Elements of Geometry and Trigonometry |
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Page 41
Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ...
Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E eter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ...
Page 44
... are equal , it is plain that the radius CD will fall on the radius OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater ...
... are equal , it is plain that the radius CD will fall on the radius OG , and the point D on the point G ; therefore the arc AMD is equal to the arc ENG . PROPOSITION V. THEOREM . In the same circle , or in equal circles , a greater ...
Page 45
The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and CG the ra dius perpendicular to it : then will AD = DB , and the arc AG - GB .
The radius which is perpendicular to a chord , bisects the chord , and bisects also the subtended arc of the chord . Let AB be a chord , and CG the ra dius perpendicular to it : then will AD = DB , and the arc AG - GB .
Page 46
... are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given ...
... are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given ...
Page 47
A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe- rence .
A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe- rence .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Edition | 4 |
| Publisher | A.S. Barnes and Company, 1834 |
| Original from | the University of California |
| Digitized | 14 Oct 2010 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |