Elements of Geometry |
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Page 26
... 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 ...
... 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 29
... described from the centres C and D will cut each other in A and B. 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 , these two circles will touch each ...
... described from the centres C and D will cut each other in A and B. 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 , these two circles will touch each ...
Page 31
... 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 ...
... 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 ...
Page 32
... 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 ...
... 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 36
... 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 subdivis- ions , we may divide an angle or arc into ...
... 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 subdivis- ions , we may divide an angle or arc into ...
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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