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 18
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
... drawn joining two given points . 12. The shortest distance from one point to another is measured on the straight line which joins them . 13. Through the same point , only one straight line can be drawn parallel to a given straight line ...
Page 19
... drawn joining any two points . 2. A straight line may be prolonged to any length . 3. If two straight lines are ... drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be ...
... drawn joining any two points . 2. A straight line may be prolonged to any length . 3. If two straight lines are ... drawn to a given straight line , either from a point without , or from a point on the line . 7. A straight line may be ...
Page 28
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to DE , and draw GC . Then the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle of the other ...
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to DE , and draw GC . Then the triangles AGC and DEF have two sides and the included angle of the one equal to two sides and the included angle of the other ...
Page 31
... drawn from the vertex of an isosceles tri- angle to the middle of the base , bisects the angle at the vertex , and ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
... drawn from the vertex of an isosceles tri- angle to the middle of the base , bisects the angle at the vertex , and ... draw DC . Then , in the triangles ABC , DBC , we have the side BD equal to AC , by construction , the side BC common ...
Page 33
... drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and ...
... drawn to a given straight line . Let A be a given point , and AB a perpendicular to DE : then can no other perpendicular to DE be drawn from A. For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and ...
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Common terms and phrases
ABē ABCD ACē 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