## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 37

Page 182

...

...

**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

... triangle is a portion of the surface of a sphere , bounded by three arcs of great circles . These arcs are named the sides of the triangle , and are always supposed to be each less than a ...

... triangle is a portion of the surface of a sphere , bounded by three arcs of great circles . These arcs are named the sides of the triangle , and are always supposed to be each less than a ...

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

Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . In every

Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . In every

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

...

...

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

...

...

**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 , let ...### Other editions - View all

### 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