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 . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which ...
... chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the circum- ference . The sides are chords . 10. A SECANT is a straight line which cuts the circumference in two points . 11. A TANGENT is a straight line which ...
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 . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. 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 . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. 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 will the ... 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 will the ... 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 . 1 ° . 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 . A P DO For , place the circle ...
... chord ; and conversely , a greater chord subtends a greater arc . 1 ° . 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 . A P DO For , place the circle ...
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Common terms and phrases
ABē ACē 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