Elements of Geometry and Trigonometry |
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Page 214
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 , or of the angle ACM . The tangent of an arc is a line ...
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 , or of the angle ACM . The tangent of an arc is a line ...
Page 215
The versed sine of an arc , is the part of the diameter intercepted 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 intercepted 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 216
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 S B or P ' 0 R E sin 90 ° cos 0 ° -R , and cos 90 ° sin 0 ° 0 .
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 S B or P ' 0 R E sin 90 ° cos 0 ° -R , and cos 90 ° sin 0 ° 0 .
Page 217
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 218
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c -cos AM . Now when the arc AM becomes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot ...
The versed sine AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM = R - c -cos AM . Now when the arc AM becomes AM ' the versed sine AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot ...
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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 |