Elements of Geometry and Trigonometry |
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Page 49
... distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or mutually bisect each ...
... distances from a line , and on the same side of it , the line joining them will be parallel to the given line . PROPOSITION XXXI . THEOREM . The diagonals of a parallelogram divide each other into equal parts , or mutually bisect each ...
Page 66
... less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
... less is at the greater distance from the centre . 1o . In the equal circles ACH and KLG , let the chords AC and KL be equal : then will they be equally distant from the centres . For , let the circle KLG be placed upon ACH 66 GEOMETRY .
Page 67
... distances of the two chords from the centre ( B. I. , P. XV . , C. 1 ) : hence , the less chord is at the greater distance from the centre ; which was to be proved . Scholium . All the propositions relating to chords and arcs of equal ...
... distances of the two chords from the centre ( B. I. , P. XV . , C. 1 ) : hence , the less chord is at the greater distance from the centre ; which was to be proved . Scholium . All the propositions relating to chords and arcs of equal ...
Page 70
... distances from it . Let the circumferences , whose centres are C and D , Intersect at the points A and B : then will CD be perpen- dicular to AB , and AF will be equal to BF For , the points A and B , being on the circumference whose ...
... distances from it . Let the circumferences , whose centres are C and D , Intersect at the points A and B : then will CD be perpen- dicular to AB , and AF will be equal to BF For , the points A and B , being on the circumference whose ...
Page 71
... distance be tween their centres will be less than the sum , and greater than the difference , of their radii . Let ... distance between the centres of two circles is equal to the sum of their radii , they will be tangent externally . Let ...
... distance be tween their centres will be less than the sum , and greater than the difference , of their radii . Let ... distance between the centres of two circles is equal to the sum of their radii , they will be tangent externally . Let ...
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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...