Elements of Geometry |
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Page 158
... 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 ...
... 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 spherical polygon is less than the circumference of a great circle . Demonstration . Let there be , for example , the pentagon ABCDE ( fig . 225 ) ; produce the sides AB ...
Adrien Marie Legendre. THEOREM . 462. The sum of the sides of any spherical polygon is less than the circumference of a great circle . Demonstration . Let there be , for example , the pentagon ABCDE ( fig . 225 ) ; produce the sides AB ...
Page 162
... spherical triangles may be compared with each other by means of the arcs of great circles , described from their vertices as poles and comprehended between their sides ; thus it is easy to make an angle equal to a given angle . 473 ...
... spherical triangles may be compared with each other by means of the arcs of great circles , described from their vertices as poles and comprehended between their sides ; thus it is easy to make an angle equal to a given angle . 473 ...
Page 164
... spherical triangle DAB are equal to those of the triangle CAB , namely , DAB = BAC , DBA CBA , and ᎯᎠᏴ = ᏁᏟᏴ ; therefore the sides and the angles of the triangle ADB are equal to the sides and angles of the triangle ACB . = 479 ...
... spherical triangle DAB are equal to those of the triangle CAB , namely , DAB = BAC , DBA CBA , and ᎯᎠᏴ = ᏁᏟᏴ ; therefore the sides and the angles of the triangle ADB are equal to the sides and angles of the triangle ACB . = 479 ...
Page 165
... spherical triangle the angles opposite to the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle is isosceles . Demonstration . 1. Let AB be equal to AC ( fig . 231 ) ; we say Fig ...
... spherical triangle the angles opposite to the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle is isosceles . Demonstration . 1. Let AB be equal to AC ( fig . 231 ) ; we say Fig ...
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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