Posts tagged 'parallelepiped'
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.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.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.