Elements of Geometry and Trigonometry |
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Page 96
... angled , the one at D , the E other at A : also the angle B - E ; these tri- angles are therefore similar , and they ... solid , for a reason that shall be seen afterwards . Its value is easily con- ceived , by imagining that the lines ...
... angled , the one at D , the E other at A : also the angle B - E ; these tri- angles are therefore similar , and they ... solid , for a reason that shall be seen afterwards . Its value is easily con- ceived , by imagining that the lines ...
Page 126
... angle or mutual inclination of two planes is the quan- tity , greater or less , by which they separate from each other ; this angle is measured by the angle contained between two lines , one in each plane , and both ... Solid Angles,
... angle or mutual inclination of two planes is the quan- tity , greater or less , by which they separate from each other ; this angle is measured by the angle contained between two lines , one in each plane , and both ... Solid Angles,
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
... angle ASD < ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a solid angle is always less than four right angles . Cut the ...
... angle ASD < ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a solid angle is always less than four right angles . Cut the ...
Page 140
Adrien Marie Legendre Charles Davies. Let the angle ASC = DTF , the angle ASB ... angled at A , and the triangle TDE at D ( Prop . VI . ) : and since the angle ... solid angles are contained by three plane angles , respectively equal to ...
Adrien Marie Legendre Charles Davies. Let the angle ASC = DTF , the angle ASB ... angled at A , and the triangle TDE at D ( Prop . VI . ) : and since the angle ... solid angles are contained by three plane angles , respectively equal to ...
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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