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[Commentary:
This and the pages that follow outline a general method of finding the area of a parabola,
based on the fact that sections of the parabola are in constant ratio to their inscribed triangles;
and the squares of those triangles increase as the cubes of integers.
The calculations on this page are for a parabola whose equation in modern notation is ; thus if the altitude of a given triangle is (the distance along the axis) then the base is (twice the ordinate). ]
The calculations on this page are for a parabola whose equation in modern notation is ; thus if the altitude of a given triangle is (the distance along the axis) then the base is (twice the ordinate). ]
1.) The triangles of the parabola. The first base by the
The bases.
The altitude.
The superficies of the triangle.
The superficies of the
The altitude.
The superficies of the triangle.
The superficies of the
The progression of the
The first triangles base passeth by
the
the
The progression of the numerators
of the
of the
Note.
Every triangle is of
his parabola.
Therefore as:
Triangle to triangle
so: parabola to parabola:
correspondente.
Every triangle is of
his parabola.
Therefore as:
Triangle to triangle
so: parabola to parabola:
correspondente.
The halfe triangles: or: parabolæ:
or: The rate of the triangles in minimis
or: The rate of the triangles in minimis
That is: the square of the first triangle
is the cube of 1.
of the second, the cube of 2.
of the third, the cube of 3. &
is the cube of 1.
of the second, the cube of 2.
of the third, the cube of 3. &