## Elements of Geometry |

### From inside the book

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**intersection**, A , is the vertex of the angle ; the lines AB , AC , are its sides . An angle is sometimes denoted simply by the letter at the ver- tex , as A ; sometimes by three letters , as BAC or CAB , the letter at the vertex always ... Page 7

... ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their

... ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their

**intersection**A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of Perpendicular and Oblique Lines . 7. Page 18

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**intersection**from the fixed point F , is not exactly double the distance of the preceding point of**intersection**; since FN , for example , is less than FM + MN , or 2 FM ; we have , in like manner , FP < 2 FN , FQ < 2 FP , & c . But ... Page 30

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**intersection**, and will bisect it . Demonstration . The line AB ( fig . 57 , 58 ) , which joins the points of**intersection**, is a chord common to the two circles ; and , if a perpendicular be erected upon the middle of this chord , it ... Page 31

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**intersection**may take place , the triangle ACD ( fig . 57 , 58 ) must be possible . It is necessary , then , not only that CD ( fig . 57 ) should be less than AC + AD , but also that the greater radius AD ( fig . 58 ) should be less ...### 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