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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 188r, page id 00068194:0375
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NNan hoc modo facilius apparet quae possint innicem conjuns
gi et abbreviari multiplcatio etiam et divisie facilius fiet:
exempli causa scribumus
5ab f + af b - 2 abfb - b+ egb + e
ordinando secundum b. fiet
b X +5 afb + afb +c
-2af + eg.
sive - b X + 3afb + afb +8
+ etg
Nota: qualitates quae gradum sive potentiam ipsius b multi
plicant, snempe quadrato quadratum b cubum b quadratum b
simplicem dignitatem b) appellari solere voefficienites, ita in
termino primo-s
b per - 1 dat - b2) et +3af est coefficiens in termino 3afb et
tota quantitas composita af t eg est coefficiens in termino +a
fb. et solet interdum compendu causa pro integra ejus mo
dis quantitate poni una literi ut pro af + eg poncinclo 
(sire supponendo k aequ. a f + eg) tunc pro ab seu pro uf b
+ egb. fiet: Sib
c
Jam ut explicemus multiplicationem divisionem et extractionem
Sciendum est illa fieri posse eluobus modis scilicet tum pet sim,
plicem indicationem tum per actualem operationem per simplis
cem indicationem sic siet multiplicatio, ponamus olebere
a + b maltiplicari per c + d, scribemus: a +b c+ d perinde enim
est acsi pro aib per compendium ponendo e et pro et d ponen,
dof, scripsissemus ef. Si vero ita scriptemus. a + b + cd sens
sas soret ad a debere addi b +c et seu prodluctum ex multiplica
tione ipsius b+C in d et proc ponendo g tunc loco a+ b+ cd
fiet a +gd.
Nonnulli alii a +b debere multiplicari per c+ d ita signifiare
selent: a +b X C + d item sic: a + b, c+d.
Actu ipso autem multiplicatio fiet hoc modo.
a + b
C + d.
tad + bd
+ac + bc
a + b
a
UbOD
+ aa + ab
summa tac tad + bd + aa X - bb
et bc
quod af b