## Elements of Geometry |

### From inside the book

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Page 33

... measure Fig . 64 , the half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the ... measure the arc BE ; therefore the angle BAC has for its

... measure Fig . 64 , the half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the ... measure the arc BE ; therefore the angle BAC has for its

**measure the half**of BE . For a simi- lar reason the angle CAD ... Page 34

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**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 40

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**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 the ... Page 47

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**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 . 164 . parallelogram ABCE , which ... Page 48

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**measure**EF × AL . But AL = DK ; and , since the triangle IBL is equal to the triangle KCI , the side BLCK ; therefore AB + CD = AL + DK = 2AL ; thus AL is**half**the sum of the sides AB , CD ; and consequently the area of the trapezoid ...### Other editions - View all

### 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