Elements of Geometry |
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Page 22
... 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 . 95. A straight line is said to be inscribed in a circle , when its Fig . 47. extremities are in the ...
... 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 . 95. A straight line is said to be inscribed in a circle , when its Fig . 47. extremities are in the ...
Page 32
... 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 , are to each other , as the arcs AB ...
... 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 , are to each other , as the arcs AB ...
Page 43
... sectors , simi- lar segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle O , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c ...
... sectors , simi- lar segments , are such as correspond to equal angles at the cen- tre . Thus , the angle A ( fig . 92 ) being equal to the angle O , the Fig . 92 . arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c ...
Page 87
... 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 polygon , so that the perimeters of the two polygons Of the Measure of the ...
... 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 polygon , so that the perimeters of the two polygons Of the Measure of the ...
Page 89
... 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 upon ...
... 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 upon ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence