Elements of Geometry and Trigonometry |
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Page 73
... difference of the radii , they intersect each other in two points : 4. When this distance is equal to the difference of their radii , one is tangent to the other , internally : 5 ° . When this distance is less than the difference of the ...
... difference of the radii , they intersect each other in two points : 4. When this distance is equal to the difference of their radii , one is tangent to the other , internally : 5 ° . When this distance is less than the difference of the ...
Page 78
... difference of BAE and DAE , is measured by half of the difference of BE and DE , or by A B DE half of the arc BD ; ' which was to be proved . Cor . 1. All the angles BAC , BDC , 78 GEOMETRY .
... difference of BAE and DAE , is measured by half of the difference of BE and DE , or by A B DE half of the arc BD ; ' which was to be proved . Cor . 1. All the angles BAC , BDC , 78 GEOMETRY .
Page 80
... difference of the included arcs . Let AB , AC , be two secants : then will the angle BAC be measured by half the ... difference of BC A F and EC , or by half the difference of BC and DF ; which was to be proved . PROPOSITION XXI ...
... difference of the included arcs . Let AB , AC , be two secants : then will the angle BAC be measured by half the ... difference of BC A F and EC , or by half the difference of BC and DF ; which was to be proved . PROPOSITION XXI ...
Page 81
... difference of by half the difference of the arcs DCA and DC , or by half the arc CA. 6 PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
... difference of by half the difference of the arcs DCA and DC , or by half the arc CA. 6 PRACTICAL APPLICATIONS . PROBLEM I. To bisect a given straight BOOK III . 81.
Page 87
... difference ( B. I. , P. VII . , S. ) . PROBLEM XI . Given , two sides of a triangle , and the angle opposite one of them , to construct the triangle . Ở Let A and B be the given sides , and the given angle . Draw an indefinite line DG ...
... difference ( B. I. , P. VII . , S. ) . PROBLEM XI . Given , two sides of a triangle , and the angle opposite one of them , to construct the triangle . Ở Let A and B be the given sides , and the given angle . Draw an indefinite line DG ...
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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...