by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]
[Central Entry Directory]
[Mathematics, Calculus, Geometry, Entry Directory]
[Archimedes, Quadrature of the Parabola, Entry Directory]
Archimedes
Quadrature of the Parabola
Proposition 19 [quoting]
If Qq he a chord of a parabola bisected in V by the diameter PV, and if RM he a diameter bisecting QV in M, and RW be the ordinate from R to PV, then
PV = 4/3 RM.
For, by the property of the parabola,
PV : PW = QV2 : RW2
= 4RW2 : RW2,
so that PV=4PW,
whence PV =4/3RM.
Archimedes. “Quadrature of the Parabola.” In The Works of Archimedes. Ed. T.L. Heath. Cambridge UP, 1897. Obtained at
https://archive.org/details/worksofarchimede00arch
No comments:
Post a Comment