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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23
# Folio 4v, page id 00068236:0008
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et quomam generaliter constat esse a vel majus vel certe
non minus quam vb. itaque haec sucurrit methodus generalis
ut pro a substituendo vb sit certi sumus ipsi a attribuisse
vatorem ve non justo majorem, et pro a substituendo
vs+ b. Certi simus attribuisse valorem non justo minorem,
Est autem fct in aequ. _ 11. fractio: vvabb + a- b3. ergo
va3
(15)
aergo
pro aponendo vab fier haec fractio: v3b + vb- b seu 20- B
D463
Ulnde statim patet, si p sit HD. esse procedere sub tractionem
et loco aequ. 11. scribemus aa aequ 2. aequ. 14. sed
si vp1. erit V p.2V- 1um Nam si ve2. foret v,
seu vep 2V2- 1 seu v p v - 1. sed si v p. erit v p 203
ergo multo major qu vi multo p 2V - 1.
Si vero pro a ponamus vb + b. tunc ex fractione
aequationis 11. fer  (add. aequ. 15) fiet:
3
vvvb+ Vvb + vV + 3Vb + 3vb+ b3- b
9a b + 3V b+ 3V b + vb3
aequ.
aeqo 2V + 4 v +3V, ubi itidem posito vaequ. 1. est
v3 + 3V+ 30 + 1
nominat numerator major homina
tore. sed posito v p. 1. marti
fistum est, nominatorem festum fore majorem, nec proinde
amplius subtrahi posse, itaque, sive aa ratio a ad b
assumatur justo major, sive justo minor, semper ut idem
provenit. Ut ergo generaliter loquamur, sumendo
loco V, V aequ 1 1 () fiet primus quotiens:
++ (V) dividendo a por b fiet primus quotiens 2
1 + (V) secundus 1 + 2(v) + (v;
si aequatio 1. b+ vaeb aequ De a. fiet 
aequ  V +
ubi B significat 1. quando
v0 + + v aequ. 1. sed 0, quando Yp 1-
etc.
residuum autem primum erit a- vb. quod subtraedo mulliplum
per v + subtrahendo _ a b. fiet residuum secundum -va + h.
t
-
Videamus an jam possimus conie absque superiori illa consideratione
rationum ex ipsa aequatione ductarum, nunc porro progredi
Nempe a refiduon omisso (compendii causa) + videamus
an possimus  quaerere quotientem non novum per
quem multiplicari debet tresiduum novissimum. va +vb+b
ut quantum satis est sub trahi possit a praecedenti a - vb sit ille
Quotiens quaesitus n. Ifiet:
- v
tea + 17
+nsa - nv ib ubi pro
a substituendo vb deber esse = v 
nPan ubi res non succedit, quia sumta
josto minor. Sumatur ergo a aequ Vb+ b fiet X+1 + pB n + nV in
ili vol lunedit, atitus enim it moo pn. Vitnter sumitui jam 1F
bon