P. HISTORY OF ' AATHEMATICAL - School of Mathematics

CONTINUED FRACTIONS, INFINITE SERIES 51
since in printing when proceeding hurriedly, one cannot conveniently
form fractions, and fractions of fractions, in this form
as here we are forcing ourselves to do it, we can easily denote all of
them by adopting this imitation
placing a point after the denominator 8. in each fraction, to signify
that the fraction following is a fraction of the denominator.") But, in
his simplified form of writing, as it appears further on in his book, the
point is not placed after the numbers in the denominator, but is
placed higher up, on a level with the "&." This is seen in Cataldi's
approximation to /18 (p. 71):
'(Di 18. la & sia 4.& +.& g.& go& g.& g.& 8
b vogliamo dire 4.1% +.& +.& +.& g.&
cioB 4.& +.& +.& g.& g.& &
b vogliamo dire 4.& 9.1% +.& +.& P &
che B 4.& g.& $.& g.& ,f&
cioB 4.& go& g.&
bvogliamodire 4.& g.&+ &$+
che B 4.& +.& #+
cioB 4. & &&$& ."
+.& t
Except for the "&" in place of "+," this notation conforms closely
with one of the modem notations.
425. We come next to Wdis' representation of BrounkerJs ex-
4
pression' for -, namely,
?r
1 John Wallis, Arithmetico infinitorurn (Oxford, 1655), p. 182.