## Elements of Geometry |

### From inside the book

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**segment**of a circle is the portion comprehended be- tween an arc and its chord . 92. A sector is the part of a ...**segments**; but , in speaking of these , the smaller is always to be understood , when the contrary is not expressed . And ... Page 35

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**segment**, are equal ; for they have each for their measure the half of the same arc BOC . 128. Corollary II . Every angle BAD ( fig . 67 ) , inscribed in Fig . 67 . a semicircle , is a right angle ; for it has for its measure the half ... Page 36

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**segment**greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicir- cumference . And every angle BOC , inscribed in a**segment**less than a semicircle , is an obtuse angle ; for ... Page 42

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**segment**capable of containing a given angle C , that is , a**segment**such , that each of the angles , which may be inscribed in it , shall be equal to a given angle C. Solution . Produce AB toward D , make at the point B the angle DBE ... Page 45

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**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 . 164. The altitude ...### 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