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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 8
# Folio 2r, page id 00068005:0003
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22, 2 + 83, 3 = 113 aqu
12, 2, 2 + 12, (3, 3 = (13)17 aequ. 0.
+C F12, 113 (aequ. 0 Ergo 3 so 22, 63 
290
13, 22,-
Et Z aequ 3,63, = 1, 113
1213, - 13, 22
12, 2 + (3, 3 + 14, 4. = 119 aequ. 8. 22, 2 + 23 3 + 24, 4  209agi 0. 32,2 + 38 3 424 299
V 12, 2 + 13, d - 63 aequ. 0
2)) 22 + 23,3 - 113 aequ. 0.
proba 12, 2 aequ. 24. 13, 2, aqu. 39. 39 + 244963
Proba: 32, 2, aequ. 44 23, 3 aequ 69 44 +69 aequ. 13
n 52. 2 Muctiplicatio reciproca aequationum per
() 12,222 + 12, 23, 3 = 12, 113 aequ. 0 peri  in 12 coefficientes incognitarum 2. 3.
6)413, 22, 3 -22, 63 aequ.0 aequ 3 - aequ. 4..
(6) 3  aequ. 23, 63 = 12, 113 4 aequ. 5. divita per 1372 - 12, 23.
-12, 23. +12, 113
13, 22  = 12, 23
25, 3 = 13, 113
12, 25 - 13, 22
14 aego - 63
24 equ 13
2, 63 aqu
1313
summa
+ 13, 22 aequ
= 12, 23
summa
Fit ad imitationem aequationis  mutatis mo
NAM, L invenitur ex 12. 22. 13, 23, 63, 113
in quo ingens calculi compendium consis
mutatis signis numeratoris pariter et nominatoris
in valore ipsius 2. in aequ. 7. Ratio mutationis
est, qu ut idem sit naminator
appareat aequationis valoris ipsius 3 aequ. 6. et
 1, 113 = 23,63
0020
aequ
qu i  + 133 F14. 4 - 19 aquio (troba. 24 + 39 + 56 aequ. 19 g0
10)) 12iL +233 + 24,  - 209 aqu. 0. Proba: 44 +69 + 96 aequ. 209
117. 32R. + 37,3 + 34, -299 aequ.0 proba: 64 99 136 aqu 299
Jam ut quam compendiosissime procedamus et praecedenti calculo hic
utamur, considerandum est esse
12)) 63 aequ. 119 - 14, 4 paq.   9 per aequ. 1. = aequ. 9.
per aequ. 2 = egu. 10.
quos valores literrum quantitatum 63. 113. substituendo in eorum
13)) 113, aequ. 209 - 24, 4
14) 2 aequ
proba.
Ut 3 invenitur ex 13, 23. 12, 22, 63. 113
ipsius 2. hic: 12, 113 aequ. 1469
(Proba :. - 2363 aequ 1449
summa
13, 22 = 12, 13
locum in valoribus quantitatum 2. 3. repertis aequ. 8. 6. e fiet:
13, 209 = 13, 24, 4 - 23, 119 + 23, 14, 4
13, 22 = 12, 23
Hi duo valores ducti intelliguntur ex
aequationibus 9. 10. qui si
substituantur in aequ. 11 habebitur
valor ipsius 4.
15) 3 aqu. 227 119 - 22, 14, 4 - 12, 209 + 12, 24 +
Nimirum in aequ. 11. multiplicando 34, 4- 299 per nominatorem ammunem valorum 2. 3.
13, 22 = 12, 23.
et pro ipsis 2. 3. sut in eadem, equatione 11. substituendo numeratores valorum, fiet:
16)) 13, 32, 209 - 13, 24, 32, 4 - 23, 32, 119 +  14, 23, 32, 2, 0  22, 33, 119 - 14, 22, 33, 4 - 12, 33 209 + 12, 24, 33, 4 .
e
soleo autem ne errem inter substituendum, separatim conside
Ubi notandum primo inter substituendum ac describendum solere ne exiguum semper instituers examen per partes
+ 13, 22, 34,4 - 13, 28229, - 12, 23, 34, 4 + 12, 23, 299
considerando separatim, signa, confficie terminos coefficientes. Sed quod palmarium hic est invenimus hic novissi
aequationem sine ula destructione, quod signum est caculi compendiose instituti nam quoties claque multa sub exitum
cietur, perumque signum est eo abintio vitari potuisse Bapitur quod autem nihil destrui possed, inihio potuit
 disi seaute
i e asficcas 
altera, nempe
 ecum goatiodis  des a an Pos. u
aulirm 3atiils. et . a l 1es. pae n printus un sutt
22,63 - 12, 113
13, 22 - (2, 23
+13, 22
= 12, 23
56
equ. 3
+10 ut supra
2,: 24
81o28
12, 12, 2 + 13, , 5 - 163, 2 aqud
+13 22, 3 d CB) 22,63
=12, 23..
12, 2 4 13, 3 = (63) aqu. 0
322 64
+ 13, 113 = 23, 63
aequ
+13,22 = 12, c3
aequ. 2.