## Elements of Geometry |

### From inside the book

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**base**BC ; the two triangles ABD , ADC , will have the three sides of the one equal to the three sides of the other , each to each , namely , AD common to both , AB = = AC , by hypothesis , and BD = DC , by construction ; therefore ( 43 ) ... Page 10

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**base**, is perpendicular to that**base**, and divides the vertical angle into two equal parts . In a triangle that is not isosceles , any one of its sides may be taken indifferently for a**base**; and then its vertex is that of the opposite ... Page 25

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**base**AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is contrary to the definition of a ... Page 34

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**bases**of these sectors . It will be perceived , therefore , that the arcs of a circle , which are used as a measure of angles , will also serve as the measure of different sectors of the same circle or of equal circles . ་ THEOREM . 126 ... Page 45

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**bases**and equal alti- tudes , are equivalent . Demonstration . Let AB ( fig . 96 ) be the common**base**of the Fig . 96 . two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to ...### 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