Plane and Solid Geometry |
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Page iv
... solution by any one class . They are graded so as to offer a selection to the teacher and may be used either with each theorem or at the end of each section or book . The exercises , however , do not uniformly refer to the theorems ...
... solution by any one class . They are graded so as to offer a selection to the teacher and may be used either with each theorem or at the end of each section or book . The exercises , however , do not uniformly refer to the theorems ...
Page 60
... solution , as that an angle may be bisected but once , the solution is said to be unique . NOTE ON ASSUMED CONSTRUCTIONS . It has thus far been assumed that all constructions were made as required for the theorems . Thus an equi ...
... solution , as that an angle may be bisected but once , the solution is said to be unique . NOTE ON ASSUMED CONSTRUCTIONS . It has thus far been assumed that all constructions were made as required for the theorems . Thus an equi ...
Page 61
... SOLUTION OF PROBLEMS . ally undertaking the solution of problems will be , as stated on p . 30 , very fully discussed at the close of Book III . But at present one method , already suggested , should be repeated : In attempting the ...
... SOLUTION OF PROBLEMS . ally undertaking the solution of problems will be , as stated on p . 30 , very fully discussed at the close of Book III . But at present one method , already suggested , should be repeated : In attempting the ...
Page 62
... Solution . This is merely a special case of pr . 1 , the case in which AOB is a straight angle . ( Why ? ) The con- struction and proof are iden- tical with those of pr . 1 , and the student should give them to satisfy himself of this ...
... Solution . This is merely a special case of pr . 1 , the case in which AOB is a straight angle . ( Why ? ) The con- struction and proof are iden- tical with those of pr . 1 , and the student should give them to satisfy himself of this ...
Page 63
... solution of this problem is attributed to Enopides . Problem 4. To bisect a given line . Given the line AB . Required to bisect it . Construction . 1. With centers A , B , and Proof . radius AB , describe arcs intersect- ing at P and P ...
... solution of this problem is attributed to Enopides . Problem 4. To bisect a given line . Given the line AB . Required to bisect it . Construction . 1. With centers A , B , and Proof . radius AB , describe arcs intersect- ing at P and P ...
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Common terms and phrases
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
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.