet esem 160(oe XV)
Af Sni
fia gf  da +Bac + na vY