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 72
BC : : co - tang . : tàng Since rad .: co - fine BC :: co - fine AB : co - line AC ( by
Theor . 2. ) , it will be ( by comp . and div . ) radius + co - line BC : rad . Co - f . BC
:: Co - f . AB + ' co - f . AC : co - f . AB CO - S . AC . But the radius may be
considered ...
BC : : co - tang . : tàng Since rad .: co - fine BC :: co - fine AB : co - line AC ( by
Theor . 2. ) , it will be ( by comp . and div . ) radius + co - line BC : rad . Co - f . BC
:: Co - f . AB + ' co - f . AC : co - f . AB CO - S . AC . But the radius may be
considered ...
Side 75
CD + co - f.CBXCO - SCD rad . ( by Cor . 1. to Prop . 2. ) it is evident , that co - f .
BD : co - f . CD :: А S.CBXS.CD + co - f.CB x co-f.CD rad . S. CB x S. CD : co - f .
CD :: + co - f.CB : rad . ( by Co - f . CD S.CD mult , each term by T.CD , Co-S.CD ...
CD + co - f.CBXCO - SCD rad . ( by Cor . 1. to Prop . 2. ) it is evident , that co - f .
BD : co - f . CD :: А S.CBXS.CD + co - f.CB x co-f.CD rad . S. CB x S. CD : co - f .
CD :: + co - f.CB : rad . ( by Co - f . CD S.CD mult , each term by T.CD , Co-S.CD ...
Side 76
1 Co - f . CB : rad . ( : : 20 - f . BD : 20 - f . CD ) :: Co - fa AB : co - f . AC ( by Corol .
to Theor . 2. ) whence , by multiplying means and extremes , we have co - f . S.
CB x co - f . AC XT . CD AB x radius = + rad . co - f . AC x 20 - . BC . But ( by Theor
.
1 Co - f . CB : rad . ( : : 20 - f . BD : 20 - f . CD ) :: Co - fa AB : co - f . AC ( by Corol .
to Theor . 2. ) whence , by multiplying means and extremes , we have co - f . S.
CB x co - f . AC XT . CD AB x radius = + rad . co - f . AC x 20 - . BC . But ( by Theor
.
Side 77
11 : It appears from the last Prop . that co - f . AB x R is = co - f . AC x co - f . BC +
S. AC x S. BC x co - f . C R in which , for co - f . C. let its equal R - V be fubstituted ,
and then we shall have co - fine AB x R =F Co - fine AC x co - fine BC B + fine .
11 : It appears from the last Prop . that co - f . AB x R is = co - f . AC x co - f . BC +
S. AC x S. BC x co - f . C R in which , for co - f . C. let its equal R - V be fubstituted ,
and then we shall have co - fine AB x R =F Co - fine AC x co - fine BC B + fine .
Side 79
1 2R x Co - f . AF - CO - CAB , Lastly , because V = co - f . AF – co - f . AE we shall
, by transforming the equation , and putting W for ( 2R – V ) the versed sine of
BCE ( the supplement of the vertical angle ) have co f . AE = 2R x Co - f , AB - W X
...
1 2R x Co - f . AF - CO - CAB , Lastly , because V = co - f . AF – co - f . AE we shall
, by transforming the equation , and putting W for ( 2R – V ) the versed sine of
BCE ( the supplement of the vertical angle ) have co f . AE = 2R x Co - f , AB - W X
...
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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 |