## Elements of Geometry |

### From inside the book

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**described**from the centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in the same ... Page 31

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**described**from the centres C and D will cut each other in A and B. Fig . 57 , 58 . Fig . 57 . Fig . 58 THEOREM . 115. If the distance CD ( fig . 59 ) of the centres of two circles is Fig . 59 . equal to the sum of their radii CA , CD ... Page 33

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**described**from their vertices , as centres , with equal radii . Demonstration . Let us suppose the less angle placed in the greater ; if the proposition enunciated be not true , the angle ACB will be to the angle ACD as the arc AB is to ... Page 34

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**described**with equal radii . This is to be understood in the preceding propositions . 124. Scholium . It may seem more natural to measure a quan- tity by another quantity of the same kind , and upon this princi- ple it would be ... Page 38

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**described**. It is evident that the line CD will bisect the angle ACB . 138. Scholium . By the same construction , we may bisect each of the halves AE , EB , and thus , by successive subdivisions , we may divide an angle or arc into four ...### 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