## Elements of Geometry |

### From inside the book

Results 1-5 of 52

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**Let**the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will ...**fall**upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ... Page 7

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**let**the angle A be equal to the angle D , the side AB equal to the side DE , and the side AC equal to the side DF ...**fall**upon A , and the point E upon B. But , since the angle D is equal to the angle A , when the side DE is placed upon ... Page 9

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**fall**upon the side BC , then Fig . 26 it is evident that GC , or its equal EF , is less than BC . Case III . If the ...**Let**the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the angles will be equal , namely , A = D ... Page 17

... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we

... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we

**let fall**upon AB a perpendicular FG . In the triangle EFG , the sum of ... Page 26

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**fall**upon G ; therefore the chord AD is equal to the chord EG . Conversely , AC being supposed equal to EO , if the ...**Let**the arc AH ( fig . 50 ) be greater than AD , and**let**the chords AD and AH , and the radii CD , CH , be drawn ...### 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