## Elements of Geometry |

### From inside the book

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**sides**AC , CB , are in the same straight line . Demonstration . For if CB is not the line AC produced , let CE be ...**number**of straight lines , as CA , CB ( fig . 22 ) , & c . , meet in the same point C , the sum of all the successive ... Page 16

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**number of sides**minus two . Demonstration . Let ABCDE , & c . ( fig . 42 ) , be the proposed polygon ; if , from the vertex of the angle A , we draw to the ver- tices of the opposite angles the diagonals AC , AD , AE , & c . , it is ... Page 34

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**sides**have such a connexion , that , when one increases or diminishes in any ratio whatever , the other increases or ...**number**comprehended between O and 1 , and an obtuse angle by a**number**between 1 and 2 . But this manner of ... Page 48

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**number**of linear units contained in the altitude . This measure , however , is not absolute , but relative ; it sup- poses that we estimate , in a similar manner , another rectangle by measuring its**sides**by the same linear unit ; we ... Page 49

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**number**by itself . The squares of the**numbers**1 , 2 , 3 , & c . , are 1 , 4 , 9 , & c . Thus a double line gives a ...**sides**AB , CD . GEOM 7 Fig . 106 . Demonstration . Through the point I Of the Proportions of Figures . 49.### 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