## Elements of Geometry |

### From inside the book

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**namely**, the angle AD , the side AB DE , and the = side AC = DF , we may thence infer , that the other three are also equal ,**namely**, the angle B = E , the angle C = F , and the side BC EF . THEOREM . 38. Two triangles are equal , when ... Page 8

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**namely**, BC = EF , B = E , and C = F , we may thence infer , that the other three are also equal ,**namely**, AB = DE , AC DF , and A = = D . THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The ... Page 9

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**namely**, A = D , BE , and CF. For , if the angle A were greater than the angle D , as the sides AB , AC , are equal to the sides DE , DF , each to each , the side BC would be greater than EF ( 42 ) ; and if the angle A were less than ... Page 14

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**namely**, C'K = IB = CI , and KB ' — AKAI , since we have supposed AB ' = 2 AI = 2AK . Therefore the two triangles B'C'K , ACI , are equal ( 36 ) , and , consequently , the side C'B ' = AC , and the angle B'C'K = ACB , and the angle KB'C ... Page 22

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**namely**, AB = CD , and AD = CB , the equal sides will be parallel , and the figure will be a parallelogram . Demonstration . Draw the diagonal BD ; the two triangles ABD , BDC , have the three sides of the one equal to the three sides ...### 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