Elements of Geometry |
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Page 22
... circumference is called a radius or semidiameter , and every straight line , as AB , which passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are ...
... circumference is called a radius or semidiameter , and every straight line , as AB , which passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are ...
Page 23
... 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 . 59 , when they have only one point common . 60 . A polygon is said to be ...
... 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 . 59 , when they have only one point common . 60 . A polygon is said to be ...
Page 24
... circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Fig . 50 . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD ...
... circumference , the greater arc is subtended by the greater chord ; and , conversely , the greater chord is subtended by the greater arc . Fig . 50 . Demonstration . Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD ...
Page 25
... circumference of a circle may be made to pass through any three points , A , B , C ( fig . 52 ) , which are not in the same Fig . 52 . Geom . 4 straight line , but the circumference of only one circle Of the Circle . 25.
... circumference of a circle may be made to pass through any three points , A , B , C ( fig . 52 ) , which are not in the same Fig . 52 . Geom . 4 straight line , but the circumference of only one circle Of the Circle . 25.
Page 26
... circumference , described from the centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in ...
... circumference , described from the centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in ...
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Common terms and phrases
ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed 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 proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment sides similar solid angle Solution sphere spherical square straight line suppose surface taken THEOREM third triangle ABC triangular pyramids vertex vertices whence
Bibliographic information
| Title | Elements of Geometry |
| Author | Adrien Marie Legendre |
| Edition | 2 |
| Publisher | Hilliard and Metcalf, 1825 |
| Original from | the University of Virginia |
| Digitized | 29 Oct 2010 |
| Length | 224 pages |
| Export Citation | BiBTeX EndNote RefMan |