## Elements of Geometry |

### From inside the book

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**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 , tending to show their connexion , their restric- tion , their extension , or the ... Page 5

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**Corollary**1. If one of the angles ACD , BCD , is a right angle , the other is also a right angle . 30.**Corollary**11. If the line DE ( fig . 18 ) is perpendicular to Fig . 18 . AB ; reciprocally , AB is also perpendicular to DE . For ... Page 7

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**Corollary**. When , in two triangles , these three things are equal , namely , the angle A = D , the side AB DE , and the side AC = DF , we may thence infer , that the other three are also equal , namely , the angle B = E , the angle C ... Page 8

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**Corollary**. When , in two triangles , these three things are equal , namely , BC = EF , B = E , and CF , we may thence infer that the other three are also equal , namely , AB = DE , AC DF , and A = D. = THEOREM . 40. One side of a ... Page 9

... B is equal to the angle C. 46.

... B is equal to the angle C. 46.

**Corollary**. An equilateral triangle is also equiangular , that is , it has its angles equal . Geom . 2 47. Scholium . From the equality of the triangles ABD Of Perpendicular and Oblique Lines ,### 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