Elements of Geometry and Trigonometry |
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Page 160
... plane hence , two parallels determine the position of a plane . : A -B C- D F PROPOSITION III . THEOREM . The ... MN be the plane of the two lines BB , CC , and let AP be perpendicular to these lines at P : then will AP be perpendicular ...
... plane hence , two parallels determine the position of a plane . : A -B C- D F PROPOSITION III . THEOREM . The ... MN be the plane of the two lines BB , CC , and let AP be perpendicular to these lines at P : then will AP be perpendicular ...
Page 161
Adrien Marie Legendre Charles Davies. AP be perpendicular to every line of the plane which passes through P , and consequently , to the plane itself . For , through P , draw in the plane MN , any line PQ ; through any point of this line ...
Adrien Marie Legendre Charles Davies. AP be perpendicular to every line of the plane which passes through P , and consequently , to the plane itself . For , through P , draw in the plane MN , any line PQ ; through any point of this line ...
Page 162
... plane from a point of that plane . For , suppose that two perpen- diculars could be drawn to the plane MN , from the point P. Pass a plane through the perpendiculars , and let PQ be its intersection with MN ; then we should have two per ...
... plane from a point of that plane . For , suppose that two perpen- diculars could be drawn to the plane MN , from the point P. Pass a plane through the perpendiculars , and let PQ be its intersection with MN ; then we should have two per ...
Page 163
... plane MN in the circumference of a circle , whose centre is P , and whose radius is PB : hence , to draw a perpendi- cular to a given plane MN , from a point A , without that plane , find three points B , C , D , of the plane equally ...
... plane MN in the circumference of a circle , whose centre is P , and whose radius is PB : hence , to draw a perpendi- cular to a given plane MN , from a point A , without that plane , find three points B , C , D , of the plane equally ...
Page 164
... plane MN , P its foot , BC the given line , and A any point of the perpendicular ; draw PD at right angles to BC , and join the point D with A then will AD be perpendicular to BC . For , lay off DB equal to DC , and draw PB , PC , AB ...
... plane MN , P its foot , BC the given line , and A any point of the perpendicular ; draw PD at right angles to BC , and join the point D with A then will AD be perpendicular to BC . For , lay off DB equal to DC , and draw PB , PC , AB ...
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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...