## Elements of Geometry |

### From inside the book

Results 1-5 of 100

Page 3

...

...

**drawn**between two points . 26. Two magnitudes , whether they be lines , surfaces , or solids , are equal , when , being applied the one to the other , they coin- cide with each other entirely ; that is , when they exactly fill the same ... Page 5

...

...

**drawn**from A to B , which is impossi- ble ( 25 ) . Now let us suppose , if it be possible , that the lines , when produced , separate from each other at a point C , the one becoming CD and the other CE . At the point C , let CF be**drawn**... Page 8

...

...

**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 D ; the ... Page 10

...

...

**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 = AD + ... Page 11

...

...

**drawn**to that line Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that ...**drawn**between the same two points A and F , which is impossible ( 25 ) ; it is , then , equally impossible to**draw**...### 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