## Elements of Geometry |

### From inside the book

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**ABC**, DEF ( fig . 23 ) , Fig . 23**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 ; the two triangles**ABC**, DEF , will be equal . Indeed , the triangles may be so placed ... Page 8

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**ABC**, there be drawn straight lines OB , OC , to the extremities of BC , one of its sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration .**Let**BO be produced till it meet the side AC in ... Page 10

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**Let**the angle**ABC**ACB ( fig . 29 ) , the side AC will be equal to the side AB . For , if these sides are not equal ,**let**AB be the greater . Take BDAC , and join DC . The angle DBC is , by hypothesis , equal to ACB , and the two sides ... Page 11

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**let**there be two AB and AC ; produce one of them AB , so that BF AB , and join CF. = = : The triangle CBF is equal to the triangle**ABC**. For the angle CBF is a right angle ( 29 ) , as well as CBA , and the side BF BA ; therefore the ... Page 12

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**ABC**, and the right angle ABE**ABC**, the triangle ABE is equal to the triangle**ABC**, and AE = AC . 3. In the triangle ...**Let**I be a point out of the perpendicular ; join IA , IB , one of these lines must cut the perpendicular in D ; join ...### 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