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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 350r, page id 00068196:0695
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per 4 et 63
per 13. )aegul (B) n3. 123n + 100. 112f = 313, 323n + 300. 31h  112. 123m + 100. 113f = 312. 327M + 300. 313a
seu a) 100 () +313. 323n + 300031 h, : 12  +312. 323M + 300. 313h, : 113  100f qua alores
12. 123
aequando fiet. 300h 12 312. 323 m 4 113, 113, 1231,:, 112. 313-113.312 et pari jure permulando 3.. et 1..
in his duobus valore
oppotis ynisfiet
=112. 112. 123,1 = 113. 323.313
100 f+,2. 1n3. 312M + 313. 313. 313N, :, 113, 312 = 112. 313
- 312. 312.323..- 113. 123.313..
s
similiter per aequ. 7 et g itemque 4 et 6 fiet:
nhis duobus valoribus
n et l differunt ut 23 et (3)
oppositis siguis
Aex 13 et 14, permutando l et n, item R. 12 et .23
123. v2. 323 m + 313 1B. m l,:, 1333L1 13. 313
1
- 323. 323. 312.- - 113. 112.313..
= 123. 123. 112 . = 113. 312, 313.
=p2. 113. 123. 3r2. 323)M + 113. 313313213. 323n 4 112. 113. 127. 312. 323 M
n
Aequando valorus 13 et 15, fiet
=112. 123, 123.312. (213
 123. 313. 313. 343). 323
327
- 113. 113 123 (31
.
113. 31. 31 2313313)L
= 112. 317. 313. 313319..
= 112. 112. 123.313,323
=113. 312. 312. 323.323).= 112. 113. 113.312813..
+ 112. 312. β313) 323323.. + 112. 112. 113,313BB..
Agmerdind pe Mecta N L et n differunt ut. 12 et .23, item m es una parte ab m ex altera parte 
+123, 312. 312313, 325 1. - 113. 123. 123. B13)317
113. 312 312. 313. 325)
intera quando valores 14 et 16  prodibit aequatio (19), quae ab aequ. 17 differet sola perimration
It teth
nemal
in lest 42 et 213 et quidem loci
12 eto 23
12
 ea  ontes
initialium notarum 3 et  l et n) differunt ut 012 et 12Z ouB
et M ab
in hac aequatione 17 itemque mabipera parte
x
it
b
13
erat
ab altiqoinquam latere, vel quod idem est, in eodem sed oppositis signis; si mulque ibidem
qudestruendis, factaque divis
prodilne er aequatione  3
a
ut s
Similiter aequando valores 4 et ab, prodibit aequatio fig), quae ab aeqiy differet sola
permuatione initialium notarum 1.. et g. et eadtem lges quae in aeq.1, locum hrabebunt
3
 in ltjor
E t tota combinationis lex ratio sic explicari potet: in lest. 12( et + e quarto
in lest  12 et ∞13 Has notas posteriores in quovis Amosunit
I
n
quinto
012 et 023 voco correspondentes quatuor quantitates
B et 023 in litera a qua
divessarum literarum memora
oppes uidem signi sunt quae duo
habent producentis communes
sed mota ultiali et 3
ocunno
pantuus, quaet
una in prmbro
in iis utraque notarum
semel, altera tet
nascircur. Quodris membrum continet duos producentes aequales
Ad eadem literam cuivis
n opponitur
aliud diversum.
nota initiali
sta
posteriore corrispondn
iael
ae possibile seu est prena
es hac lege possibiles seu est plena
Nempe similiter aequando valores ipsius h duos nempe ex aeq. 19 et 16 prodibit aequatia 19)
quae ab eod aequatione 17 in eo solo difert, quod permutantur 1 et 3. Sed quia
opos  cont
iprodbit ex procedenti lege combinationis differt in speciem tantum; nam quia ex corollario
etiam coincidunt item quod aequatio
legis combia ationis paule anl ante posito omnes combinationes nobalinitiali  et 3, et posterio
Fribus 12, 13, 23, secundum literas l, m, n prodeunt in aequatione 17,  nec aliquam novam combi-
inandi materiam  legem praebet aequ. 19. necesse est eam  coincidere, cum aequ. 
jam praebeat
Unde aequatio valorum h,  ex aequ. 14 et 16, nihil praebet, quod non exhibeant puestitis et omissis
13, 14, 15, 16,t
sumere initio 2i, 2423, 24
aquabiae valorum f ex aegu. 13 et 15. Quod feliciter evenit
322 + 159 = 3 + 16a jumque 25, 26, 27 28, 29
22m+ 239= 1 + 267
sana s esset p = () ron tun rn +  14f
1242 (ad 41t 245=
 + 35g = 13 t. +3Es
3n taS = 33n = 16fr. sit f =+ 9 + 16h, : 14 ut a 345 = 131 + 3bh. fit f- l
(7) = H l. + 34
31M. 7,9. ita et procedemus ex valoribus 1, 2; 4, 5; 2, 8
(34
prodibunt
3 et 2, et pro E ponitur 4. et fiet f = (20) ut 13 et . 2009 = (21) at 14 et 1005. (22) utls et 2009 23) e
Porro ut prolissimus ex a valoribus 113; 4, 67
qum Etsi autem superfluum sit ultra progredi, post quam enim aequabimus ub quae ex 1.. et
et .. M +.. n =()... M +..  ut 14 pro 3. ponendo 2..
quae ex 3.. itemque quae rex 1.. et quae ex 2.. etiam aequabuntur quae ex 2. et quae ex 3..
38s29 quae ab ipsis 20 (21, 22, 297
praestati tamen et aec postrema ascribere, nempe a49. 23, 26, 
2009 = (26) ut 14 et 30oh = (27) ut 15, et 2009 = (26)  16 et .m +. B = (29). M +. l, ut 17 tantum
(29
hot solo different quod pro manente 2. pro t
1. ponendo 2 (24 tuI2M. 113 21 l + (13. 113. 227. 22G A((in ag. (4 31. 3n.313. 2yM L +31. 312. 313 21 L +319)31, 213 213 n
1alago (Fu2. 1Z. 12 V3M= -2. 22. 213. 43
12. 212, 723, 133
24 eit = Ar. 123. 123. 12
4, 27. 212. 212. 123
Haec sex aquationam
=112. 113. 113. 212.
4113. 21222. 213
membra ponamus
t rao . B) + s. s a f  ut big it
= 113. 212. 223. 2235 29eri - 312. 12. 213. 28. =312. 213213,215. - 313. 213, 23, 2270
-1B. 213. 213. 21)
4113. 123, 123. 213
aea
2. g Bi 
= 312. 323 43. 212. 3t. 313. 313. 212. 343, 213. 213. 23.
+3123. 212. 212223. 4313. 212. 212. 213. 4313.523,313.213.
 limus bis, quam
 aib; et
vis ex his terminis quansitalibus 22, 3  +bf9 20
212, 223 ponendo f9 fint +
f. itus or (99+bb) t. (6 +2 b9g1 b 4bb9a
+ 46. 438 1. h b69 vrgo bel a 5 b. 9 vil c 15 = 3b 360