## Elements of Geometry |

### From inside the book

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**Proposition**is given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral**propositions**. A Scholium is a remark upon one or more**propositions**which have gone before ... Page 13

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**proposition**will evidently be true , if the third side BC be equal to the third side EF . If it be possible , let these sides be unequal , and let BC be the greater . Take BG EF , and join AG ; then the triangle ABG is equal to the ... Page 14

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**proposition**. We shall resume the subject with a view to a rigorous demonstration in the third of the notes subjoined to these elements . Fig . 36 . THEOREM . 60. If two straight lines AC , BD , ( fig . 36 ) , make with a third AB two ... Page 18

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**proposition**, namely , that the side EF be directed the same way as AC , and ED the same way as AB ; the reason is this ; if we produce FE toward H , the angle DEH would have its sides parallel to those of the angle BAC , but the two ... Page 20

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**proposition**to poly- gons , which have any re - entering † angles , each of these angles is to be considered as greater than two right angles . But , in order to avoid confusion we shall confine ourselves in future to those polygons ...### 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