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 61
... arc and its chord . • 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . GEOMETRY . 8. An INSCRIBED ANGLE is an angle whose BOOK III The Circle, and the Measurement of Angles,
... arc and its chord . • 7. A SECTOR is a part of a circle included between an arc and the two radii drawn to its extremities . GEOMETRY . 8. An INSCRIBED ANGLE is an angle whose BOOK III The Circle, and the Measurement of Angles,
Page 62
... INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight ...
... INSCRIBED ANGLE is an angle whose vertex is in the circumference , and whose sides are chords . 9. An INSCRIBED POLYGON is a poly- gon whose vertices are all in the cir- cumference . The sides are chords . 10. A SECANT is a straight ...
Page 79
... inscribed angle is measured by half of the are included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
... inscribed angle is measured by half of the are included between its sides . There may be three cases : the centre of the circle may lie on one of the sides of the angle ; it may lie within the angle ; or , it may lie without the angle ...
Page 80
... inscribed angle , and let the centre lie within it : then the angle is measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by ...
... inscribed angle , and let the centre lie within it : then the angle is measured by half of the arc BED . For , draw the diameter AE . Then , from what has just been proved , the angle DAE is measured by half of DE , and the angle EAB by ...
Page 81
... inscribed in the same segment , are equal ; because they are measured by half of the BOC . each same arc B A 81 Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum ...
... inscribed in the same segment , are equal ; because they are measured by half of the BOC . each same arc B A 81 Cor . 2. Any angle BAD , inscribed in a semicircle , is a right angle ; because it is measured by half the semi - circum ...
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Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.