Posts tagged 'inscribed-in-circle'

G.148 polygon inscribed in a circle

A:term:polygon <G.12> is said to be:term:**inscribed in a circle** <inscribed-in-circle> when each:term:angle <G.22> of the inscribed:term:figure <G.9> lies on the arc of the:term:circle <G.10>.

G.149 inscribe a triangle in a circle equiangular with a triangle

Inscribe in a given circle a triangle equiangular with a given triangle.

G.158 inscribe a square in a circle

Inscribe a square in a given circle.

G.163 inscribe a regular pentagon in a circle

Inscribe an equilateral and equiangular pentagon in a given circle.

G.167 inscribe a regular hexagon in a circle

Inscribe an equilateral and equiangular hexagon in a given circle.

G.168 inscribe a regular pentadecagon in a circle

Inscribe an equilateral and equiangular fifteen-angled figure in a given circle.

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.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.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.587 side hexagon decagon

If the side of the hexagon and that of the decagon inscribed in the same circle be added together, the whole segment has been cut in extreme and mean ratio, and its greater segment is the side of the hexagon.

G.588 equilateral pentagon inscribed

If an equilateral pentagon be inscribed in a circle, the square on the side of the pentagon is equal to the squares on the side of the hexagon and on that of the decagon inscribed in the same circle.

G.590 equilateral triangle inscribed

If an :term:`equilateral triangle <G.13>` be :term:`inscribed in a circle <G.148>`, the :term:`square <G.63>` on the side of the :term:`triangle <G.12>` is triple of the square on the radius of the :term:`circle <G.10>`.

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.

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.

G.601 set out sides

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