Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 41
... formed by a line cutting two parallel lines obliquely , the four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third straight line , making the sum of ...
... formed by a line cutting two parallel lines obliquely , the four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third straight line , making the sum of ...
Page 46
... forming the exterior angles a , b , c , d , e ; then the sum of these exterior angles is equal to four right angles . For , each interior angle , together with the corresponding exterior angle , is equal C / c to two right angles ...
... forming the exterior angles a , b , c , d , e ; then the sum of these exterior angles is equal to four right angles . For , each interior angle , together with the corresponding exterior angle , is equal C / c to two right angles ...
Page 50
... formed by a straight line meeting two parallels , is one - half of a right angle ; what is the other angle equal to ? 4. The sum of two angles of a triangle is of a right angle ; what is the other angle equal to ? 5. One of the acute ...
... formed by a straight line meeting two parallels , is one - half of a right angle ; what is the other angle equal to ? 4. The sum of two angles of a triangle is of a right angle ; what is the other angle equal to ? 5. One of the acute ...
Page 73
... forming Then CD is less AC and AD , and D greater than their difference ( B. I. , P. VII . ) ; which was to be proved . PROPOSITION XIII . THEOREM . If the distance between the centres of two circles is equal to the sum of their radii ...
... forming Then CD is less AC and AD , and D greater than their difference ( B. I. , P. VII . ) ; which was to be proved . PROPOSITION XIII . THEOREM . If the distance between the centres of two circles is equal to the sum of their radii ...
Page 81
... the angle DCB by half the arc DAB : hence , the two angles , Ө taken together , are measured by half the circumference : hence , their sum is equal to two right angles . PROPOSITION XIX . THEOREM . Any angle formed by two BOOK III . 81.
... the angle DCB by half the arc DAB : hence , the two angles , Ө taken together , are measured by half the circumference : hence , their sum is equal to two right angles . PROPOSITION XIX . THEOREM . Any angle formed by two BOOK III . 81.
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AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence