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Elements of Geometry: With Practical Applications to Mensuration
No preview available - 2016
Elements of Geometry; with Practical Applications to Mensuration
No preview available - 2012
ABCD adjacent angles altitude angle ACB base bisect centre chord circumference circumscribed cone convex surface cylinder diagonal diameter divided draw the straight edges equal angles equal Prop equiangular equilateral triangle equivalent exterior angle four right angles frustum given straight line gles greater homologous homologous sides hypothenuse inches inscribed circle interior angles intersection isosceles less Let ABC line A B line CD mean proportional measured by half multiplied number of sides parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron prism Prob PROBLEM PROPOSITION pyramid quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area right angles Prop right-angled triangle Scholium secant line segment side A B similar slant height sphere spherical polygon spherical triangle square described tangent THEOREM triangle ABC vertex
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 101 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles triangle, in which the side AB is equal to the side AC ; then will the angle B be equal to the angle C.
Page 36 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 166 - ... the same, or a like inclination to one another, which two other planes have, when the said angles of inclination are equal to one another.
Page 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.