Elements of Geometry |
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Page 73
... Chord of a circle is any straight line having its extremities in the circumference , as A B , Fig . 3 . Every chord subtends two arcs whose sum is the cir- cumference . Thus the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc ...
... Chord of a circle is any straight line having its extremities in the circumference , as A B , Fig . 3 . Every chord subtends two arcs whose sum is the cir- cumference . Thus the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc ...
Page 74
... chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 ... chords of that circumference , as ZABC , Fig . 1 . A polygon is inscribed in a circle when its sides are chords of the ...
... chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 ... chords of that circumference , as ZABC , Fig . 1 . A polygon is inscribed in a circle when its sides are chords of the ...
Page 75
... chord . PROPOSITION I. THEOREM . 177. The diameter of a circle is greater than any other Let A B be the diameter of the circle A MB , and A E any other chord . We are to prove AB > A E. From C , the centre of the O , draw C E. But CE ...
... chord . PROPOSITION I. THEOREM . 177. The diameter of a circle is greater than any other Let A B be the diameter of the circle A MB , and A E any other chord . We are to prove AB > A E. From C , the centre of the O , draw C E. But CE ...
Page 79
... chords . 4 པ R S R B A BI P P In the equal circles ABP and A'B ' P ' let arc RS = arc R ' S ' . We are to prove chord RS chord R ' S ' . Draw the radii O R , OS , O ' R ' , and O ' S ' . In the ROS and R ' O'S " = OR O'R ' , ( being ...
... chords . 4 པ R S R B A BI P P In the equal circles ABP and A'B ' P ' let arc RS = arc R ' S ' . We are to prove chord RS chord R ' S ' . Draw the radii O R , OS , O ' R ' , and O ' S ' . In the ROS and R ' O'S " = OR O'R ' , ( being ...
Page 80
... chords subtend equal arcs . A R S B A R BI P PI In the equal circles ABP and A'B ' P ' , let chord RS = chord R'S ' . We are to prove = arc RS arc R ' S ' . Draw the radii O R , O S , O ' R ' , and O ' S ' . In the ROS and R ' O'S ' RS ...
... chords subtend equal arcs . A R S B A R BI P PI In the equal circles ABP and A'B ' P ' , let chord RS = chord R'S ' . We are to prove = arc RS arc R ' S ' . Draw the radii O R , O S , O ' R ' , and O ' S ' . In the ROS and R ' O'S ' RS ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 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.
Page 202 - In any proportion, the product of the means is equal to the product of the extremes.
Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 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.
Page 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.
Page 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'.