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 10
... shows how many times it is to be taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality , = : Thus , A of B and C. B + C , indicates that A is equal to the sum The expression ...
... shows how many times it is to be taken . Thus , 3 ( A + B ) , indicates that the sum of A and B is to be taken three times . The Sign of Equality , = : Thus , A of B and C. B + C , indicates that A is equal to the sum The expression ...
Page 49
... ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
... ; they are , therefore , equal in all respects : hence , the angles AEB , BEC , are equal , and therefore , the two diagonals bisect each other at right angles . EXERCISES . 1. Show that the lines which bisect ( BOOK I. 49.
Page 50
... Show that the lines which bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B with D and A with E , and show that BD + AE is greater than BE + AD . ( P. VIL ) B- D 3 ...
... Show that the lines which bisect ( halve ) two verti- cal angles , form one and the same straight line . 2. Given two lines , BE and AD ; join B with D and A with E , and show that BD + AE is greater than BE + AD . ( P. VIL ) B- D 3 ...
Page 51
... Show that any two adjacent angles of a parallelo- gram are supplements of each other . 15. Show that if two parallelograms have one angle in each equal , their remaining angles are equal each to each . 16. Show that if two sides of a ...
... Show that any two adjacent angles of a parallelo- gram are supplements of each other . 15. Show that if two parallelograms have one angle in each equal , their remaining angles are equal each to each . 16. Show that if two sides of a ...
Page 95
... Show that the sum of the alternate angles of an inscribed hexagon is equal to four right angles . 10. The sides of a triangle are 3 , 5 , and 7 feet ; con- struct the triangle . 11. Show that the three perpendiculars erected at the ...
... Show that the sum of the alternate angles of an inscribed hexagon is equal to four right angles . 10. The sides of a triangle are 3 , 5 , and 7 feet ; con- struct the triangle . 11. Show that the three perpendiculars erected at the ...
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Common terms and phrases
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