11. A Prisma is either a Pentaedrum, or Compounded of pentaedra's.
Here the resolution sheweth the composition.
12 If of two pentaedra's, the one of a triangular base, the other of a parallelogramme base, double unto the triangular, be of equall heighth, they are equall 40. p xj.
The cause is manifest and briefe: Because they be the halfes of the same prisma: As here thou maist perceive in a prisma cut into two halfes by the diagoni's of the opposite sides.
Euclide doth demonstrate it thus: Let the Pentaedra's aeiou, and ysrlm, be of equall heighth: the first of a triangular base eio: The second of a parallelogramme base sl, double unto the triangular. Now let both of them be double and made up, so that first be aeioun. The second ysrlvf. Now againe, by the grant, the base sl, is the double of the base eio,: whose double is the base eo, by the [12 e x]. Therefore the bases sl, and eo, are equall: And therefore seeing the prisma's, by the grant, here are of equall heighth, as the bases by the conclusion are equall, the prisma's are equall; And therefore also their halfes aeiou, and ysmlr, are equall.
The measuring of a pentaedrall prisma was even now generally taught: The matter in speciall may be conceived in these two examples following.
The plaine of 18. the perimeter of the triangular base,