Plane and Solid GeometryMacmillan, 1901 - 370 σελίδες |
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Σελίδα 7
... theorem or a problem . 46. A corollary is a theorem easily derived from another theorem . 47. A scholium is a remark . 48. A postulate is a construction so simple that its possibility is admitted without further demonstration . 49. The ...
... theorem or a problem . 46. A corollary is a theorem easily derived from another theorem . 47. A scholium is a remark . 48. A postulate is a construction so simple that its possibility is admitted without further demonstration . 49. The ...
Σελίδα 9
Arthur Schultze, Frank Louis Sevenoak. BOOK I LINES AND RECTILINEAR FIGURES * PRELIMINARY THEOREMS 52. All straight angles are equal . A B C D E F ... THEOREM 59. Vertical angles are equal . 30 9 PLANE GEOMETRY Lines and Rectilinear Figures.
Arthur Schultze, Frank Louis Sevenoak. BOOK I LINES AND RECTILINEAR FIGURES * PRELIMINARY THEOREMS 52. All straight angles are equal . A B C D E F ... THEOREM 59. Vertical angles are equal . 30 9 PLANE GEOMETRY Lines and Rectilinear Figures.
Σελίδα 17
... THEOREM . Two straight lines which are parallel to a third straight line are parallel to each other . For if the two lines should meet , we would have two intersecting straight lines parallel to a third straight line , which contradicts ...
... THEOREM . Two straight lines which are parallel to a third straight line are parallel to each other . For if the two lines should meet , we would have two intersecting straight lines parallel to a third straight line , which contradicts ...
Σελίδα 18
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION V. THEOREM 80. Two lines are parallel if a transversal to these lines makes the alternate interior angles equal . A B с D E F Hyp . AC and DF are intersected by BE so that LABE = BEF ...
Arthur Schultze, Frank Louis Sevenoak. PROPOSITION V. THEOREM 80. Two lines are parallel if a transversal to these lines makes the alternate interior angles equal . A B с D E F Hyp . AC and DF are intersected by BE so that LABE = BEF ...
Σελίδα 19
... THEOREM 83. Two lines are parallel if a transversal to these lines makes the corresponding angles equal . E- H B F Hyp . CD and EF are intersected by AB in H and I respec- tively , and To prove ZAHD = △ HIF . CD || EF . HINT . - Prove ...
... THEOREM 83. Two lines are parallel if a transversal to these lines makes the corresponding angles equal . E- H B F Hyp . CD and EF are intersected by AB in H and I respec- tively , and To prove ZAHD = △ HIF . CD || EF . HINT . - Prove ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Σελίδα 180 - 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.
Σελίδα 45 - 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.
Σελίδα 337 - 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...
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Σελίδα 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Σελίδα 328 - Every section of a sphere made by a plane is a circle.
Σελίδα 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.