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 13
CF : FE :: CA : CT ; whence the tangent is known . 2. CF : CE ( CA ) :: CA : CT ;
whence the secant is known . 3. EF : CF :: CD : DH ; whence the co - tangent is
known . 1 4. EF : EC ( CD ) :: CD : CH ; whence the co - secant is known . Hence it
...
CF : FE :: CA : CT ; whence the tangent is known . 2. CF : CE ( CA ) :: CA : CT ;
whence the secant is known . 3. EF : CF :: CD : DH ; whence the co - tangent is
known . 1 4. EF : EC ( CD ) :: CD : CH ; whence the co - secant is known . Hence it
...
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 55
whence and BH parallel to AO , meeting GD in v and H : then it is plain , because
Dm = Bm , that Dv is = Hv , and mv = nG = En ; and that the triangles OCF , Omn
and mDv are similar ; whence we have the following proportions , OC : Om :: CF ...
whence and BH parallel to AO , meeting GD in v and H : then it is plain , because
Dm = Bm , that Dv is = Hv , and mv = nG = En ; and that the triangles OCF , Omn
and mDv are similar ; whence we have the following proportions , OC : Om :: CF ...
Side 65
whence , also , CD = Cd , and HD = Hd ( by 15. 1. ) Therefore , the right - angled
triangles HAD and HBd , having AH = HB and HD = Hd , have , likewise , AD = Bd
( by 15. 1. ) From whence it is manifest , that CD will be equal to half the sum ...
whence , also , CD = Cd , and HD = Hd ( by 15. 1. ) Therefore , the right - angled
triangles HAD and HBd , having AH = HB and HD = Hd , have , likewise , AD = Bd
( by 15. 1. ) From whence it is manifest , that CD will be equal to half the sum ...
Side 73
AB : B whence , by arguing as in the last Prop . it will appear , that , co - tang . { A :
tang . { A : : ' rad . + Co - f . A : rad . — Co - f . A ( :: T. AC + T. AB : T . AC - T . AB ) ::
S. AC + AB : S . AC – AB ( by Prop . ' 4. ) . Hence it appears , that , As the co ...
AB : B whence , by arguing as in the last Prop . it will appear , that , co - tang . { A :
tang . { A : : ' rad . + Co - f . A : rad . — Co - f . A ( :: T. AC + T. AB : T . AC - T . AB ) ::
S. AC + AB : S . AC – AB ( by Prop . ' 4. ) . Hence it appears , that , As the co ...
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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 |