Elements of Geometry |
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Page 22
... radii are all equal , and all the diameters also are equal and double of the radius . 92. An arc of a circle is any portion of its circumference , as FHG . The chord or subtense of an arc is the straight line FG , which joins its ...
... radii are all equal , and all the diameters also are equal and double of the radius . 92. An arc of a circle is any portion of its circumference , as FHG . The chord or subtense of an arc is the straight line FG , which joins its ...
Page 23
... radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100. Corollary . Hence the greatest straight line that can ...
... radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100. Corollary . Hence the greatest straight line that can ...
Page 24
... radii CD , OG , be drawn , the two triangles ACD , EOG , will have the three sides of the one equal to the three sides of the other , each to each , namely , AC = EO , CD = OG and AD = EG ; therefore these triangles are equal ( 43 ) ...
... radii CD , OG , be drawn , the two triangles ACD , EOG , will have the three sides of the one equal to the three sides of the other , each to each , namely , AC = EO , CD = OG and AD = EG ; therefore these triangles are equal ( 43 ) ...
Page 25
... radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique lines , there- fore they are equally distant from the perpendicular ( 52 ) , and AD = DB . Again , since AD = BD , and CG is a perpendicular ...
... radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique lines , there- fore they are equally distant from the perpendicular ( 52 ) , and AD = DB . Again , since AD = BD , and CG is a perpendicular ...
Page 27
... radii CA , CD . The right - angled triangles CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles then are equal ( 59 ) , and consequently ...
... radii CA , CD . The right - angled triangles CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles then are equal ( 59 ) , and consequently ...
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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