Question about Cg and the Speed of Gravity in Newton's Theory

[MathematicalPhysicist]

i read in scientific american that in Newton's theory of gravity the speed of gravity was proposed to be infinite.
my question isn't this implying that the distance and/or time are also infinite (if so, doesn't it defie Newton's theory[and thus contradict itself]?)?

 

[Integral]

Infinite speed of gravity is fine with Newton, it only runs into trouble with Einstein.