Elements of Geometry and Trigonometry |
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Page 145
... S - ABCDE , of which SO is the altitude , S be cut by the plane abcde ; then will Sa : SA :: So : SO , and the same for the other edges : and the polygon abcde , a C b will be similar to the base ABCDE . E D First . Since the planes ABC ...
... S - ABCDE , of which SO is the altitude , S be cut by the plane abcde ; then will Sa : SA :: So : SO , and the same for the other edges : and the polygon abcde , a C b will be similar to the base ABCDE . E D First . Since the planes ABC ...
Page 162
Adrien Marie Legendre Charles Davies. Let S - ABCDE be a pyra- mid cut by the plane abcde , parallel to its base ; let T - FGH be a triangular pyramid hav- ing the same altitude and an equivalent base with the pyra- mid S - ABCDE . The ...
Adrien Marie Legendre Charles Davies. Let S - ABCDE be a pyra- mid cut by the plane abcde , parallel to its base ; let T - FGH be a triangular pyramid hav- ing the same altitude and an equivalent base with the pyra- mid S - ABCDE . The ...
Page 165
... S common . S ? e a 6 E D In that position , the bases ABCDE , abcde , A will be parallel ; because , since the homolo- gous faces are similar , the angle Sab is equal to SAB , and Sbc to SBC ; hence the plane ABC is parallel to the ...
... S common . S ? e a 6 E D In that position , the bases ABCDE , abcde , A will be parallel ; because , since the homolo- gous faces are similar , the angle Sab is equal to SAB , and Sbc to SBC ; hence the plane ABC is parallel to the ...
Contents
BOOK | 7 |
BOOK III | 41 |
Problems relating to the First and Third Books | 57 |
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Common terms and phrases
adjacent altitude angle ACB ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang 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 number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM 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