## Elements of Geometry |

### From inside the book

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Page 157

... 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 159

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**spherical triangle**ABC ( fig . 222 ) either side is Fig . 222 , less 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 ... Page 160

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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 161

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**polygon is less than the circumference of a ...**triangle**AFG ; but this last is less than the circumference of a great circle ( 461 ) ; therefore , for a still ... Page 164

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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 ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence