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LVI. Jn Explication of an obfcure PaJJage 
in Albert GirardV Commentary upon Simon 
StevinV Works (Vide Les Oeuvres Ma- 
them. de Simon Stevin, a Leyde, 1634, 
p. 169, 170) ; by Mr. Simfon, Profeffor 
of Mathematics at the Univerfity of Glaf- 
gow : Communicated by the Right Honour- 
able Philip Earl Stanhope. 
Read Dec. 
>7 53 - 
20, 
fC 
cc 
( c 
P UIS que je fuis entre en la ma- 
<e tiere des nombres rationaux, 
j’adjoufteray encore deux ou trois particularitez, 
non encor paf cy devant pradtiquees, comme d’ex- 
pliquer les radicaux extremement pres, Gfc.” 
The firft thing Albert Girard gives in this place is 
a method of expreffing the ratio of the fegments of a 
line cut in extreme and mean proportion, by rational 
numbers, that converge to the true ratio. For this 
purpofehe takes the progreffion o, 1, 1, 2, 3, f, 8, 13, 
2 r , &c. every term of which is equal to the fum of 
the two terms that precede it : and fays, any number 
in this progreffion has unto the following the fame 
ratio ("nearly] that any other has to that, which fol- 
lows it. Thus y has to 8 nearly the fame ratio, that 
8 has to 1 3 ; confequently, any 3 numbers next one 
another as 8, 13, 21, nearly exprefs the fegments of 
a line cut in extreme and mean proportion, and the 
whole line; fo that 13, 21, 21, ( N. B . 13 is wrong 
printed for the fecond number, inftead of 21) con- 
hitute 
