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 59
... CHORD is a straight line joining the extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord .. 7. A ...
... CHORD is a straight line joining the extremities of an arc . Any chord belongs to two arcs : the smaller one is meant , unless the contrary is expressed . 6. A SEGMENT is a part of a circle included between an arc and its chord .. 7. A ...
Page 60
... chords . о 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line ...
... chords . о 9. An INSCRIBED POLYGON is a poly- gon whose vertices are in the circumfer- ence , and whose sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line ...
Page 61
... chord . Let AD be a chord , and AB a diameter through one extremity , as A : then will AB be greater than AD . Draw the radius CD . angle ACD , we have In the tri- AD less than ( B. I. , P. the sum of AC and CD VII . ) . But this sum is ...
... chord . Let AD be a chord , and AB a diameter through one extremity , as A : then will AB be greater than AD . Draw the radius CD . angle ACD , we have In the tri- AD less than ( B. I. , P. the sum of AC and CD VII . ) . But this sum is ...
Page 62
... chords ; and conversely , equal chords subtend equal arcs . 1o . In the equal cir- D cles ADB and EGF , M let the arcs AMD and A ENG be equal then G N BE will ... chord AD will coincide with EG ( A. 11 ) , and is , therefore 62 GEOMETRY .
... chords ; and conversely , equal chords subtend equal arcs . 1o . In the equal cir- D cles ADB and EGF , M let the arcs AMD and A ENG be equal then G N BE will ... chord AD will coincide with EG ( A. 11 ) , and is , therefore 62 GEOMETRY .
Page 63
... chord ; and conversely , a greater chord subtends a greater arc . 1o . In the equal circles ADL and EGK , let the arc EGP be greater than the arc AMD : then will the chord EP be greater than the chord AD . DH P M G K For , place the ...
... chord ; and conversely , a greater chord subtends a greater arc . 1o . In the equal circles ADL and EGK , let the arc EGP be greater than the arc AMD : then will the chord EP be greater than the chord AD . DH P M G K For , place the ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence