Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 33
Page 59
... included between an are and its chord . 7. A SECTOR is a part of a circle included within an 8. An INSCRIBED ANGLE is an angle whose vertex is. an arc and the radii drawn to its extremities . The Circle, and the Measurement of Angles,
... included between an are and its chord . 7. A SECTOR is a part of a circle included within an 8. An INSCRIBED ANGLE is an angle whose vertex is. an arc and the radii drawn to its extremities . The Circle, and the Measurement of Angles,
Page 60
Adrien Marie Legendre Charles Davies. 8. An 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 in the circumfer- ence , and whose ...
Adrien Marie Legendre Charles Davies. 8. An 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 in the circumfer- ence , and whose ...
Page 77
... inscribed angle is measured by half of the arc 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 arc 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 78
... inscribed angle , and let the centre lie within it : then will the angle be 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 ...
... inscribed angle , and let the centre lie within it : then will the angle be 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 ...
Page 79
... inscribed in a segment less than a semi - circle , is B D 0 A B C obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are ...
... inscribed in a segment less than a semi - circle , is B D 0 A B C obtuse ; for it is measured by half the arc BAC , greater than a semi - circumference . Cor . 4. The opposite angles A and C , of an inscribed quadrilateral ABCD , are ...
Other editions - View all
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
ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cos²a 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 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 semi-circumference similar sine 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
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...