Posts tagged 'equilateral'
G.13 equilateral, isosceles, and scalene triangles
Of trilateral figures, an equilateral triangle < A B C > has three equal sides, an isosceles triangle < D E F > has two equal sides, and a scalene triangle < G H K > has three unequal sides.
G.17 construct an equilateral triangle
Construct an equilateral triangle on a given segment.
G.63 square, oblong, rhombus, and rhomboid
Of quadrilateral figures, a square is equilateral and right-angled; an oblong is right-angled but not equilateral; a rhombus is equilateral but not right-angled; a rhomboid has opposite sides and angles equal but is neither equilateral nor right-angled.
G.163 inscribe a regular pentagon in a circle
Inscribe an equilateral and equiangular pentagon in a given circle.
G.164 circumscribe a regular pentagon about a circle
Circumscribe an equilateral and equiangular pentagon about a given circle.
G.165 inscribe a circle in a regular pentagon
Inscribe a circle in a given equilateral and equiangular pentagon.
G.166 circumscribe a circle about a regular pentagon
Circumscribe a circle about a given equilateral and equiangular pentagon.
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.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.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.585 angles equilateral pentagon
If three angles of an equilateral pentagon, taken either in order or not in order, be equal, the pentagon is equiangular.
G.586 equilateral equiangular pentagon
If in an equilateral and equiangular pentagon segments subtend two angles taken in order, they cut one another in extreme and mean ratio, and their greater segments are equal to the side of the pentagon.
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.589 circle diameter rational
If in a circle which has its diameter rational an equilateral pentagon be inscribed, the side of the pentagon is the irrational segment called minor.
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.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.