Elements of Geometry and Trigonometry |
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Page 62
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet ... semi - circle ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB ...
... circumference in more than two points . Let AEBF be a circumference , and AB a straight line : then AB cannot meet ... semi - circle ADB be applied to the semi - circle EGF , it will coincide with it , and the semi - circumference ADB ...
Page 79
... semi - circumference BOD , or by a quadrant ( P. XVII . , S. ) . B A 0 in- A Cor . 3. Any angle BAC , scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi ...
... semi - circumference BOD , or by a quadrant ( P. XVII . , S. ) . B A 0 in- A Cor . 3. Any angle BAC , scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi ...
Page 81
... half of the arc AMC . M D 1 1 I For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVII . , S. ) ; the the angle DAC is measured by half of the arc DC ( P ...
... half of the arc AMC . M D 1 1 I For , draw the diameter AD . The angle BAD is a right angle ( P. IX . ) , and is measured by half the semi - circumference AMD ( P. XVII . , S. ) ; the the angle DAC is measured by half of the arc DC ( P ...
Page 121
... semi - circumference BAC , chords be drawn to the A B D extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right - angled tri- angle , right - angled at A ; and from what was ...
... semi - circumference BAC , chords be drawn to the A B D extremities B and C of the diam- eter BC , and a perpendicular AD be drawn to the diameter : then will ABC be a right - angled tri- angle , right - angled at A ; and from what was ...
Page 223
... is less than the difference of their radii , one is wholly within the other : 6 ° . When this distance is equal to zero , they have a common centre , or , are concentric . DEFINITIONS . 1o . If a semi - circumference be BOOK VIII . 223.
... is less than the difference of their radii , one is wholly within the other : 6 ° . When this distance is equal to zero , they have a common centre , or , are concentric . DEFINITIONS . 1o . If a semi - circumference be BOOK VIII . 223.
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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
AB² ABCD AC² 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...