Elements of Geometry and Trigonometry |
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Page 208
GENERAL IDEAS RELATING TO THE TRIGONOMERICAL LINES V. The sine of an arc is the perpendicular let fall from one extremity of the arc , on the diameter which passes through the other extremity . Thus , MP is the sine of the arc AM ...
GENERAL IDEAS RELATING TO THE TRIGONOMERICAL LINES V. The sine of an arc is the perpendicular let fall from one extremity of the arc , on the diameter which passes through the other extremity . Thus , MP is the sine of the arc AM ...
Page 209
The versed sine of an arc , is the part of the diameter inter- cepted between one extremity of the arc and the foot of the sine . Thus , AP is the versed sine of the arc AM , or the angle ACM . These four lines MP , AT , CT , AP , are ...
The versed sine of an arc , is the part of the diameter inter- cepted between one extremity of the arc and the foot of the sine . Thus , AP is the versed sine of the arc AM , or the angle ACM . These four lines MP , AT , CT , AP , are ...
Page 210
When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc B M M R E P zero , are zero , and the cosine and secant of this ...
When the point M is at A , or when the arc AM is zero , the three points T , M , P , are confounded with the point A ; whence it appears that the sine and tangent of an arc B M M R E P zero , are zero , and the cosine and secant of this ...
Page 211
Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + M'B is equal to a semicircumference ; besides , if M'M is drawn parallel to AB , the arcs AM , BM ' , which ...
Thus M'P ' is the sine of the arc AM ' , and M'Q , or CP ' its cosine . But the arc M'B is the supplement of AM ' , since AM ' + M'B is equal to a semicircumference ; besides , if M'M is drawn parallel to AB , the arcs AM , BM ' , which ...
Page 212
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be ...
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . Now when the arc AM be- comes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be ...
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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 |