Elements of Geometry and Trigonometry |
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Page 18
... Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ( Def . 3. ) ; hence AC + CB is greater A ...
... Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short- est distance between the points A and B ( Def . 3. ) ; hence AC + CB is greater A ...
Page 19
... ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB ... Let the side ED = BA , the side EF BOOK I. 19.
... ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB ... Let the side ED = BA , the side EF BOOK I. 19.
Page 21
... Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . For , if these sides are not equal , suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC ...
... Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to the side AB . For , if these sides are not equal , suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles BDC ...
Page 29
... Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . A D For , produce the side CA towards D , and at the point A , draw AE parallel to BC . Then , since AE , CB , are parallel , and CAD cuts them ...
... Let ABC be any triangle : then will the an- gle C + A + B be equal to two right angles . A D For , produce the side CA towards D , and at the point A , draw AE parallel to BC . Then , since AE , CB , are parallel , and CAD cuts them ...
Page 30
... ABC , the exterior angle BAD is equal to the sum of the two interior opposite angles B and C. For , AE being ... Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B. AC , AD , AE , AF , be drawn to ...
... ABC , the exterior angle BAD is equal to the sum of the two interior opposite angles B and C. For , AE being ... Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B. AC , AD , AE , AF , be drawn to ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex