Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Results 1-5 of 14
Page 160
... plane . But either line , as AB , and any point of the other , as F , determine the posi- tion of a plane hence ... MN be the plane of the two lines BB , CC , and let AP be perpendicular to these lines at P : then will AP be ...
... plane . But either line , as AB , and any point of the other , as F , determine the posi- tion of a plane hence ... MN be the plane of the two lines BB , CC , and let AP be perpendicular to these lines at P : then will AP be ...
Page 161
... 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 , as Q , draw the line BC , 80 that BQ shall be equal to QC ( B. IV . , Prob ...
... 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 , as Q , draw the line BC , 80 that BQ shall be equal to QC ( B. IV . , Prob ...
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 , Pits 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 , Pits 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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Common terms and phrases
ABē ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence