Elements of Geometry and Trigonometry |
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Page 194
... spherical tri- angle , as poles , the circumferences of two circles be described which shall pass through the third angle of the triangle ; if then , through the other point in which these circumferences intersect and the two first ...
... spherical tri- angle , as poles , the circumferences of two circles be described which shall pass through the third angle of the triangle ; if then , through the other point in which these circumferences intersect and the two first ...
Page 196
... spherical triangle , the angles opposite the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle is isosceles . First . Suppose the side AB - AC ; we shall have the angle C = B . For ...
... spherical triangle , the angles opposite the equal sides are equal ; and conversely , if two angles of a spherical triangle are equal , the triangle is isosceles . First . Suppose the side AB - AC ; we shall have the angle C = B . For ...
Page 197
Adrien Marie Legendre. PROPOSITION XIV . THEOREM . In any spherical triangle , the greater side is opposite the greater angle ; and conversely , the greater angle is opposite the greater side . Let the angle A be greater than the angle B ...
Adrien Marie Legendre. PROPOSITION XIV . THEOREM . In any spherical triangle , the greater side is opposite the greater angle ; and conversely , the greater angle is opposite the greater side . Let the angle A be greater than the angle B ...
Page 198
... spherical triangle is less than six right angles , and greater than two For , in the first place , every angle of a spherical triangle is less than two right angles : hence the sum of all the three is less than six right angles ...
... spherical triangle is less than six right angles , and greater than two For , in the first place , every angle of a spherical triangle is less than two right angles : hence the sum of all the three is less than six right angles ...
Page 199
... triangles make half a hemisphere , four make a hemisphere , and the tri - rectangular triangle is obviously con- tained eight times in the surface of a sphere . Scholium . In all the preceding observations , we have supposed , in ...
... triangles make half a hemisphere , four make a hemisphere , and the tri - rectangular triangle is obviously con- tained eight times in the surface of a sphere . Scholium . In all the preceding observations , we have supposed , in ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex