Elements of Geometry and Trigonometry |
From inside the book
Page 41
Every straight line , CA , CE , CD , drawn from the centre to the circumference , is called a radius or semidiameter ; 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 circumference , is called a radius or semidiameter ; every line which , like AB , passes through the centre , and is terminated on both sides by the circumference ...
Page 44
... 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 arc is ...
... 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 arc is ...
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 radius 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 radius perpendicular to it : then will AD = DB , and the arc AG - GB .
Page 46
... are equal ; therefore 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 ; therefore 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
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfeF K H A A straight line perpendicular to a radius , at its extremity , is a tangent to the circumference . E D rence .
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Common terms and phrases
ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole
Bibliographic information
| Title | Elements of Geometry and Trigonometry DAVIES' COURSE OF MATHEMATICS |
| Author | Adrien Marie Legendre |
| Editor | Charles Davies |
| Translated by | David Brewster |
| Publisher | A.S. Barnes and Company, 1839 |
| Original from | Harvard University |
| Digitized | 14 Jan 2008 |
| Length | 359 pages |
| Export Citation | BiBTeX EndNote RefMan |