Posts in category 'problem'

H G P F T O V Q U W R A E S B C D L M K N

G.240 segment apply parallelogram

To a given segment to apply a parallelogram equal to a given polygon and deficient by a parallelogrammic figure similar to a given one: thus the given polygon must not be greater than the parallelogram described on the half of the segment and similar to the defect.
B A C E D F H G K

G.528 construct a solid angle out of three plane

Construct a solid angle out of three plane angles two of which, taken together in any manner, are greater than the remaining one: thus the three angles must be less than four right angles.
H A L B E K G M D N C F

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.
O R U Q T P S X Z B V W K G C H A F E M L N D

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.
A B C D E F G H K L

G.592 construct pyramid comprehend

To construct a :term:`pyramid <G.553>`, to comprehend it in a given :term:`sphere <G.575>`, and to prove that the :term:`square <G.63>` on the :term:`diameter of the sphere <G.576>` is one and a half times the square on the side of the pyramid.
A B C D L E H K F G M

G.594 construct an octahedron and comprehend it in a

Construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the diameter of the sphere is double of the square on the side of the octahedron.
A B C D E H K N F G L M

G.595 construct a cube and comprehend it in a

Construct a cube and comprehend it in a sphere, like the pyramid; and to prove that the square on the diameter of the sphere is triple of the square on the side of the cube.
R Q L F E M Z P W A' V X G K S U N O H T A C D B

G.597 construct an icosahedron and comprehend it in a

Construct an icosahedron and comprehend it in a sphere, like the aforesaid figures; and to prove that the side of the icosahedron is the irrational segment called minor.
U X V M E F R N P S O B H C T W Z G Q K A L D

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.
A K C D L B G H E F M N

G.601 set out sides

To set out the sides of the five figures and to compare them with one another.