squares, cubes and reciprocals of natural numbers

Computed trigonometric functions

laws of nature as laws giving a dependence of one quantity on another

relations between variables, mapping between sets, one to one correspondence

"...other kinds of lines which, in a given figure perform some function."

composition of a variable and constants

1755, functions of x

one quantity depends on another

dependence between functions

abscissa x and ordinates f(x), not necessary a common law

required it to be continuous

Modern Definition

Precise definition, for a x,y,z, f(x)=y and f(x)=z, then y=z