## Elements of Geometry |

### From inside the book

Results 1-5 of 92

Page vi

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**circle**, treats of the most sim- ple properties of the**circle**, and those of chords , of tangents , and of the measure of angles by the arcs of a**circle**. These two sections are followed by the resolution of certain problems relating to ... Page vii

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**circle**. Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the manner of Archimedes . We have then given two methods of approximation for squaring the**circle**, one of which is that of James ... Page 24

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**Circle**and the Measure of Angles . DEFINITIONS . 87. THE circumference of a**circle**is a curved line all the points of which are equally distant from a point within called the centre . The**circle**is the space terminated by this curved ... Page 25

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**circle**. In this case , the**circle**is said to be circumscribed about the figure . 96. A secant is a line , which meets the circumference in two points , as AB ( fig . 48 ) . 97. A tangent is a line , which has only one point in common ... Page 26

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**circle**, or in equal**circles**, if the arc be less than half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence