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 Charles Davies. 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 ...
Adrien Marie Legendre Charles Davies. 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 ...
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 . B 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 . B 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 centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex