Plane and Solid GeometryMacmillan, 1901 - 370 σελίδες |
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Σελίδα 183
... polygon is 1 sq . ft . What is the area of the smaller polygon ? Ex . 833 ... regular pentagon into two equivalent parts so that one part is again a ... polygons are constructed AREAS OF POLYGONS 183.
... polygon is 1 sq . ft . What is the area of the smaller polygon ? Ex . 833 ... regular pentagon into two equivalent parts so that one part is again a ... polygons are constructed AREAS OF POLYGONS 183.
Σελίδα 194
Arthur Schultze, Frank Louis Sevenoak. BOOK V REGULAR POLYGONS . MEASUREMENT OF THE CIRCLE REGULAR POLYGONS PROPOSITION I. THEOREM ( 382 ' . ) DEF . A regular polygon is one which is equiangular and equilateral . 383. A circle can be ...
Arthur Schultze, Frank Louis Sevenoak. BOOK V REGULAR POLYGONS . MEASUREMENT OF THE CIRCLE REGULAR POLYGONS PROPOSITION I. THEOREM ( 382 ' . ) DEF . A regular polygon is one which is equiangular and equilateral . 383. A circle can be ...
Σελίδα 195
... polygon . .. a circle can be circumscribed about the given polygon . Q.E.D. PROPOSITION II . THEOREM 384. A circle can be inscribed in any regular polygon . HINT . Circumscribe a circle about the given polygon and prove that the center ...
... polygon . .. a circle can be circumscribed about the given polygon . Q.E.D. PROPOSITION II . THEOREM 384. A circle can be inscribed in any regular polygon . HINT . Circumscribe a circle about the given polygon and prove that the center ...
Σελίδα 196
... regular inscribed polygon . ( 2 ) Tangents drawn at the points of division form a regular circumscribed polygon . F G B E H Нур . The circumference ACE is divided into the equal arcs AB , BC , CD , etc. ( 1 ) To prove ABCDE is a regular ...
... regular inscribed polygon . ( 2 ) Tangents drawn at the points of division form a regular circumscribed polygon . F G B E H Нур . The circumference ACE is divided into the equal arcs AB , BC , CD , etc. ( 1 ) To prove ABCDE is a regular ...
Σελίδα 197
... polygon FGHIK is regular . 392. COR . 1. The perimeter of an inscribed polygon is less than the perimeter of an inscribed polygon of double the number of sides . 393. COR . 2. The perimeter of a circumscribed polygon ... REGULAR POLYGONS 197.
... polygon FGHIK is regular . 392. COR . 1. The perimeter of an inscribed polygon is less than the perimeter of an inscribed polygon of double the number of sides . 393. COR . 2. The perimeter of a circumscribed polygon ... REGULAR POLYGONS 197.
Άλλες εκδόσεις - Προβολή όλων
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.