Elements of Geometry |
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Page 93
... sector is equal to the arc of this sector multiplied by half of the radius . For the sector ACB ( fig . 168 ) is to the entire circle , as the Fig . 168 arc AMB is to the entire circumference ABD ( 125 ) , or as AMB × AC is to ABD × AC ...
... sector is equal to the arc of this sector multiplied by half of the radius . For the sector ACB ( fig . 168 ) is to the entire circle , as the Fig . 168 arc AMB is to the entire circumference ABD ( 125 ) , or as AMB × AC is to ABD × AC ...
Page 106
... sector ODE , hence P : CAIX CI : DE × OE :: CI : OE . Let there be drawn to the point E the tangent EG meeting OD ... sector DOE triangle GOE ; but the sector is less than the triangle ; consequently P is less than C ; therefore the ...
... sector ODE , hence P : CAIX CI : DE × OE :: CI : OE . Let there be drawn to the point E the tangent EG meeting OD ... sector DOE triangle GOE ; but the sector is less than the triangle ; consequently P is less than C ; therefore the ...
Page 158
... 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 a plane ...
... 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 a plane ...
Page 195
... sector AOD , situated on the same side of the diameter FG , to make a revolution about this diameter , the solid ... sector AOD , has for its measure & « × TỈ ( MN + NP + PQ ) , or 3 « × TỈ × MQ . T Fig . 269 . THEOREM . 546. Every ...
... sector AOD , situated on the same side of the diameter FG , to make a revolution about this diameter , the solid ... sector AOD , has for its measure & « × TỈ ( MN + NP + PQ ) , or 3 « × TỈ × MQ . T Fig . 269 . THEOREM . 546. Every ...
Page 196
... 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 ‡ « × AС ...
... 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 ‡ « × AС ...
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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