Elements of Geometry and Trigonometry |
From inside the book
Page 215
These four lines MP , AT , CT , AP , are dependent upon the arc AM , and are always determined by it and the radius ; they are thus designated : MP sin AM , or sin ACM , AT = tang AM , or tang ACM , CT sec AM , or sec ACM , AP - ver ...
These four lines MP , AT , CT , AP , are dependent upon the arc AM , and are always determined by it and the radius ; they are thus designated : MP sin AM , or sin ACM , AT = tang AM , or tang ACM , CT sec AM , or sec ACM , AP - ver ...
Page 216
Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 = R , sec 0 = R . A VIII . As the point M advances towards D , the sine increases , and so likewise does the tangent and the secant ; but the cosine ...
Hence if R represents the radius of the circle , we have sin 0 = 0 , tang 0 = 0 , cos 0 = R , sec 0 = R . A VIII . As the point M advances towards D , the sine increases , and so likewise does the tangent and the secant ; but the cosine ...
Page 217
This is expressed by saying that the tangent of 90o is infinite ; and we write tang 90o– ∞ The complement of 90o being zero , we have tang 0 = cot 90o and cot 0 = tang 90o . cot 90 ° = 0 , and cot 0 = ∞ .
This is expressed by saying that the tangent of 90o is infinite ; and we write tang 90o– ∞ The complement of 90o being zero , we have tang 0 = cot 90o and cot 0 = tang 90o . cot 90 ° = 0 , and cot 0 = ∞ .
Page 218
When the point M ' reaches the point B the tangent AV will become equal to zero : that is , tang 180 ° = 0 . When the point M ' passes the point B , and comes into the position N ' , the tangent of the arc ADN ' will be the line AT ...
When the point M ' reaches the point B the tangent AV will become equal to zero : that is , tang 180 ° = 0 . When the point M ' passes the point B , and comes into the position N ' , the tangent of the arc ADN ' will be the line AT ...
Page 219
At E the tangent becomes infinite : that is , tang 270 ° = ∞ . When the point has passed along into the fourth quadrant to N , the tangent of the arc ADN'N will be the line AV : hence , the tangents of all arcs which terminate in the ...
At E the tangent becomes infinite : that is , tang 270 ° = ∞ . When the point has passed along into the fourth quadrant to N , the tangent of the arc ADN'N will be the line AV : hence , the tangents of all arcs which terminate in the ...
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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 |