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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
# Folio 7v, page id 00068002:0014
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Quodsi quis malit non tantum larionem in exemplo, sed
ari.
eti repraelentri, sed etiam universaliter oculis subjici velit
phuic vota sa fisfiet
huic ita risfiet s t
e- 1
sit dividendus +10X FUX inX etc. usquead (A)X essenru  mad finet
Divisor - 20X +21X 1 22Y etc
e.n
Proveniensis
Quotiens BOX +31FP. n- 1
txn
Residens 3e) 43(DX + 3(C. 9X etc usque ad 3(e nH1) X inclusive
Residuns
-20 X + 2, Xn -1 + 22 Xn-2 et
ubi (e) significit es vel le 1) signisia etc significat notam ultimam coefficientis
prodibit coefficientium quidem inque votiente valor qui paulo ants
ante; sed coefficientium Residui valor sic enuntiandus erit
ut s quoniam e indeterm indefinita eum non ingreditur;
sed Residui valor in residuo coefficientium valor ita
proveniet: 32) = 00. 1(2) + 2(n). 3 (C -n), : 00 et 3 (e-1) = 00. 1 (C-1)
+2 (n - 1). 3 ((-n) + 2(n). 3 (C - n - 1), : 00 et 3(P -2) = 00. 1 (e- 2)+
2 (n - 2). 3 (C-n) + 2(n - 1). 3 (( - n - 1) + 2 (7). 3(- n - 2), :00. Et ita porro
pergendo usque ad  3 (C n + 1) inclusive
Ex eo autem quod pro coefficientibus quaesiti quotientis
idem se dat valor, quicunque sit gradus divitor dividendi aut
divisoris. illud mmodi consequimur, ut eadem opera possimus
egregium
vel finitum exhibere quotientem, et ub cum suo residuo,
vel continuata divisione in infinitum ex sine quotiente
vel neglecto residuo et continuata divisione in infinitum, valone
quotientem invenire in formula quidem rationali integra, sed
in infinitum procurrente, id est per seriem infinitam. prossus
et in communi calculo Decimali; sed majore c longe fructu,
 analytico, quod serierum hc datur progressus facilis, quod non aeque in
porro.
fractionibus decimalibus in promtu est; unde hic non tam appro-
pinquationes quam veri valores licet serie infinita expressi exhi-
bentur. Sic si divisur ponatur esse dividendus ponatur
esse  et divisor R 10X sen  et dividet divisor sit
obtineamus inverso ordine incipiarmns ab inferioribus termin
sed ut hoc melius consequamurponamus Ddividendum esse
~ 20X F Z1
10 + uX + 12X + 13X3 + 14 X, erc. et divisorem esse - 20 + 21X + 22X
+ etc. Provenientem autem quotientem (neglecto vel dissimulato
Residuo) esse 30 +31X +32 X + et. fiet ducendo quo eum in
divisorem fit - 20. 30  = 20. 3X - 20. 31X - 20. 33X etC
quae
+21. 30 +21. 31 + 21. 32
nda est
+22. 30 +22. 31
+23. 30
oformula coincidentiacum sequenbi, posito 0o significare - 1
200. 10 - 00. HIX = 00. 12X - 00. 13X et C
et patet eosdem quae prius pro 30, 31, 32, pd 33 etc prodire valo
res. Hinc si  poneremus 11, 12, 13, 14 etc. Item 22, 23, etC
aequari h nihilo, seu terminos, quorum sunt coefficientes abesse
redibitur ad exemplum jam cognitum, ul seu 10 debet dividi
per -20 +21X, qu et 36 erit 00. 10: 20. et 31 = 24. 30: 20 seu 00x 10.20
et 32 = 21. 31: 20 seu 4 00. 10. 21: 203 et 33 = 21. 32 : 20 seu 00. 10, 28. 20
Et ita porro hinc fiet 14 Hiac si sit 20 = - a et 21 = 1 et pro 00
on prr 1a effe r, et 00 c = (ut supposuimus) esse r. perinde est ac si
1 dividi debeat per a +X, et pro ob ponendo -1; pre to,t; pro 20, na
pont,  fiet 30 +: a et 31 = = i: R et 32 = + 1: 3, et 34 = - 1: 4
atx
quidem constabat
ut si e sit 8, uti in exemplo
paulo ante posito sit siat
3 (() quide538, et 3 (2. 1) HC3
et ita porro. His positis
idem erit mex in  1 (8) id est 18
vel 1(e- 1) id est 17. Et cum n
in eodem exemplo fuerit 5,
eit utique 2(1) erit 25 et 3 (C- n)
erit 33. His positis