Elements of Geometry and Trigonometry |
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Page 141
... solid angles will wholly coincide . This coincidence , however , takes place only when we sup- pose that the equal plane angles are arranged in the same man- ner in the two solid angles ; for if they were arranged in an in- verse order ...
... solid angles will wholly coincide . This coincidence , however , takes place only when we sup- pose that the equal plane angles are arranged in the same man- ner in the two solid angles ; for if they were arranged in an in- verse order ...
Page 179
... solid described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- B scribed by BCEF will be the difference ΕΑ C D of the two cylinders described by AFBD ...
... solid described by ABC will , in that case , be the difference of the two cones described by ABD and ACD ; but at the same time , the cylinder de- B scribed by BCEF will be the difference ΕΑ C D of the two cylinders described by AFBD ...
Page 204
... solid angles at the vertices of these pyramids , are also as their bases ; hence , for comparing any two solid angles , we have merely to place their vertices at the centres of two equal spheres , and the solid angles will be to each ...
... solid angles at the vertices of these pyramids , are also as their bases ; hence , for comparing any two solid angles , we have merely to place their vertices at the centres of two equal spheres , and the solid angles will be to each ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC 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 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex