Posts tagged 'extremity'
G.3 extremities of a segment
The extremities of a segment / A B / are points A, B.
G.6 extremities of a surface
The extremities of a surface are lines or arcs.
G.8 boundary
A boundary is the extremity of anything.
G.10 circle
A circle ( A B ) is a plane figure contained by one arc defined by a center A and a point B establishing its defining radius / A B /, such that all segments / A B /, / A C /, / A D / falling upon the arc from A are equal.
G.20 transfer a segment to a point
Construct at a given point a segment equal to a given segment.
G.28 uniqueness of triangle sides on a base
On the same segment and on the same side, there cannot be constructed two distinct triangles with both pairs of conterminous sides equal.
G.29 congruent triangles by SSS
Triangles with all three corresponding sides equal have their corresponding angles equal (SSS).
G.46 interior segments of a triangle
Segments constructed from the endpoints of one side of a triangle to an interior point have a lesser sum but contain a greater angle than the other two sides.
G.60 segments joining equal and parallel segments
Segments joining the endpoints of equal and parallel segments in the same directions are themselves equal and parallel.
G.65 parallelograms on equal bases in the same parallels
Parallelograms on equal bases and in the same parallels are equal in area.
G.74 construct a parallelogram equal to a polygon
Construct, in a given angle, a parallelogram equal in area to a given polygon.
G.118 perpendicular at extremity of a diameter is tangent
The line drawn at right angles to the diameter of a circle from its extremity falls outside the circle, no other line can be interposed between it and the arc, and the angle of the semicircle is greater than any acute rectilineal angle.
G.119 draw a tangent to a circle from a point
From a given point, construct a line tangent to a given circle.
G.138 angle in a circle segment
An:term:**angle in a segment** <angle-in-segment> is the:term:angle <G.22> which, when a:term:point <G.1> is taken on the arc of the segment and:term:segments <G.4> are joined from it to the:term:extremities <G.6> of the segment which is the:term:**base of the segment** <base-of-segment>, is contained by the segments so joined.
G.141 construct a circle segment on a chord admitting a given angle
On a given segment, construct a segment of a circle admitting an angle equal to a given rectilineal angle.
G.145 converse of the tangent-secant theorem
If from a point outside a circle a secant and a segment to the circle are drawn such that the rectangle on the whole secant and its external part equals the square on the segment, the segment is tangent to the circle.
G.146 segment fitted into a circle
A:term:segment <G.4> is said to be:term:**fitted into a circle** <fitted-into-circle> when its:term:extremities <G.6> are on the arc of the:term:circle <G.10>.
G.154 inscribe a circle in a triangle
Inscribe a circle in a given triangle.
G.160 inscribe a circle in a square
Inscribe a circle in a given square.
G.165 inscribe a circle in a regular pentagon
Inscribe a circle in a given equilateral and equiangular pentagon.
G.504 planes cut common
If two planes cut one another, their common section is a segment.
G.527 there plane angles
If there be three plane angles of which two, taken together in any manner, are greater than the remaining one, and they are contained by equal segments, it is possible to construct a triangle out of the segments joining the extremities of the equal segments.
G.533 extremity of a solid
An:term:extremity <G.6> of a:term:solid <G.529> is a:term:**surface** <surface>.
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.545 there equal plane
If there be two equal plane angles, and on their vertices there be set up elevated segments containing equal angles with the original segments respectively, if on the elevated segments points be taken at random and perpendiculars be drawn from them to the planes in which the original angles are, and if from the points so arising in the planes segments be joined to the vertices of the original angles, they will contain, with the elevated segments, equal angles.
G.549 sides opposite planes
If the sides of the opposite planes of a cube be bisected, and planes be carried through the points of section, the common section of the planes and the diameter of the cube bisect one another.
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.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.