## Elements of Geometry |

### From inside the book

Results 1-5 of 79

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**corollaries**, & c . , in one continued series . Moreover , the work is divided into two parts , one treating of plane figures , and the other of solids ; and the subdivisions of each part are denominated sections . As a knowledge of ... Page 3

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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 . II . 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 AD , 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 C = F , 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 ...### Other editions - View all

### 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