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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
A B C ABCD altitude base called centre chord circle circumference circumscribed common cone consequently construct contained convex surface cylinder described diagonal diameter difference distance divided draw drawn edges equal equal Prop equilateral equivalent EXAMPLES faces feet figure formed four frustum given gles greater half hence homologous inches included inscribed intersection join length less magnitudes manner mean measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perimeter perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid radii radius ratio rectangle regular remain right angles rods Scholium segment shown sides similar slant height solidity sphere spherical square straight line tangent THEOREM third triangle triangle ABC vertex VIII whole
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.