Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S. |
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Resultat 1-5 av 5
Side 30
D : tang . BC ) we shall ( by reasoning as in Cor . 1. Tbeor . 1. ) have Sine AB :
sine DB :: tang . D : tang . A. B THEOREM V. In any right - angled spherical
triangle it will be , as radius is to the co - fine of the hypothenuse , so is the
tangent of ...
D : tang . BC ) we shall ( by reasoning as in Cor . 1. Tbeor . 1. ) have Sine AB :
sine DB :: tang . D : tang . A. B THEOREM V. In any right - angled spherical
triangle it will be , as radius is to the co - fine of the hypothenuse , so is the
tangent of ...
Side 32
AC + BC . AC - BC : tang i 2 and co - fine AD + co - fine BD : co - fine ADAD + BD
Con - fine BD :: Co - tang.of AE tang 2 DE / AD - BD ( AD BD ) ; whence ; by
equality , co - tang . - 2 AC + BC AC - BC : tang :: Co - tang . AE : tang . 2 DE .
AC + BC . AC - BC : tang i 2 and co - fine AD + co - fine BD : co - fine ADAD + BD
Con - fine BD :: Co - tang.of AE tang 2 DE / AD - BD ( AD BD ) ; whence ; by
equality , co - tang . - 2 AC + BC AC - BC : tang :: Co - tang . AE : tang . 2 DE .
Side 36
Two fides AC , The included Upon AB produced ( if need be ) let BC and an an-
angle ACB fall the perpendicular CD ; then ( by Igle A oppofite Tbeor . 5. ) rad . :
co - fine AC :: Ito one of them tang . A .: co - tang . ACD , but ( by Cor . 2. to Tbeor .
Two fides AC , The included Upon AB produced ( if need be ) let BC and an an-
angle ACB fall the perpendicular CD ; then ( by Igle A oppofite Tbeor . 5. ) rad . :
co - fine AC :: Ito one of them tang . A .: co - tang . ACD , but ( by Cor . 2. to Tbeor .
Side 37
whence 6 fide AC beBCD is also known ; then ( by Cor . twixt them . to Theor . 3. )
as fine ACD i fiue BCD :: co - fine A : co fine B. Two augles A , Either of the As
rado : co - fue C : : tang . A : ACB and the other fides , co - tang . ACD ( by Theor .
5. ) ...
whence 6 fide AC beBCD is also known ; then ( by Cor . twixt them . to Theor . 3. )
as fine ACD i fiue BCD :: co - fine A : co fine B. Two augles A , Either of the As
rado : co - fue C : : tang . A : ACB and the other fides , co - tang . ACD ( by Theor .
5. ) ...
Side 72
By Thomas Simpson, F.R.S. Thomas Simpson. PROP . XXI . One leg BC and the
fun , or difference , of the bypothenuse and the other leg AB being given , to
determine the hypothenuse ( see the last figure . ) BC : : co - tang . : tàng Since
rad .
By Thomas Simpson, F.R.S. Thomas Simpson. PROP . XXI . One leg BC and the
fun , or difference , of the bypothenuse and the other leg AB being given , to
determine the hypothenuse ( see the last figure . ) BC : : co - tang . : tàng Since
rad .
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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 demonſtrated determine diameter difference divided drawn Edition equal equal to half evident exceſs extremes fame fides fine fines firſt follows given gives gles great-circles greater half the difference half the ſum Hence hyperbolic logarithm hypothenuſe known laſt logarithm manifeſt meeting method minute Moreover natural Note oppoſite parallel perpendicular plane triangle ABC preceding PROP proportion propoſed radius reſpectively ſame ſecant ſee ſeries ſhall ſides ſince ſine 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. By Thomas Simpson, F.R.S. Eighteenth century collections online |
| Forfatter | Thomas Simpson |
| Utgave | 5 |
| Utgiver | F. Wingrave, successor to Mr. Nourse, 1799 |
| Original fra | The British Library |
| Digitalisert | 30. sep 2016 |
| Lengde | 79 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |