Plane and Solid Geometry |
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Page 7
... suppose a = many degrees in each ? ( b ) suppose a = 3 b , how many ? 2 b , how 11. How many straight lines are , in general , determined by three points ? by four ? by five ? ( The points in the same plane . ) 12. How many points are ...
... suppose a = many degrees in each ? ( b ) suppose a = 3 b , how many ? 2 b , how 11. How many straight lines are , in general , determined by three points ? by four ? by five ? ( The points in the same plane . ) 12. How many points are ...
Page 11
... suppose that the theorem is false and show that this supposition is absurd . Such proofs have long been known by the name “ reductio ad absurdum , ” a reduction to an absurdity . They are also called indirect proofs . Theorem 2. At a ...
... suppose that the theorem is false and show that this supposition is absurd . Such proofs have long been known by the name “ reductio ad absurdum , ” a reduction to an absurdity . They are also called indirect proofs . Theorem 2. At a ...
Page 12
... Suppose that another 1 , ZZ ' , could be drawn . x = 2. Then XOZ would be a rt . Z. Def . L O -X ( If two lines meet and form a rt . L , each is said to be to the other . ) 3. But XOY is a rt . . Given ; def . I ( For it is given that ...
... Suppose that another 1 , ZZ ' , could be drawn . x = 2. Then XOZ would be a rt . Z. Def . L O -X ( If two lines meet and form a rt . L , each is said to be to the other . ) 3. But XOY is a rt . . Given ; def . I ( For it is given that ...
Page 14
... Suppose another point of bisec tween M and B. 2. Then since AM and AP are bot are equal . ( State ax . 7. ) 3. But this is impossible , for AM ( State ax . 8. ) 4. .. the supposition that there bisection is absurd . Theorem 8. An angle ...
... Suppose another point of bisec tween M and B. 2. Then since AM and AP are bot are equal . ( State ax . 7. ) 3. But this is impossible , for AM ( State ax . 8. ) 4. .. the supposition that there bisection is absurd . Theorem 8. An angle ...
Page 17
... suppose in each of the other angles , YOB , BOY ' , AOY = 30 ° , how many degrees ? 27. In the figure of th . 10 , suppose △ AOY = 45 ° ; prove that if the lines are drawn as stated in that theorem , YY ' XX ' . 28. If four points , A ...
... suppose in each of the other angles , YOB , BOY ' , AOY = 30 ° , how many degrees ? 27. In the figure of th . 10 , suppose △ AOY = 45 ° ; prove that if the lines are drawn as stated in that theorem , YY ' XX ' . 28. If four points , A ...
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Common terms and phrases
a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors called central angle chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equal bases equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles lateral area line-segment lune mid-points oblique opposite sides orthocenter parallel lines parallelogram perigon perimeter perpendicular plane polar polyhedral angle polyhedron prism prismatic space Prismatoid produced Proof pyramid quadrilateral radii radius ratio rectangle rectangular parallelepiped regular regular polygon respectively rhombus right angle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices volume
Popular passages
Page 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 24 - The third side is called the base of the isosceles triangle, and the equal sides are called the sides. A triangle which has no two sides equal is called a scalene triangle. The distance from one point to another is the length of the straight line-segment joining them. The distance from a point to a line is the length of the perpendicular from that point to that line. That this perpendicular is unique will be proved later. This is the meaning of the word distance in plane geometry. In speaking of...
Page 295 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Page 37 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 225 - Theorem. If each of two intersecting planes is perpendicular to a third plane, their line of intersection is also perpendicular to that plane. Given two planes, Q, R, intersecting in OP, and each perpendicular to plane M. To prove that OP _L M.
Page 265 - A Plane Surface, or a Plane, is a surface in which if any two points are taken, the straight line which joins these points will lie wholly in the surface.
Page 159 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.