Elements of Geometry and Trigonometry |
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Page 31
... opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , the triangle will be isosceles ...
... opposite to them are also equal , and consequently , the triangle is isos- celes . In the triangle ABC , let the angle ABC be equal to the angle ACB : then will AC be equal to AB , and consequently , the triangle will be isosceles ...
Page 32
... opposite the greater angle ; and , conversely , the greater angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then will the side AB be greater than the side AC . C For , draw CD ...
... opposite the greater angle ; and , conversely , the greater angle is opposite the greater side . In the triangle ABC , let the angle ACB be greater than the angle ABC : then will the side AB be greater than the side AC . C For , draw CD ...
Page 38
... opposite sides of the secant and without the other two lines . Thus , AGE and FHD are alternate exterior angles . 5 ° . OPPOSITE EXTERIOR AND INTERIOR ANGLES , are those that lie on the same side of the secant , the one within and the ...
... opposite sides of the secant and without the other two lines . Thus , AGE and FHD are alternate exterior angles . 5 ° . OPPOSITE EXTERIOR AND INTERIOR ANGLES , are those that lie on the same side of the secant , the one within and the ...
Page 39
... opposite exterior and interior angles equal , the two straight lines will be parallel . Let the angles EGB and GHD be equal : Now EGB and AGHI are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGH and GHD ...
... opposite exterior and interior angles equal , the two straight lines will be parallel . Let the angles EGB and GHD be equal : Now EGB and AGHI are equal , because they are verti- cal angles ( P. II . ) ; and consequently , AGH and GHD ...
Page 41
... opposite exterior and interior angles will be equal . The angles DHG and HGA are equal , from what has just been shown . The angles HGA and BGE are equal , because they are verti- cal : hence , DHG and BGE are equal . In like manner ...
... opposite exterior and interior angles will be equal . The angles DHG and HGA are equal , from what has just been shown . The angles HGA and BGE are equal , because they are verti- cal : hence , DHG and BGE are equal . In like manner ...
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Common terms and phrases
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence