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 19
... drawn joining any two points . may be prolonged to any length . lines are unequal , the length of the less may be ... 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 . may be prolonged to any length . lines are unequal , the length of the less may be ... 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 will 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 ...
... drawn , making the angle CAG equal to the angle D ( Post . 7 ) ; make AG equal to DE , and draw GC . Then will 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 ...
Page 31
... drawn from the vertex of an isosceles triangle to the middle of the base , bisects the angle at the vertex , and is ... 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 triangle to the middle of the base , bisects the angle at the vertex , and is ... 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 from A. D B F For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and draw CF Then , the triangles ABC and FBC will have AB equal to BF , by construction , CB common , and the included angles ...
... drawn from A. D B F For , suppose a second perpendicular AC to be drawn . Prolong AB till BF is equal to AB , and draw CF Then , the triangles ABC and FBC will have AB equal to BF , by construction , CB common , and the included angles ...
Page 34
... drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line . 2 ° . Any two oblique ... draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction , the side BC ...
... drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line . 2 ° . Any two oblique ... draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction , the side BC ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence