Elements of Geometry |
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Page 35
... measure the half of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first ... measure the arc BE ; therefore the angle BAC has for its measure the half of BE . For a similar reason , the angle CAD ...
... measure the half of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first ... measure the arc BE ; therefore the angle BAC has for its measure the half of BE . For a similar reason , the angle CAD ...
Page 36
... 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 it has for its measure the half of the arc BAC greater than a ...
... 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 it has for its measure the half of the arc BAC greater than a ...
Page 42
... measure the half of the arc AKB ( 131 ) ; besides , the angle AMB , as an inscribed angle , has also for its measure the half of the arc AKB ; con- sequently the angle AMB = ABF = EBD = C ; therefore = = each of the angles inscribed in ...
... measure the half of the arc AKB ( 131 ) ; besides , the angle AMB , as an inscribed angle , has also for its measure the half of the arc AKB ; con- sequently the angle AMB = ABF = EBD = C ; therefore = = each of the angles inscribed in ...
Page 49
... measure AB × BE ( 173 ) ; therefore AB × BE is equal to the area of the parallelogram ABCD . 175. Corollary ... half of its altitude . Demonstration . The triangle ABC ( fig . 104 ) is half of the Fig . 104 . parallelogram ABCE , which ...
... measure AB × BE ( 173 ) ; therefore AB × BE is equal to the area of the parallelogram ABCD . 175. Corollary ... half of its altitude . Demonstration . The triangle ABC ( fig . 104 ) is half of the Fig . 104 . parallelogram ABCE , which ...
Page 50
... measure EF × AL . But AL = DK ; and , since the triangle IBL is equal to the triangle KCI , the side BL = CK ; therefore AB + CD = AL + DK = 2 AL ; thus AL is half the sum of the sides AB , CD ; and consequently the area of the ...
... measure EF × AL . But AL = DK ; and , since the triangle IBL is equal to the triangle KCI , the side BL = CK ; therefore AB + CD = AL + DK = 2 AL ; thus AL is half the sum of the sides AB , CD ; and consequently the area of the ...
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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