Principles. 
SECTION I. 
. Fonpamentat Pruxcirces or THe Tuzory or 
Fiuxions. 
Anticts I. In the branch of mathematical 
If ymax*4-b2+4c; or if y=s/ (a* bs) if Lim 
yoart+br+ y= oa y=e 
the quantities 
because ae are. supposed. 
to be ies conechaphes chen 
A quantity which d upon two or more variable 
Pree pome a function of these quantities : 
peer wn if y=at bey then y is called a function of v 
x 
giagith debsidend ans-tatetinwel sons 
i ee cet not di- 
recy expressed by tt quietgy:nedl wean auhagh 
Ebatcosting ails tot town: Thee 
the equation yma puet nae 
tion of 2, and, on the hand, « as a function 
= that 4+ this is ee dant 
to x, t= in case an im 
. ary, y 
‘dienes atin divided into algebraic and trans: 
cendental. Algebraic functions are such as, when re- 
FLUXIONS. 
duced to their proper 
terms, or ecient aoe. 
i 
ely ie lo rithm, o 
tna ithe isi ocboaeeetia 
then, in case, y is a 
4 A chiar notions ofthe tatusolie fahatibh dtarve- 
riable quantity ‘ecies be obtained by: 
_ 
ties may in like manner be’ 1 _geome- 
“on ‘which the 
other two, 
. The hypothesis, : may 
hich Pa state of tan a. ps 
. gives 
<ipropetty. with, beldsige’ 40. all tintin 
is the foundation of the theory of fluxions. 
The existence of this propérty re ea 
neral way, without any Fefercase, 061 ao 
examination cases, we: 
method, at least i in the outset! of a 
a, the function u to.w's tae wisndbige 
Srh? + h3,, therefore CoE Rpts mere 
od Av) 2% ren et er 
S343 204M, that is, , Hh ~ Aishoot 8 sare 
wv “5 
. ain , CH seg ners! ’ 
dirtes atau 
The first: meni of this nation is @ of 
= member we ere function 
; ms 
tobe entirely i Sapsabeicecien | ther 
: thas 
Ld See a Memoir in the 13th Cahier of Journal de L' Ecole Polytechnique, entitled, Recherches sor gustquesipehatsiile Aa Whderie de 
Ponctions derivées, Gc. By M. Ampére. 
+ Consulting brevity, we shall in general express any ratio by 7 fracticn ee ee ee eee eee 
the =a thus, the ratio of N to D will be expressed by the fraction © , and, consequently, the ratio of N. to 1 will be ex- 
sin ofthe ince 
dont ae , 
