## Elements of GeometryGinn and Heath, 1881 |

### From inside the book

Results 1-5 of 17

Page 76

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**circle**) . § 163 .. if HK could intersect the**circumference**in three points , we should have three equal straight lines OH , OP , and OK drawn from the same point to a**given**straight line , which is impossible , § 56 ( only two equal ... Page 96

... B D. Q. E. D. Ex . Show that the least chord that can be drawn through a

... B D. Q. E. D. Ex . Show that the least chord that can be drawn through a

**given**point in a**circle**is perpendicular to the diameter drawn through the point . PROPOSITION XVI . THEOREM . 209. An angle formed by 96 BOOK II . GEOMETRY . - Page 102

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**circle**BCE let the arcs AECB and BAEC together be greater than the**circumference**, and let arc AEC B be greater than arc BAE C. We are to prove chord A B < chord B C. From the**given**arcs take the common arc A E C ; we have left two arcs ... Page 104

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**given**points is less than the difference of the distances of the required point from the two**given**points . Let the distance from A to B be less than no . From A as a centre , with a**radius**equal to n , describe a**circle**; and from B as ... Page 110

... the arc of the chord . ... arc A O = arc O B , = ..LAEC BEC , ( in the same

... the arc of the chord . ... arc A O = arc O B , = ..LAEC BEC , ( in the same

**circle**equal arcs subtend equal at the centre ) . $ 184 § 180 Q. E. F. PROPOSITION XXIX . PROBLEM . 227. Through a**given**point 110 GEOMETRY . BOOK II .### Other editions - View all

### 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'.