## Elements of Geometry and Trigonometry |

### From inside the book

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Page 182

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**sphere**( Prop . X. Cor . ) : hence the solidity of a**sphere**is equal to its surface multiplied by a third of its radius . Scholium 1. The solidity of every**spherical**sector is equal to the zone which forms its base , multiplied by a ... Page 186

... spherical sector , H the altitude of the zone , which forms its base : the solidity of the sector will be 7R2H . Let P and Q be the two bases of a ... triangle , any 186 GEOMETRY . BOOK IX Of

... spherical sector , H the altitude of the zone , which forms its base : the solidity of the sector will be 7R2H . Let P and Q be the two bases of a ... triangle , any 186 GEOMETRY . BOOK IX Of

**Spherical Triangles**and Spherical Polygons, Page 187

Adrien Marie Legendre. PROPOSITION I. THEOREM . In every

Adrien Marie Legendre. PROPOSITION I. THEOREM . In every

**spherical triangle**, any side is less than the snm of the other two . Let O be the centre of the sphere , and ACB the triangle ; draw the radii OA , OB , OC . Imagine the planes ... Page 188

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**spherical triangle**is less than the circumference of a great circle . Let ABC be any spherical trian- gle ; produce the sides AB , AC , till they meet again in D. The arcs ABD , ACD , will be semicircumferences , since two great circles ... Page 192

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**spherical triangle**, as poles , three arcs be described forming a second triangle , the vertices of the angles of this second triangle , will be respectively poles of the sides of the first . From the vertices A , B , C , as poles ...### Other editions - View all

### 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 convex surface Cosine 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 logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex