Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 59
... CHORD is a straight line joining the extremities of 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 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 ...
... 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 ...
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. equal to A the sum of AC and CD VII . ) . But ...
... 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. equal to A the sum of AC and CD VII . ) . But ...
Page 62
... chords ; and conversely , equal chords subtend equal arcs . 1 ° . In the equal cir- D cles ADB and EGF , M N let the arcs AMD and A BE ENG be equal : then will ... chord AD will coincide with EG ( A. 11 ) , and is , therefore 62 GEOMETRY .
... chords ; and conversely , equal chords subtend equal arcs . 1 ° . In the equal cir- D cles ADB and EGF , M N let the arcs AMD and A BE ENG be equal : then 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 D H P M G arc EGP be greater than AMD then will A E 0 K the arc the chord EP be greater than the chord AD . For , place ...
... chord ; and conversely , a greater chord subtends a greater arc . 1o . In the equal circles ADL and EGK , let the D H P M G arc EGP be greater than AMD then will A E 0 K the arc the chord EP be greater than the chord AD . For , place ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following