Elements of Geometry |
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Page 24
A straight line is said to be inscribed in a circle , when its extremities are in the circumference of the circle , as AB ( fig 47 ) . 94. An inscribed angle is one whose vertex is in the circumference , and which is formed by two ...
A straight line is said to be inscribed in a circle , when its extremities are in the circumference of the circle , as AB ( fig 47 ) . 94. An inscribed angle is one whose vertex is in the circumference , and which is formed by two ...
Page 25
And , in general , an inscribed figure is one , all whose angles have their vertices in the circumference of the circle . In this case , the circle is said to be circumscribed about the figure . 96. A secant is a line , which meets the ...
And , in general , an inscribed figure is one , all whose angles have their vertices in the circumference of the circle . In this case , the circle is said to be circumscribed about the figure . 96. A secant is a line , which meets the ...
Page 35
The inscribed angle BAD ( fig . 64 , 65 ) , has for its 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 ...
The inscribed angle BAD ( fig . 64 , 65 ) , has for its 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 ...
Page 36
66 ) , inscribed in a segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicircumference . And every angle BOC , inscribed in a segment less than a semicircle , is an ...
66 ) , inscribed in a segment greater than a semicircle , is an acute angle ; for it has for its measure the half of the arc BOC less than a semicircumference . And every angle BOC , inscribed in a segment less than a semicircle , is an ...
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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 |