Schultze and Sevenoak's Plane and Solid Geometry |
From inside the book
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Page 189
... projection of a point upon a line is the foot of the perpendicular from the point to the line . 329. DEF . The projection of one line upon another is the seg- ment between the projections of the extremities of the first line upon the ...
... projection of a point upon a line is the foot of the perpendicular from the point to the line . 329. DEF . The projection of one line upon another is the seg- ment between the projections of the extremities of the first line upon the ...
Page 190
... projection of AB upon AC , of AB upon BC , of AC upon AB . Ex . 936. If AB XY , prove that the projection of AB upon XY equals AB . Ex . 937. If the side of an equilateral triangle equals 10 in . , what is the length of the projection ...
... projection of AB upon AC , of AB upon BC , of AC upon AB . Ex . 936. If AB XY , prove that the projection of AB upon XY equals AB . Ex . 937. If the side of an equilateral triangle equals 10 in . , what is the length of the projection ...
Page 191
... projection of AB upon XY if AB = m , and the angle included by AB and XY equals 135 ° . Ex . 945. Find the projection of AB upon XY if AB = m , and the angle included by AB and XY equals 150 ° . Ex . 946. If in triangle ABC , AB = 8 ...
... projection of AB upon XY if AB = m , and the angle included by AB and XY equals 135 ° . Ex . 945. Find the projection of AB upon XY if AB = m , and the angle included by AB and XY equals 150 ° . Ex . 946. If in triangle ABC , AB = 8 ...
Page 192
... projection of the other side upon it . P Given in △ abc , p the projection of b upon c , and the angle opposite a an acute angle . To prove c2 a = b + c − 2 ep . Proof . Denote the perpendicular upon e by h . In the figure on the left ...
... projection of the other side upon it . P Given in △ abc , p the projection of b upon c , and the angle opposite a an acute angle . To prove c2 a = b + c − 2 ep . Proof . Denote the perpendicular upon e by h . In the figure on the left ...
Page 193
... projection Ex . 963. The sides of a triangle are 10 , 17 , 21. Find the projection of 10 upon 21 . [ See practical problems , pp . 298 and 299. ] PROPOSITION XXXVII . THEOREM 333. In any obtuse triangle , the square of the side opposite ...
... projection Ex . 963. The sides of a triangle are 10 , 17 , 21. Find the projection of 10 upon 21 . [ See practical problems , pp . 298 and 299. ] PROPOSITION XXXVII . THEOREM 333. In any obtuse triangle , the square of the side opposite ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.