Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 209
... polygon re- quired , homologous to A B. For CD CHCE : CY , $ 275 ( a line drawn through two sides of a △ , to the third side , divides the two sides proportionally ) ... REGULAR POLYGONS AND CIRCLES . 363. DEF . CONSTRUCTIONS . 209 10.
... polygon re- quired , homologous to A B. For CD CHCE : CY , $ 275 ( a line drawn through two sides of a △ , to the third side , divides the two sides proportionally ) ... REGULAR POLYGONS AND CIRCLES . 363. DEF . CONSTRUCTIONS . 209 10.
Σελίδα 210
George Albert Wentworth. BOOK V. REGULAR POLYGONS AND CIRCLES . 363. DEF . A Regular Polygon is a polygon which is equilateral and equiangular . PROPOSITION I. THEOREM . 364. Every equilateral polygon inscribed in a circle is a regular ...
George Albert Wentworth. BOOK V. REGULAR POLYGONS AND CIRCLES . 363. DEF . A Regular Polygon is a polygon which is equilateral and equiangular . PROPOSITION I. THEOREM . 364. Every equilateral polygon inscribed in a circle is a regular ...
Σελίδα 211
... regular polygon . II . A circle may be inscribed in a regular polygon . B C D E Let ABCD , etc. , be a regular polygon . We are to prove that a O may be circumscribed about this regular polygon , and also a ○ may be inscribed in this ...
... regular polygon . II . A circle may be inscribed in a regular polygon . B C D E Let ABCD , etc. , be a regular polygon . We are to prove that a O may be circumscribed about this regular polygon , and also a ○ may be inscribed in this ...
Σελίδα 212
... polygon . 4 rt . s .. ZAOB = n Q. E. D. 371. COROLLARY . The radius drawn to any vertex of a regular polygon bisects the angle at that vertex . PROPOSITION IV . THEOREM . 372. Two regular polygons of 212 BOOK V. GEOMETRY . -
... polygon . 4 rt . s .. ZAOB = n Q. E. D. 371. COROLLARY . The radius drawn to any vertex of a regular polygon bisects the angle at that vertex . PROPOSITION IV . THEOREM . 372. Two regular polygons of 212 BOOK V. GEOMETRY . -
Σελίδα 213
George Albert Wentworth. PROPOSITION IV . THEOREM . 372. Two regular polygons of the same number of sides are similar . E E ' DI F Q ' CI F Q C B B ' Let Q and Q ' be two regular polygons , each having 2 rt . n sides . We are to prove Q ...
George Albert Wentworth. PROPOSITION IV . THEOREM . 372. Two regular polygons of the same number of sides are similar . E E ' DI F Q ' CI F Q C B B ' Let Q and Q ' be two regular polygons , each having 2 rt . n sides . We are to prove Q ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 202 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 146 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.