## Elements of Geometry |

### From inside the book

Page 155

... are the angles of the triangle . 443. A

... are the angles of the triangle . 443. A

**spherical triangle**takes the name of right - angled , isos- celes and equilateral , like a plane triangle , and under the same circumstances . Fig . 220 . 444. A spherical polygon is a Of the Sphere . Page 157

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**spherical triangle**ABC ( fig . 222 ) either side is less Fig than the sum of the other two . Demonstration . Let O be the centre of the sphere , and let the radii OA , OB , OC , be drawn . If the planes AOB , AOC , COB , be supposed ... Page 158

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**spherical triangle**is less than the circumference of a great circle . Demonstration . Let ABC ( fig . 224 ) be any**spherical triangle**; produce the sides AB , AC , till they meet again in D. The arcs ABD , ACD , will be the ... Page 159

Adrien Marie Legendre. THEOREM . 462. The sum of the sides of any

Adrien Marie Legendre. THEOREM . 462. The sum of the sides of any

**spherical**...**triangle**AFG ; but this last is less than the circumference of a great ...**sphere**, we can suppose at the point O a solid angle formed by the plane angles ... Page 162

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**spherical triangles**may be compared with each other by means of the arcs of great circles , described from their ... triangle ABC ( fig . 227 ) being given , if , from the points A , B , C , as poles , the arcs EF , FD , DE , be described , ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence