## Elements of Geometry |

### From inside the book

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Page 158

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**circular sector**, as DCF , or FCH , describes a solid , which is called a spherical sector . THEOREM . Fig . 221 . 452. Every section of a sphere made by a plane is a circle . Demonstration . Let AMB ( fig . 221 ) be a section , made by ... Page 196

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**circular sector**, which , by its revolution about AC , generates the spherical sec- tor ; the zone described by AB being AD × circ . AC , or 2X ACX AD ( 538 ) , we say that the spherical sector will have for its measure this AC , or ... Page 197

... sector . 2. We say that this same product cannot be the measure of a less spherical sector . For , let CEF be the

... sector . 2. We say that this same product cannot be the measure of a less spherical sector . For , let CEF be the

**circular sector**which by its revolution generates the given spherical sector , and let us suppose , if it be possible ... Page 199

... circle are to each other as their perimeters . PROBLEM . 551. The

... circle are to each other as their perimeters . PROBLEM . 551. The

**circular segment**BMD ( fig . 271 ) being supposed to Fig . 271 revolve about a diameter exterior to this segment , to find the value of the solid generated . Solution ...### 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