Elements of Geometry: With Practical Applications to Mensuration |
Common terms and phrases
ABCD ABCDEF adjacent angles altitude angle ACB angle BAC bisect centre chord circumference circumscribed cone consequently convex surface cylinder diagonal diameter divided draw the straight edge equal angles equal Prop equiangular equilateral triangle equivalent 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 opposite 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 rods Scholium secant line segment semicircle side BC similar slant height sphere spherical polygon spherical triangle square described tangent THEOREM triangle ABC triangular prism vertex VIII
Popular passages
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 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 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
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.
Page 159 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 38 - 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 254 - RULE. — Multiply the base by the altitude, and the product will be the area.
Page 35 - If a side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles.
Page 32 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line...