## Elements of Geometry |

### From inside the book

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**sector**is the part of a circle comprehended between an arc DE and the two radii CD , CE , drawn to the extremities of this arc . 93. A straight line is said to be inscribed in a circle , when its extremities are in the circumference of ... Page 34

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**sectors**with arcs ; for**sectors**are equal , when their arcs are equal , and in general they are proportional to the angles ; hence two**sectors**ACB , ACD , taken in the same circle , or in equal circles , ≈re to each other as the arcs ... Page 45

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**sectors**, similar segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal to the angle Fig . 92 . O , the arc BC is similar to the arc DE , the**sector**ABC to the**sector**ODE , & c ... Page 89

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**sectors**FCG , ICH , we can likewise inscribe , in the greater , a portion of a regular polygon , or circumscribe , about the smaller , a portion of a similar GEOM . 12 polygon , so that the perimeters of the two polygons Of the Measure ... Page 91

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**sectors**ACB , DOE , are as the squares of their radii . For , since the arcs are similar , the angle C is equal to the angle O ( 163 ) ; now , the angle C is to four right angles as the arc AB is to the entire circumference described ...### 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