## Elements of Geometry |

### From inside the book

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**Draw**the straight line AD from the vertex A to the point D , the middle of the base BC ; the two triangles ABD , ADC , will have the three sides of the one equal to the three sides of the other , each to each , namely , AD common to ... Page 10

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**drawn**from the vertex of an isosceles triangle to the middle of the base , is perpendicular to that base , and ...**Draw**CD , making the angle BCD = B. In the triangle BDC , BD is equal to DC ( 48 ) ; but AD + DC > AC , and AD + DC ... Page 11

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**drawn**to that line Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that ...**draw**two perpendiculars to that line ; for , if CD and CE were these two perpendiculars , the an- gle DCB would be a ... Page 12

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**drawn**three equal straight lines terminating in a given straight line ; for , if this could be done , there would be on the same side of the perpendicular two equal oblique lines , which is impossible . THEOREM./ 55. If , from the point ... Page 13

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**draw**the straight line AI , and produce it to C ' , mak- ing ACAB ; produce also AB to B ' , making AB ' double of AI . If we designate by A , B , C , the three angles of the triangle ABC , and by A ' , B ' , C ' , the three angles of ...### 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