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Topic: Keely Geometry Stack
Section: Geometry Proposition 14
Table of Contents to this Topic
An infinity in minuteness is always such, that it is capable of increase; therefore, in material things, an infinity equals one ultimate particle of matter, such, that in the nature of the material or thing under consideration, it cannot be less.
Axioms as proven herein and self evident:
First: The circumference of a circle is a line outside of the circle thoroughly enclosing it, and of itself forms no part of the area of the circle. (Proposition V)
Second: The line approximated by geometers, if it could be correctly determined, is a line coinciding with the greatest limit of the area of the circle, but not enclosing it. (Proposition I)
Third: The line approximated by geometers is consequently the circumference of a circle whose diameter is less than one in its relative value to the area of a circle. (Proposition I, III, IV & XIII)
Fourth: The difference between a line coinciding with the greatest limit of the area of any circle and a line enclosing the same circle, is an infinity, such that it cannot be less.
Fifth: In material things an infinity equals one ultimate particle of whatever material or thing is under consideration, such that it cannot be less. (Proposition XIV)
Sixth: An infinity is a value, such that it is always capable of increase. (Proposition XIV)