Posts tagged 'book-xii'
G.551 similar polygons inscribed
Similar polygons inscribed in circles are to one another as the squares on the diameters.
G.552 circles squares diameters
Circles are to one another as the squares on the diameters.
G.554 pyramid triangular base
Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the whole and having triangular bases, and into two equal prisms; and the two prisms are greater than the half of the whole pyramid.
G.555 there pyramids height
If there be two pyramids of the same height which have triangular bases, and each of them be divided into two pyramids equal to one another and similar to the whole, and into two equal prisms, then, as the base of the one pyramid is to the base of the other pyramid, so will all the prisms in the one pyramid be to all the prisms, being equal in multitude, in the other pyramid.
G.556 pyramids height triangular
Pyramids which are of the same height and have triangular bases are to one another as the bases.
G.557 pyramids height polygonal
Pyramids which are of the same height and have polygonal bases are to one another as the bases.
G.558 prism triangular base
Any prism which has a triangular base is divided into three pyramids equal to one another which have triangular bases.
G.559 similar pyramids triangular
Similar pyramids which have triangular bases are in the triplicate ratio of their corresponding sides.
G.560 equal pyramids triangular
In equal pyramids which have triangular bases the bases are reciprocally proportional to the heights; and those pyramids in which the bases are reciprocally proportional to the heights are equal.
G.563 cone part cylinder
Any cone is a third part of the cylinder which has the same base with it and equal height.
G.565 cones cylinders height
:term:`Cones <G.561>` and :term:`cylinders <G.562>` which are of the same :term:`height <G.209>` are to one another as their bases.
G.570 similar cones cylinders
Similar cones and cylinders are to one another in the triplicate ratio of the diameters in their bases.
G.571 cylinder cut plane
If a cylinder be cut by a plane which is parallel to its opposite planes, then, as the cylinder is to the cylinder, so will the axis be to the axis.
G.572 cones cylinders equal
Cones and cylinders which are on equal bases are to one another as their heights.
G.573 equal cones cylinders
In equal cones and cylinders the bases are reciprocally proportional to the heights; and those cones and cylinders in which the bases are reciprocally proportional to the heights are equal.
G.574 circles center inscribe
Given two circles about the same center, to inscribe in the greater circle an equilateral polygon with an even number of sides which does not touch the lesser circle.
G.577 spheres center inscribe
Given two spheres about the same center, to inscribe in the greater sphere a polyhedral solid which does not touch the lesser sphere at its surface.
G.578 spheres triplicate ratio
Spheres are to one another in the triplicate ratio of their respective diameters.