Elements of Geometry and Trigonometry |
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Page 23
... until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
... until the assumed hypothesis is shown to be false . Its contradictory is thus proved to be true . This method of demonstration is often used in Geometry . PROPOSITION IV . THEOREM . If a straight line meet BOOK I. 23.
Page 27
... , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + OC less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
... , we have , BD + DC < BA + AC . But it was shown that BO + OC is less than BD + DC ; still more , then , is BO + OC less than BA + AC ; which was to be proved . PROPOSITION IX . THEOREM . If two triangles have two BOOK I. 27.
Page 35
... shown , as in the first case , that AD is equal to DF . Then , because the point C lies within the triangle ADF , the sum of the lines AD and DF will be greater than the sum of the lines AC and CF ( P. VIII . ) : hence , AD , the half ...
... shown , as in the first case , that AD is equal to DF . Then , because the point C lies within the triangle ADF , the sum of the lines AD and DF will be greater than the sum of the lines AC and CF ( P. VIII . ) : hence , AD , the half ...
Page 36
... shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA : hence , I is unequally distant from A and B ...
... shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and DB is equal to the sum of ID and DA , or IA , we have IB less than IA : hence , I is unequally distant from A and B ...
Page 39
... shown , AB and CD are parallel . Cor . 2. If two lines are cut by a third , making the oppo- site exterior and interior angles equal , the two lines will be parallel . Let the angles EGB and GHD be equal : Now , EGB and AGH are equal ...
... shown , AB and CD are parallel . Cor . 2. If two lines are cut by a third , making the oppo- site exterior and interior angles equal , the two lines will be parallel . Let the angles EGB and GHD be equal : Now , EGB and AGH are equal ...
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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
ABē ABCD ACē 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...