Plane and Solid GeometryGinn, 1895 - 320 sider |
Inni boken
Resultat 1-5 av 90
Side 7
... suppose a = 2 b , how many degrees in each ? ( b ) suppose a = - 3 b , how many ? 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 = 2 b , how many degrees in each ? ( b ) suppose a = - 3 b , how many ? 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 ...
Side 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 ...
Side 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 ...
Side 14
... Suppose another point of bisection exists , as P , be- tween M and B. 2. Then since AM and AP are both halves of AB , they are equal . ( State ax . 7. ) Ax . 7 3. But this is impossible , for AM is part of AP . Ax . 8 ( State ax . 8 ...
... Suppose another point of bisection exists , as P , be- tween M and B. 2. Then since AM and AP are both halves of AB , they are equal . ( State ax . 7. ) Ax . 7 3. But this is impossible , for AM is part of AP . Ax . 8 ( State ax . 8 ...
Side 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 ...
... 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 ...
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Plane and Solid Geometry David Eugene Smith,Wooster Woodruff Beman Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors C₁ called central angles chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles triangle line-segment locus lune meet mid-points oblique opposite sides orthocenter P₁ P₂ parallel lines parallelepiped parallelogram perigon perimeter perpendicular plane plane geometry polar polyhedral angle prism Prismatoid produced Proof prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle right-angled triangle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem trihedral vertex vertices
Populære avsnitt
Side 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Side 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...
Side 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...
Side 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Side 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Side 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.
Side 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.
Side 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.
Side 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.
Side 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.