Important Discoveries in Plane And Solid Geometry Consisting of the Relation of
Important Discoveries in Plane And Solid Geometry Consisting of the Relation of
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(Prop. C, Preliminary Demonstra- tions. ) Then through the point m, with radius Am, draw the circle SmWX, and the circumference of that circle is equal to the perimeter of the square BCDE.
Now let the perpendicular nm be the least possible part or division of a straight line, a mere point, and we see that it is half the side of a polygon whose perimeter is equal to that of the square, and whose sides are capable of only one division or bisection, and as the circumference of a circle, which is e...qual to the perimeter of a polygon, both having the same center, must intersect each side of that polygon in two places, the points of intersection being equally dis- tant from the middle of the side, therefore, the circum- ference SmWX must intersect the perpendicular nm, but nm being a mere point, cannot be either bisected, inter- sected, or divided further. Therefore the circumference SmWX must pass over and coincide with the perpendic- ular or point nm, which represents half a side of a polygon, and hence it must pass over and coincide with the remain- ing half of that side, consequently it must pass over and coincide with each and every side comprising the whole perimeter of that polygon, and the point is reached where the final figure loses its identity as a polygon, and assumes and contains all the properties of a complete circle, as rep- resented by the circle SmWX.
What to read after Important Discoveries in Plane And Solid Geometry Consisting of the Relation of?
You can find similar books in the "Read Also" column, or choose other free books by P D Patrick Daniel Woodlock to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(Prop. C, Preliminary Demonstra- tions. ) Then through the point m, with radius Am, draw the circle SmWX, and the circumference of that circle is equal to the perimeter of the square BCDE.
Now let the perpendicular nm be the least possible part or division of a straight line, a mere point, and we see that it is half the side of a polygon whose perimeter is equal to that of the square, and whose sides are capable of only one division or bisection, and as the circumference of a circle, which is e...qual to the perimeter of a polygon, both having the same center, must intersect each side of that polygon in two places, the points of intersection being equally dis- tant from the middle of the side, therefore, the circum- ference SmWX must intersect the perpendicular nm, but nm being a mere point, cannot be either bisected, inter- sected, or divided further. Therefore the circumference SmWX must pass over and coincide with the perpendic- ular or point nm, which represents half a side of a polygon, and hence it must pass over and coincide with the remain- ing half of that side, consequently it must pass over and coincide with each and every side comprising the whole perimeter of that polygon, and the point is reached where the final figure loses its identity as a polygon, and assumes and contains all the properties of a complete circle, as rep- resented by the circle SmWX.
What to read after Important Discoveries in Plane And Solid Geometry Consisting of the Relation of?
You can find similar books in the "Read Also" column, or choose other free books by P D Patrick Daniel Woodlock to read onlineMoreLess
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