Posts tagged 'solid'
G.529 solid
A:term:**solid** <solid> is that which has length, breadth, and depth.
G.530 solid contained parallel
If a solid be contained by parallel planes, the opposite planes in it are equal and parallelogrammic.
G.531 parallelepipedal solid cut
If a parallelepipedal solid be cut by a plane which is parallel to the opposite planes, then, as the base is to the base, so will the solid be to the solid.
G.533 extremity of a solid
An:term:extremity <G.6> of a:term:solid <G.529> is a:term:**surface** <surface>.
G.536 describe on a given segment a parallelepipedal solid
Describe on a given segment a parallelepipedal solid similar and similarly situated to a given parallelepipedal solid.
G.537 prism
A:term:**prism** <prism> is a:term:solid figure <G.529> contained by:term:planes <G.7> two of which, namely those which are opposite, are equal, similar and:term:parallel <G.52>, while the rest are parallelograms.
G.538 parallelepipedal solid cut
If a parallelepipedal solid be cut by a plane through the diagonals of the opposite planes, the solid is bisected by the plane.
G.539 parallelepipedal solids base
Parallelepipedal solids which are on the same base and of the same height, and in which the extremities of the sides which stand up are on the same segments, are equal.
G.540 parallelepipedal solids base
Parallelepipedal solids which are on the same base and of the same height, and in which the extremities of the sides which stand up are not on the same segments, are equal.
G.541 parallelepipedal solids equal
Parallelepipedal solids which are on equal bases and of the same height are equal.
G.542 parallelepipedal solids height
Parallelepipedal solids which are of the same height are to one another as their bases.
G.543 similar parallelepipedal solids
Similar parallelepipedal solids are to one another in the triplicate ratio of their corresponding sides.
G.544 equal parallelepipedal solids
In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciprocally proportional to the heights are equal.
G.546 segments proportional parallelepipedal
If three segments be proportional, the parallelepipedal solid formed out of the three is equal to the parallelepipedal solid on the mean which is equilateral, but equiangular with the aforesaid solid.
G.547 segments proportional parallelepipedal
If four segments be proportional, the parallelepipedal solids on them which are similar and similarly described is proportional; and, if the parallelepipedal solids on them which are similar and similarly described be proportional, the segments will themselves also be proportional.
G.548 cube
A:term:**cube** <cube> is a:term:solid figure <G.529> contained by six equal:term:squares <G.63>.
G.550 there prisms equal
If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the parallelogram be double of the triangle, the prisms is equal.
G.553 pyramid
A:term:**pyramid** <pyramid> is a:term:solid figure <G.529>, contained by:term:planes <G.7>, which is constructed from one plane to one:term:point <G.1>.
G.556 pyramids height triangular
Pyramids which are of the same height and have triangular bases are to one another as the 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.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.
G.593 octahedron
An:term:**octahedron** <octahedron> is a:term:solid figure <G.529> contained by eight equal and:term:equilateral triangles <G.13>.
G.596 icosahedron
An:term:**icosahedron** <icosahedron> is a:term:solid figure <G.529> contained by twenty equal and:term:equilateral triangles <G.13>.
G.599 dodecahedron
A:term:**dodecahedron** <dodecahedron> is a:term:solid figure <G.529> contained by twelve equal,:term:equilateral <G.13>, and equiangular pentagons.
G.600 construct a dodecahedron and comprehend it in a
Construct a dodecahedron and comprehend it in a sphere, like the aforesaid figures, and to prove that the side of the dodecahedron is the irrational segment called apotome.