## Elements of Geometry |

### From inside the book

Results 1-5 of 93

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 between two**given**points . But in order to this it would have been necessary ... 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 demonstrated 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 several propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show their ... Page 11

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**given**point A ( fig . 31 ) , without a straight line DE , Fig 31 . 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 . Fig . 32 55. If from the point C ( fig . 32 ) , the middle of the ...### Other editions - View all

### Common terms and phrases

ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment sides similar solid angle Solution sphere spherical square straight line suppose surface taken THEOREM third triangle ABC triangular pyramids vertex vertices whence