Trigonometry, Plane and Spherical;: With the Construction and Application of Logarithms |
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Side 24
... spherical angle CAD * is an arch of a great circle intercepted by the two circles
ACB , ADB forming that angle , and whose pole is the angular point A. For let the
diameter AB be the intersection of the great - circles ADB and ACB ( see Corol .
... spherical angle CAD * is an arch of a great circle intercepted by the two circles
ACB , ADB forming that angle , and whose pole is the angular point A. For let the
diameter AB be the intersection of the great - circles ADB and ACB ( see Corol .
Side 55
... by R ; then will the fine of their sum Sc + SC R SC SC the sine of their
difference = R the co - fine of their sum = CCSS R the co - fine of their difference =
Cc + Ss R E4 COROL • COROLLARY II . fine = Hence , the line Sines , Tangents ,
& c .
... by R ; then will the fine of their sum Sc + SC R SC SC the sine of their
difference = R the co - fine of their sum = CCSS R the co - fine of their difference =
Cc + Ss R E4 COROL • COROLLARY II . fine = Hence , the line Sines , Tangents ,
& c .
Side 73
Whence it appears , that , As the co - tangent of half the hypothenuse , is to its
tangent ; so is the co - fine of the difference of the angles at the hypothenuse , to
the fine of the excess of their sum above a right - angle . COROL COROLLAR Y.
Whence it appears , that , As the co - tangent of half the hypothenuse , is to its
tangent ; so is the co - fine of the difference of the angles at the hypothenuse , to
the fine of the excess of their sum above a right - angle . COROL COROLLAR Y.
Side 76
With the Construction and Application of Logarithms Thomas Simpson. co - f . CB
: rad . ( : : co - f . BD : co - f . CD ) :: 00-1 . AB : co - f . AC ( by Corol , to Theor . 2. )
whence , by multiplying means and extremes , we have co - f . . S. CB x co - f .
With the Construction and Application of Logarithms Thomas Simpson. co - f . CB
: rad . ( : : co - f . BD : co - f . CD ) :: 00-1 . AB : co - f . AC ( by Corol , to Theor . 2. )
whence , by multiplying means and extremes , we have co - f . . S. CB x co - f .
Side 77
therefore it will be co - s . AB X R = co - f . AF XR S. AC X S. BC X V and
consequently V = R R ? x co - f . AF Co - f . AB Which is the first S. AC X S. BC
case . Again , because S. AC X S. BC is = 4RX Co - f . AF — Co - f . AE ( by Corol
. 3. to Prop ...
therefore it will be co - s . AB X R = co - f . AF XR S. AC X S. BC X V and
consequently V = R R ? x co - f . AF Co - f . AB Which is the first S. AC X S. BC
case . Again , because S. AC X S. BC is = 4RX Co - f . AF — Co - f . AE ( by Corol
. 3. to Prop ...
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Vanlige uttrykk og setninger
added alſo appears arch balf baſe becauſe called caſe chord circle co-f co-fine AC co-tang common complement conſequently Corol COROLLARY determine diameter difference divided drawn equal equal to half evident exceſs extremes fide AC fine fines firſt follows given gives gles greater half the ſum half their difference Hence hyperbolic logarithm hypothenuſe laſt logarithm manifeft meeting method minute moreover Note oppoſite parallel perpendicular plane triangle ABC preceding progreſſion PROP proportion propoſed radius rectangle reſpectively right-angled ſame ſecant ſee ſeries ſhall ſides ſince ſine ſpherical Spherical triangle ABC ſubtracted ſum ſuppoſed tang tangent of half Tbeor Theor THEOREM thereof theſe thoſe unity verſed vertical angle whence
Bibliografisk informasjon
| Tittel | Trigonometry, Plane and Spherical;: With the Construction and Application of Logarithms Trigonometry, Plane and Spherical;: With the Construction and Application of Logarithms, Thomas Simpson |
| Forfatter | Thomas Simpson |
| Bidragsyter | John Nourse |
| Utgiver | J. Nourse, bookseller in ordinary to his Majesty., 1765 |
| Original fra | Oxford University |
| Digitalisert | 27. feb 2009 |
| Lengde | 79 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |