## Elements of Geometry |

### From inside the book

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Page iii

... work , under the title of an Introduction . The parts onitted in the first edition of this translation on

... work , under the title of an Introduction . The parts onitted in the first edition of this translation on

**spherical**isoperimetrical polygons , and on the regular poly- L513 1300 485457 234126 edrons , are inserted in this , at the end. Page vii

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**spherical**triangles . This treatise does not ordina- rily make a part of the elements of geometry ; still we have thought it proper to consider so much of it as may form an intro- duction to**spherical**trigonometry . The fourth section ... Page 157

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**spherical**triangle is a part of the surface of a sphere comprehended by three arcs of great circles . These arcs ...**spherical**triangle takes the name of right - angled , isos- celes and equilateral , like a plane triangle , and under ... Page 158

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**spherical**wedge the part of a sphere com- prehended between the halves of two great circles , and to which the lunary surface answers as a base . 447. A**spherical**pyramid is the part of a sphere comprehended between the planes of a ... 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 ...### 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