Elements of Geometry and Trigonometry |
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Page 40
Adrien Marie Legendre Charles Davies. PROPOSITION XX . THEOREM . I a straight line intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles . Let the parallels AB , CD , be ...
Adrien Marie Legendre Charles Davies. PROPOSITION XX . THEOREM . I a straight line intersect two parallel straight lines , the sum of the interior angles on the same side will be equal to two right angles . Let the parallels AB , CD , be ...
Page 41
... intersect a third line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if sufficiently produced . Let the two lines CD , IL , meet the line EF , making the sum of the ...
... intersect a third line , making the sum of the interior angles on the same side less than two right angles , the two lines will meet if sufficiently produced . Let the two lines CD , IL , meet the line EF , making the sum of the ...
Page 66
... intersection O , is the only point . that is equally distant from A , B , and C : hence , one circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in ...
... intersection O , is the only point . that is equally distant from A , B , and C : hence , one circumference may be made to pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in ...
Page 70
... intersect each other , the points of in- tersection will be in a perpendicular to the line joining their centres , and at equal distances from it . Let the circumferences , whose centres are C and D , Intersect at the points A and B ...
... intersect each other , the points of in- tersection will be in a perpendicular to the line joining their centres , and at equal distances from it . Let the circumferences , whose centres are C and D , Intersect at the points A and B ...
Page 71
... intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then will CD be less than the sum of AC and AD , D and greater than ...
... intersect at A : then will CD be less than the sum , and greater than the difference of the radii of the two circles . For , draw AC and AD , forming the triangle ACD . Then will CD be less than the sum of AC and AD , D and greater than ...
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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...