Elements of Geometry |
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Page vi
The second section , entitled the circle , treats of the most simple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution ...
The second section , entitled the circle , treats of the most simple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution ...
Page 25
A tangent is a line , which has only one point in common with the circumference , as CD . The common point M is called the point of contact . Also two circumferences are tangents to each other ( fig . 59 , 60 ) , Fig.69 . when they have ...
A tangent is a line , which has only one point in common with the circumference , as CD . The common point M is called the point of contact . Also two circumferences are tangents to each other ( fig . 59 , 60 ) , Fig.69 . when they have ...
Page 29
54 . radius AC , is a tangent to the circumference . Demonstration . Since every oblique line CE is greater than the perpendicular CA ( 52 ) , the point E is without the circle , and the line BD has only the point A in common with the ...
54 . radius AC , is a tangent to the circumference . Demonstration . Since every oblique line CE is greater than the perpendicular CA ( 52 ) , the point E is without the circle , and the line BD has only the point A in common with the ...
Page 30
56 ) , one be a secant and the other a tangent , to the point of contact H draw the radius CH ; this radius will be perpendicular to the tangent DE ( 110 ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP ...
56 ) , one be a secant and the other a tangent , to the point of contact H draw the radius CH ; this radius will be perpendicular to the tangent DE ( 110 ) , and also to its parallel MP . But , since CH is perpendicular to the chord MP ...
Page 31
And if , through the point A , we draw AE perpendicular to CD , the straight line AE will be a tangent common to all these circles . a THEOREM .
And if , through the point A , we draw AE perpendicular to CD , the straight line AE will be a tangent common to all these circles . a THEOREM .
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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 |