## Elements of Geometry |

### From inside the book

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**half**of AF is less than AC**half**of AC + CF ; that is , the perpendicular is less than any one of the oblique lines . - 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right angle ABE ABC , the triangle ... Page 18

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**half**the angle GFN , or one fourth of the angle GFM . = We are able , therefore , in this manner , to take successively the**half**, the fourth , the eighth , & c . , of the angle GFM , and the lines which form these divisions meet the ... Page 26

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**half**a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and ... Page 29

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**half**of AB , is equal to the side DG , the**half**of DE ; the triangles , then , are equal ( 56 ) , and consequently the third side CF is equal to the third side CG ; therefore the two equal chords AB , DE , are at the same distance from ... Page 35

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**half**of the arc BD comprehended between its sides . = Demonstration . Let us suppose , in the first place , that the ...**half**of BE . For a similar reason , the angle CAD has for its measure the**half**of ED ; therefore BAC + CAD , or BAD ...### 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