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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 341r, page id 00068196:0677
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ppoliia trausici posse
Hoc loci tamen videntur omnia minus
1. stit (t
(31.2. 20 A2 21
4
Ar  Ex aeg. 3. fit 180. 34d = 20. 1a+30 (3) 2t. 1r1, +ba
2. 10. 30,50
faciamus
110. 2. 1 -72. 20
50, 10. 3( - 11, 30 690= 50, 10. 31 - 11. 30
han
equ. 5. fil. 10. 340 = 10. 21 + 11 20 + 20. 31+ 21.38
2. 50. 10. 31 + 11. 30 40. 30ba
benique ex
Unde ex aq. 9 fit 1031. 2031 + 11. 2030. 31  10. 1. 21. 30 + 10. 21. 30. 31C vel 20l1)1030,. 11F31
Ex 10 et 8. fil 20. 104 30. 10.31Y1130  10.30. 21. 10+ 30 + 10. 30. 20. 11431 fit 20
,. 16. 36 100
10470. 10. 31+ 11. 30 - 10. 30. 114 31
Ex 10 et 9 fit 21. 11431. 10. 31+1130 = 11. 31. 20. IF31 + 11.31. 21 Fo1 50 fit 21 C) 11.31- M F2
possemus jam jungere egq, 13 et 15. qui ambos leges homdeoplotorum observant, 11131. 10. 3) + 130 - 11. 31. 102
ed praestat
tamen alteratiam harum Conjungere cum aeg. 11, nam eo ipso quia sic proditiae quatio
quae si non observat leges homoe oploton, necesse est quaedam in ea evanescere, ut ad homveopu
F homoeoploton redigatur; cum, quae hc proditura est, sam tum sit simplicior
quam quae ex 14  13 et 15 orietur, 2an ex 1 et 13
10+30, 11+31, 1031 +430 = 10. 30. 1143,  = 11. 31. 10F30
fiet
sit 10+ 50. I+ 31 1931 +130 = 10. 30. II431 + 11. 31. 10 + 50 quoe aefontio est honocoptotos
quod si fiugeremus 1 10430 = 11 + 31 ifieret 10. 31 + 11. 30 = 10. 30 + 1. 3) e ex 1 per1s. fere    3
jam quaeramus 140. 340 ex b et 7. fiet 140346 = 2. Y18.31 282] - 10. 14 21. 2 - 3034 30 20 + 11. 30. 20. 21
50. 10. 31 = 11. 30 et fiet
ubi numeratorem explicemus, et primum pro 21 ponamus 20. 11. 31: 10.30 ex aequ. id
10. 3(. 20. 21 = 10. 11. 21.21 - 30. 31. 20. 20 + 11. 30. 20. 21 = 20. 2
10, 30, 11 31, . 31 + 20. 1 = 10 31. m  B. M1. M. 31. L. 10. 30. 3. 3o = . 10. 11. 31.31. 10.3∞ - 1. 15 + 10. 30. 3031. 1111 - 10.30
10. 10. 30. 30
Ergo ex numeratore epharento fit 20. 20. 26. 3,  1. 3130. 30, 10.30- 11. 1 L
10. 10. 30. 3
aliter 10. Z0  H31 -30. 30 + 30. 30, 1. 1- 10 50
aieoque fit 1010 =  10 
31. 20  H1. 1.28 31, 16. 11 26. 31 = 30 30, - 2. 40. 3, 110 30 1 M, 1131 3030
A13. 3B3, 10. 30 - 11 a
10. 31 = 11.3 antequam
a contrahi adhuc amplius calculus in aeg. 21 possit,
eam quadremus, p  lollamus inde prius  et it et 31 quorum valores quaecenus ope ce 9g. 17. et 18.
ex ag. 17. fit _ 31 = 10+ 30 - 11 quo valore substituto in req. 18 fit 10. 10(410.30 -10. 11 H(11. 39 = (0. 3d + 11. 16 13 . 1 1
Contequam   Uet vero apparea
seu 10.10 + 11. 11 - 2. 10.11 = 0 seu 10 -11 = 0 seu 01 1 = 10
 E Et similiter 31= 30 ita in aeqqu. 6 et 7. evaneselrent 140 et 340, nec invenitentur
sed arbilrae sed semi arbitrarcae manerent, facto tantum ex ipsis dato; et
lunde fiet  10. 1t0 - 1) = 11. 10 - 11 
ex aequ. 6. 1t fier (explicata 21) fieret 10.30 - 111. = 0 et 11. 31 - 30. 30 =0, ande ob 22 et 23
feret 30= 10 _ utrobiqus, quod placet, quod ita non prodit nimia determinatio
sed video jam in quo peccaperim, omsomisi perliceti ba, sunt. ex XX + ba
tende falsae aequ 1. 14, 15. itaque rem resumamus
 20, 10+30. 11. 31 = 10. 30. 21. 31+31 + 10. 30b9 et fit
10. 30. . 11+ 31. Et ex 8 et 10 fol 20. 160430. 10. 31 +11 50 = 1033, 10021 + 103. 142, 2
1 sd ergo nunc in aeg. 4 suppleo
sed quia in C3 et n rursus labet 140.340 et fit 21= 20, 10+ 30. 10. 31F11. 50 = 10. 3a. 1+31 3: 10. 20, 10430- Quos duos valores ptru 21 exegg. 11. et 13.
ompe ex
ideo haec aequalio aeque equemue inter se, et fiet: it. 3e 10r 10. 11. 30. 31. 1ot 30 20 - 10. 10. 30. 3c. 101 30 ba = 10 10. 11 31. 10. 3( 1130. 2
1on3o 31.1 0 130 f. 1010,103B, 1131 - o+ 30. 113) 1 t 38 .
- 10. 10.3030. 11+31 29, et fit 20  (8, 10110. 30. 30 1at30 ba
10.11. 30.31. jer30 +. 10. f6. 3630. 1143, = 16.36. 104 30. 1143,. 10314430 10 vel 9 vel 10
Ego per 13 et 1sfit 2(1) 16. 3b ba 00. 31+11. 30 - 10. 30. 112)
31. 20 = 11. 21=10.21 ∞ 30.20
tollendo 140, 340 ex
fiet 140= + 340. Ergo opus est adhuc duab,s literis habemus autem arbitraries ad huc residuas:
Superest tantum una investigenda aequatio
ope a99.  6 et 7. s videamus an non licept facere
sed ita jam prodit ncommodum, quod non praevideram, et cujus remedium in hoc
calculo non apparet, quod nempe ex a (ut aq. 1 reperta est, ita similiter
10, 11, 30, 31 
ficilt 21 = 11. 31. 70 ∞ 10+ 30 = 10. 30 ca : 60. 36. 11+31 unde sequitur absurdum, fore a
Nec video quomodo hoc evitars queat, si Xx + ac et Xx+ ac
ponantur illud = 0∞ 5, hoc 59G Ergo, non licet facere ut O et e similiter se
ba = ca seu b =c
habeant cum inde hoc loco oimodum aequalitas sequatur, secusfuisset, si  sit ecrammpo adrata
 Motandus hic usus considerationis similim. sed factis ergo C et 
valore dissimilibus, perit fructus  divulionis, ut x tac et xxaac separatim aequentur
cateu  alicui