## Elements of Geometry |

### From inside the book

Results 1-5 of 98

Page v

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**given**points . For , from this essential property we can deduce all the other properties of a straight line , and particularly that of its being the shortest be- tween two**given**points . But , in order to this , it would have been ... Page vii

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**given**two methods of approximation for squaring the circle , one of which is that of James Gregory . This section is followed by an appendix , in which we have de- monstrated that the circle is greater than any rectilineal figure of the ... Page 3

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**given**indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show ... Page 11

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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 CF ... Page 12

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**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 C ( fig . 32 ) , the middle of the straight line ...### 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