Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 100
Page 34
... perpendicular be let fall on the line , and oblique lines be drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line : 2o . Any two oblique lines that meet the given line at points equally ...
... perpendicular be let fall on the line , and oblique lines be drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line : 2o . Any two oblique lines that meet the given line at points equally ...
Page 35
... perpendicular ; which is impossible . PROPOSITION XVI . THEOREM . If a perpendicular be drawn to a given straight line at its middle point : 1o . Any point of the perpendicular will be equally distant from the extremities of the line ...
... perpendicular ; which is impossible . PROPOSITION XVI . THEOREM . If a perpendicular be drawn to a given straight line at its middle point : 1o . Any point of the perpendicular will be equally distant from the extremities of the line ...
Page 37
... perpendicular to a third line , they will be parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a B point 0 , there would be two perpendiculars OA , OB , drawn A D ...
... perpendicular to a third line , they will be parallel . Let the two lines AC , BD , be perpendicular to AB : then will they be parallel . For , if they could meet in a B point 0 , there would be two perpendiculars OA , OB , drawn A D ...
Page 38
... HD be parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E. The sum of the angles GBE and GBD is equal to two right H- EB -D G K A F angles ( P. I. ) ; the sum of the 38 GEOMETRY .
... HD be parallel . Through G , the middle point of AB , draw GF perpendicular to KC , and prolong it to E. The sum of the angles GBE and GBD is equal to two right H- EB -D G K A F angles ( P. I. ) ; the sum of the 38 GEOMETRY .
Page 40
... perpendicular to one of two parallels , it is perpendicular to the other also . Cor . 2. If a straight line meet two parallels , the alternate angles will be equal . are For , if AB and CD parallel , the sum of BGH and GHD is equal to ...
... perpendicular to one of two parallels , it is perpendicular to the other also . Cor . 2. If a straight line meet two parallels , the alternate angles will be equal . are For , if AB and CD parallel , the sum of BGH and GHD is equal to ...
Other editions - View all
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...