Elements of Geometry and Trigonometry |
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Page 156
Adrien Marie Legendre Charles Davies. For , having placed the two I solids AG , AZ , so that their surfaces have the common angle BAE , produce the planes necessary for com- pleting the third parallelopi- pedon AK having the same ...
Adrien Marie Legendre Charles Davies. For , having placed the two I solids AG , AZ , so that their surfaces have the common angle BAE , produce the planes necessary for com- pleting the third parallelopi- pedon AK having the same ...
Page 157
Adrien Marie Legendre Charles Davies. the solids , and will serve to express ... solid ; thus we say the solidity of a rectangular parallelopipedon is equal ... angle , which is nearly of the same species . The solutions of which such ...
Adrien Marie Legendre Charles Davies. the solids , and will serve to express ... solid ; thus we say the solidity of a rectangular parallelopipedon is equal ... angle , which is nearly of the same species . The solutions of which such ...
Page 161
... solid angle ; in that case , there will be formed as many partial pyramids as the polyedron has faces , minus those faces which form the solid angle whence the planes of division proceed . If a pyramid be cut by a plane parallel to its ...
... solid angle ; in that case , there will be formed as many partial pyramids as the polyedron has faces , minus those faces which form the solid angle whence the planes of division proceed . If a pyramid be cut by a plane parallel to its ...
Page 163
... solid an- gles B and b , are similar , like placed , and equally inclined to each other ( Def . 17. ) : hence the solid angles B and b , are equal ( Book VI . Prop . XXI . Sch . ) . If these solid angles be applied to each other , the angle ...
... solid an- gles B and b , are similar , like placed , and equally inclined to each other ( Def . 17. ) : hence the solid angles B and b , are equal ( Book VI . Prop . XXI . Sch . ) . If these solid angles be applied to each other , the angle ...
Page 165
... solid angles at the vertices may be made to coincide , or the two pyramids may be so placed as to have the solid angle ... angle Sab is equal to SAB , and Sbc to SBC ; hence the plane ABC is parallel to the plane abc ( Book VI . Prop . XIII ...
... solid angles at the vertices may be made to coincide , or the two pyramids may be so placed as to have the solid angle ... angle Sab is equal to SAB , and Sbc to SBC ; hence the plane ABC is parallel to the plane abc ( Book VI . Prop . XIII ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex