Elements of Geometry |
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Page 12
But AF < AC + CF ( 40 ) , and AB half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the oblique lines . 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right ...
But AF < AC + CF ( 40 ) , and AB half of AF is less than AC half of AC + CF ; that is , the perpendicular is less than any one of the oblique lines . 2. If BE = BC , then , as AB is common to the two triangles ABE , ABC , and the right ...
Page 18
We are able , therefore , in this manner , to take successively the half , the fourth , the eighth , & c . , of the angle GFM , and the lines which form these divisions meet the line AB in points more and more distant , but easily ...
We are able , therefore , in this manner , to take successively the half , the fourth , the eighth , & c . , of the angle GFM , and the lines which form these divisions meet the line AB in points more and more distant , but easily ...
Page 26
In the same circle , or in equal circles , if the arc be less than half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration .
In the same circle , or in equal circles , if the arc be less than half a circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Demonstration .
Page 29
The right - angled triangles CAF , DCG , have the hypothenuses CA , CD , equal ; moreover , the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles , then , are equal ( 56 ) , and consequently the third ...
The right - angled triangles CAF , DCG , have the hypothenuses CA , CD , equal ; moreover , the side AF , the half of AB , is equal to the side DG , the half of DE ; the triangles , then , are equal ( 56 ) , and consequently the third ...
Page 35
64 measure the half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the first place , that the centre of the circle is situated in the angle BAD ( fig . 64 ) ; we Fig .
64 measure the half of the arc BD comprehended between its sides . Demonstration . Let us suppose , in the first place , that the centre of the circle is situated in the angle BAD ( fig . 64 ) ; we Fig .
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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 |