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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 192r, page id 00068201:0383
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de tormulis condivisibilibus. Continent et subtationem incognitarum
O= 20X + 21, H, 10X + 11 ut habeant communem divisorem A8X + 21 +20F 10. 21 = 11. 20)
20xX +21 X + 22+20x + 1 ,d.
20X + 21X + 25 et 10X + 11, ut habeant communem divisorem si procedemus: 1o s 10X + 1 1onumo,, et fit 10. 22 - 1B. 1121 +1 . 2d
et  20X + 21X + 22X + 23, et 10X + 11, dividenda prodit primum 30 X, et residuum primum est 21 - 1 XX, + 22 X + 23,
undi continuanda divisionem per thcorema proxime praecedens, prodit bco 20, 21, 22, ibi positorum pori devent 20. 21- 1130, 22, 25
Unde quotiens divisionis est 2 X + 10 21 - 1120 X + 18. 22 - 10. 11. 21 + 1. 1120  O et fit 18. 22 =10 10. 11. 21+ 1011. 1. 21 - 113.3020.
Et ita datur procgressus in infinitum, nam semper quotiam  fit ex quotiente praecedente una cum residuo per demul
10. 10
10. 10. 1
se quasi nihilo non aequali, totum multialicando per X; et quoliens residuus novus nihilo aequandus fit ex praecedente
pergamus ad 9 = 20XX + 21X + 22, B:, 1oXX + 11X+ 1. primus quotieus est d odsione igitur instituta
tantum pro 20 ponendo, 10,21 - 11. 20, : 10
primus quotiens est 20: 10, et primus residuus est 21 - 1120. 10X + 22 - 12. 20: 10. Et per hunc divideno 10XXI UXt
res reditud  aeq. 4. 5. 10. et sit equatio loco 20, 21, 22,, 10q 1 ponendo y: 10, 11, 12, E 19. 21 - 11. 29: 10, 50. 22- 12. 20: 10,
tunc ex ag. 6. fiet aequatio nostra ultima, X carens, 2 10. 21 - 11. 20(.16d-11121 = 11. 20. 10.22 -12. 20(10 10. 22- 12. 2010)
quotientem quaerene operae pretium, non est, cum nec in integris dari possit. Caterum si multiplcationem
in aequideta cie ipso debent sese eedem mois haber 1o, altu ubi abest 1o ut feri possito oo itiu
o= 10. 12. 21 - 2. 10. 11. 12. 20. 21 (+ 12. 12. 20) + 102 22,5- 2. 10, 12. 20. 22 +1 10: 12. 20 - 10. 11. 21. 22(4 10. 11. 12. 20. 214 1011.. 0n ( 1. 1220
rursus secundum
et ultimus character
12. 28 11. 20. 22  2 21012. 20. 2tas bteras assumtas ejus demensionis quam
et postremo, institian, qua sit, ut 20, 21, 22, se habeant ut 10, 11, c2, et 20 ut 22, et 10 ut, 12.
puto praevideri posse initio ox regulis artis combinatoriae, ponento omnia possibilia membra, in quibus quatuo snt
Nota ex his 10, 11, 12, 1, 14 15 20, 21, 32; cavendo ut sunuva c, et summa cyphrarum ultimarum
nam  sic in 18. 22, seu 10. 10, 22. 22 summa eyphrarum postremarum
0+0+2 +2 esst 4, in 12 26. seu 12. 12. 20. 20. similiter est 4ull 10. 12. 21, seu 10. 12. 21. 21 est 0+ 2+ 1+ 1, seu itidem 4.
im notis ejusdem membri non excecat 4.
et ita in caeteris, investigari quoque poterit, quando debeant praefigi signae + et L, et quamio numeri quidam
veri coefficientes, sint adhibendi ut biliarius in. 2. 10. 12. 20. 22.