Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S. |
Inni boken
Side 17
Plane and Spherical; with the Construction and Application of Logarithms. By
Thomas Simpson, F.R.S. Thomas Simpson. Prop . 1. which let be denoted by C ;
then ( by Tbeor . 1. p . 13. ) we shall have 2C x sine 1 ' sine o ' = fine 2 ' . 2C x sine
2 ...
Plane and Spherical; with the Construction and Application of Logarithms. By
Thomas Simpson, F.R.S. Thomas Simpson. Prop . 1. which let be denoted by C ;
then ( by Tbeor . 1. p . 13. ) we shall have 2C x sine 1 ' sine o ' = fine 2 ' . 2C x sine
2 ...
Side 28
D 1 B Radius : fine F :: sine CF : sine CE ; that is , Radius : co - sine BA :: co - fine
CB : co - fine AC ( Jee Cor . 4. P. 25. ) 2. E. D.J 1 COROLLARY : Hence , if two
rightangled spherical triangles ABC , CBD have the same perpendicular DBC ,
the ...
D 1 B Radius : fine F :: sine CF : sine CE ; that is , Radius : co - sine BA :: co - fine
CB : co - fine AC ( Jee Cor . 4. P. 25. ) 2. E. D.J 1 COROLLARY : Hence , if two
rightangled spherical triangles ABC , CBD have the same perpendicular DBC ,
the ...
Side 29
Plane and Spherical; with the Construction and Application of Logarithms. By
Thomas Simpson, F.R.S. Thomas Simpson. DEMONSTRATION . Let CEF be as
in the preceding proposition ; then , by Theor . I. Case 1. it will be , radius : sine C
...
Plane and Spherical; with the Construction and Application of Logarithms. By
Thomas Simpson, F.R.S. Thomas Simpson. DEMONSTRATION . Let CEF be as
in the preceding proposition ; then , by Theor . I. Case 1. it will be , radius : sine C
...
Side 30
Hence it follows , that , in right - angled spherical triangles ABC , DBC , having
the same per pendicular BC , the fines of the bases will be to each other ,
inversely , as the tangents of the angles at the bases : For radius : sine AB :: tang .
A : tang ...
Hence it follows , that , in right - angled spherical triangles ABC , DBC , having
the same per pendicular BC , the fines of the bases will be to each other ,
inversely , as the tangents of the angles at the bases : For radius : sine AB :: tang .
A : tang ...
Side 33
( See the preceding figure . ) DEMONSTRATION . It will be ( by Corol . to Theor .
3. ) co - line A : cofine B :: sine ACD : fine BCD ; and therefore , cofine A + co fine
B : co - fine A - Co - fine B :: sine ACD + fine BCD : sine ACD - sine BCD . But B +
...
( See the preceding figure . ) DEMONSTRATION . It will be ( by Corol . to Theor .
3. ) co - line A : cofine B :: sine ACD : fine BCD ; and therefore , cofine A + co fine
B : co - fine A - Co - fine B :: sine ACD + fine BCD : sine ACD - sine BCD . But B +
...
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Vanlige uttrykk og setninger
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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 |