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A C B ABCD adjacent angles altitude angle equal arc A B B A C base bisect centre chord circle circumference circumscribed cone convex surface cosecant cosine Cotang cylinder D E F diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed interior angles isosceles less line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism Problem Proposition pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B side B C similar slant height solve the triangle sphere spherical polygon spherical triangle tangent Theorem triangle ABC triangle equal trigonometric functions Trigonometry vertex
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 95 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 172 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their common section, will be perpendicular to the other plane.
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 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 94 - In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals.
Page 102 - 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'.