Elements of Geometry and Trigonometry |
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Page 138
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two , is ...
... solid angle is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two , is ...
Page 139
... solid angle S , is less than four right angles . Scholium . This demonstration is founded on the supposition that the solid angle is convex , or that the plane of no one sur- face produced can ever meet the solid angle ; if it were ...
... solid angle S , is less than four right angles . Scholium . This demonstration is founded on the supposition that the solid angle is convex , or that the plane of no one sur- face produced can ever meet the solid angle ; if it were ...
Page 140
... same manner that the inclination of the two planes ASB , ASC , must be equal to that of the two planes TDE , TDF . Scholium . If two solid angles are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .
... same manner that the inclination of the two planes ASB , ASC , must be equal to that of the two planes TDE , TDF . Scholium . If two solid angles are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .
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 142
... solid polyedron , or simple polyedron , is given to every solid terminated by planes or plane faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a ...
... solid polyedron , or simple polyedron , is given to every solid terminated by planes or plane faces ; which planes , it is evident , will themselves be terminated by straight lines . 2. The common intersection of two adjacent faces of a ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex