Elements of Geometry |
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Page 36
... 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 semicircumference . 130 ...
... 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 semicircumference . 130 ...
Page 42
... 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 the segment ...
... 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 the segment ...
Page 46
... half of a parallelogram ABCD of the same base and altitude . Demonstration . The triangles ABC , ACD , are equal ( 81 ) ; therefore each is half of the parallelogram ABCD . 169. Corollary 1. A triangle ABC is half of a rectangle BCEF of ...
... half of a parallelogram ABCD of the same base and altitude . Demonstration . The triangles ABC , ACD , are equal ( 81 ) ; therefore each is half of the parallelogram ABCD . 169. Corollary 1. A triangle ABC is half of a rectangle BCEF of ...
Page 49
... half of its altitude . Demonstration . The triangle ABC ( fig . 104 ) is half of the Fig . 104 . parallelogram ABCE , which has the same base BC and the same altitude AD ( 168 ) ; now the area of the parallelo- BC × AD ( 174 ) ...
... half of its altitude . Demonstration . The triangle ABC ( fig . 104 ) is half of the Fig . 104 . parallelogram ABCE , which has the same base BC and the same altitude AD ( 168 ) ; now the area of the parallelo- BC × AD ( 174 ) ...
Page 50
... half the sum of the sides AB , CD ; and consequently the area of the trapezoid ABCD is equal to the product of the altitude EF by half the sum of the sides AB , CD , which may be expressed in this manner ; ABCD = EF × ( B + CD ) . 179 ...
... half the sum of the sides AB , CD ; and consequently the area of the trapezoid ABCD is equal to the product of the altitude EF by half the sum of the sides AB , CD , which may be expressed in this manner ; ABCD = EF × ( B + CD ) . 179 ...
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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