Elements of Geometry and Trigonometry |
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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 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 which ...
... chords . 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 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 ( B. I. , P. A B the sum of AC and CD VII . ) . But this ...
... 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 ( B. I. , P. A B the sum of AC and CD VII . ) . But this ...
Page 62
... chords ; and conversely , equal chords subtend equal arcs . 1o . In the equal cir- cles ADB and EGF , let the arcs AMD and ENG be equal : then will the chords AD ... 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- cles ADB and EGF , let the arcs AMD and ENG be equal : then will the chords AD ... 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 . D H P M G E K upon For ...
... 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 . D H P M G E K upon For ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm 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 polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...