## Elements of Geometry |

### From inside the book

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Page 33

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**hence**the angle BCE is double of BAC . The angle BCE , having its vertex at the centre , has for its measure the arc BE ; therefore the angle BAC has for its measure the half of BE . For a simi- lar reason the angle CAD has for its ... Page 34

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**hence**the two angles BAD , BCD , taken together , have for their measure the half of the circumference ; therefore their sum is equal to two right angles . THEOREM . 131. The angle BAC ( fig . 69 ) , formed by a tangent and a chord ... Page 40

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**hence**DO = OF . It may be shown , in like manner , that the two triangles BOD , BOE , are equal ; con- sequently OD OE ; therefore the three perpendiculars OD , OE , OF , are equal to each other . Now , if from the point O , as a centre ... Page 43

... therefore DC = FE . If DC be taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ; consequently CE = DF . Fig . 97 . Fig . 98 .

... therefore DC = FE . If DC be taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ; consequently CE = DF . Fig . 97 . Fig . 98 .

**Hence**the Of the Proportions of Figures . 43. Page 44

Adrien Marie Legendre. Fig . 97 . Fig . 98 .

Adrien Marie Legendre. Fig . 97 . Fig . 98 .

**Hence**the triangles DAF , CBE , have the three sides of the one equal to the sides of the other , each to each ; they are there- fore equal ( 43 ) . But , if from the quadrilateral ABED the ...### 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