Elements of Geometry and Trigonometry |
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Page 209
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 210
... of an arc B M M R E P zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . the circle , we have Hence if R represents the radius of sin 0-0 , tang 0 = 0 , cos 0 = R , sec 0 = R . VIII .
... of an arc B M M R E P zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . the circle , we have Hence if R represents the radius of sin 0-0 , tang 0 = 0 , cos 0 = R , sec 0 = R . VIII .
Page 211
This is expressed by saying that the tangent of 90 ° is infinite ; and we write tang 90 ° —∞ The complement of 90 ° being zero , we have Hence tang 0 = cot 90o and cot 0 = tang 90o . cot 90o - 0 , and cot 0 = ∞ .
This is expressed by saying that the tangent of 90 ° is infinite ; and we write tang 90 ° —∞ The complement of 90 ° being zero , we have Hence tang 0 = cot 90o and cot 0 = tang 90o . cot 90o - 0 , and cot 0 = ∞ .
Page 212
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 213
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 årcs 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 årcs 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 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 |