Elements of Geometry |
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Page v
... at the same time , a discipline of peculiar kind , distinct from that of analysis , and which , in important mathematical researches , may afford great assistance towards discovering the most simple and elegant solutions .
... at the same time , a discipline of peculiar kind , distinct from that of analysis , and which , in important mathematical researches , may afford great assistance towards discovering the most simple and elegant solutions .
Page 3
A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the demonstration of a theorem , or in the solution of a problem . The common name of Proposition ...
A Problem is a question proposed which requires a solution . A Lemma is a subsidiary truth employed in the demonstration of a theorem , or in the solution of a problem . The common name of Proposition ...
Page 36
Solution . From the points A and B , as centres , and with a radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from the points A and B ; find , in like manner , either ...
Solution . From the points A and B , as centres , and with a radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from the points A and B ; find , in like manner , either ...
Page 37
Solution . Take the points B and C , at equal distances from A ; and from B and C , as centres , with a radius greater than BA , describe two arcs cutting each other in D ; draw AD , which will be the perpendicular required .
Solution . Take the points B and C , at equal distances from A ; and from B and C , as centres , with a radius greater than BA , describe two arcs cutting each other in D ; draw AD , which will be the perpendicular required .
Page 38
Solution 1. If it is proposed to bisect the arc AB ( fig . 74 ) , from the points A and B , as centres , with the same radius , describe two arcs intersecting each other in D ; through the point D and the centre C draw CD , which will ...
Solution 1. If it is proposed to bisect the arc AB ( fig . 74 ) , from the points A and B , as centres , with the same radius , describe two arcs intersecting each other in D ; through the point D and the centre C draw CD , which will ...
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Common terms and phrases
ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles 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 produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence
Bibliographic information
| Title | Elements of Geometry |
| Author | Adrien Marie Legendre |
| Translated by | John Farrar |
| Publisher | Hilliard, Gray, and Company, 1833 |
| Original from | University of Chicago |
| Digitized | 11 Apr 2012 |
| Length | 235 pages |
| Export Citation | BiBTeX EndNote RefMan |