Elements of Geometry |
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Page 24
91. A segment of a circle is the portion comprehended between an arc and its chord . 92. A sector is the part of a circle comprehended between an arc DE and the two radii CD , CE , drawn to the extremities of this arc . Fig .
91. A segment of a circle is the portion comprehended between an arc and its chord . 92. A sector is the part of a circle comprehended between an arc DE and the two radii CD , CE , drawn to the extremities of this arc . Fig .
Page 34
... is equally applicable to the purpose of comparing sectors with arcs ; for sectors are equal , when their arcs are equal , and in general they are proportional to the angles ; hence two sectors ACB , ACD , taken in the same circle ...
... is equally applicable to the purpose of comparing sectors with arcs ; for sectors are equal , when their arcs are equal , and in general they are proportional to the angles ; hence two sectors ACB , ACD , taken in the same circle ...
Page 45
In two different circles , similar arcs , similar sectors , similar segments , are such as correspond to equal angles at the centre . ... 0 , the arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164.
In two different circles , similar arcs , similar sectors , similar segments , are such as correspond to equal angles at the centre . ... 0 , the arc BC is similar to the arc DE , the sector ABC to the sector ODE , & c . 164.
Page 89
If we have two concentric sectors FCG , ICH , we can likewise inscribe , in the greater , a portion of a regular polygon , or circumscribe , about the smaller , a portion of a similar GEOM . 12 F e 1 t : a polygon , so that the ...
If we have two concentric sectors FCG , ICH , we can likewise inscribe , in the greater , a portion of a regular polygon , or circumscribe , about the smaller , a portion of a similar GEOM . 12 F e 1 t : a polygon , so that the ...
Page 91
166 ) , are as Fig 166 . their radii AC , DO ; and similar sectors ACB , DOE , are as the squares of their radii . . For , since the arcs are similar , the angle C is equal to the angle 0 ( 163 ) ; now , the angle C is to four right ...
166 ) , are as Fig 166 . their radii AC , DO ; and similar sectors ACB , DOE , are as the squares of their radii . . For , since the arcs are similar , the angle C is equal to the angle 0 ( 163 ) ; now , the angle C is to four right ...
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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 |