Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S. |
Inni boken
Side 29
I. Case 1. it will be , radius : sine C :: line CF : sine EF ; that is , radius : fine C :: co
- fine BC : co - fine A. 2. ... CF : tang . FE ( by the latter part of Theor . 1. ) that is ,
radius : AB :: co - tang . BC : co - tang . A :: tang . A : tang . BC ( by Corol . s . p .
I. Case 1. it will be , radius : sine C :: line CF : sine EF ; that is , radius : fine C :: co
- fine BC : co - fine A. 2. ... CF : tang . FE ( by the latter part of Theor . 1. ) that is ,
radius : AB :: co - tang . BC : co - tang . A :: tang . A : tang . BC ( by Corol . s . p .
Side 32
... and B division , co - fine AC + E F D Co - sine BC : co - fine AC - Co - sine BC ::
co - fine AD + co - fine BD : co . fine AD - Co - sine BD , But ( by the preceding
lemma ) co - fine AC + co - sine BC : co - fine ACco - fine BC :: co - tang . AC + BC
.
... and B division , co - fine AC + E F D Co - sine BC : co - fine AC - Co - sine BC ::
co - fine AD + co - fine BD : co . fine AD - Co - sine BD , But ( by the preceding
lemma ) co - fine AC + co - sine BC : co - fine ACco - fine BC :: co - tang . AC + BC
.
Side 36
5. ) rad . : co - fine AC :: Ito one of them tang . A .: co - tang . ACD , but ( by Cor . 2.
to Tbeor . 1. ) as tang . BC : tang . AC ; : co - fine ACD : co - fine BCD . Whence
ACB ACD + BCD is known . Two fides AC , The other As rad . : co - fine A : 1 tang
.
5. ) rad . : co - fine AC :: Ito one of them tang . A .: co - tang . ACD , but ( by Cor . 2.
to Tbeor . 1. ) as tang . BC : tang . AC ; : co - fine ACD : co - fine BCD . Whence
ACB ACD + BCD is known . Two fides AC , The other As rad . : co - fine A : 1 tang
.
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
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 .: co - fine BC :: co - fine AB : co - line AC ( by Theor . 2. ) ...
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 .: co - fine BC :: co - fine AB : co - line AC ( by Theor . 2. ) ...
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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 |