## Elements of Geometry |

### From inside the book

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**given point**A ( fig . 31 ) , without a straight line Fig . 3k , DE , only one perpendicular can be drawn to that line Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that BF AB , and join ... Page 12

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**point**from**a**straight line . 54. Corollary II . From the same**point**, there cannot be 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 ... Page 19

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**given**angle GFD ; and it will nevertheless be true that FZ produced will meet AB in**a**determinate**point**; therefore , for**a**still stronger reason , the straight line FD , comprehended in the an- gle EFZ , will meet AB . 2. Let us ... Page 25

... a circle in more than two points . Demonstration . If it could meet it in three , these three points being equally distant from the centre , there might be three equal straight lines drawn from a

... a circle in more than two points . Demonstration . If it could meet it in three , these three points being equally distant from the centre , there might be three equal straight lines drawn from a

**given point**to the same straight line ... Page 28

... a similar reason ; it will , then , be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is , therefore , only one circle , whose circum- ference can pass through three

... a similar reason ; it will , then , be in both of these lines at the same time . But two lines can cut each other in only one point ( 32 ) ; there is , therefore , only one circle , whose circum- ference can pass through three

**given points**...### 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