Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S. |
Inni boken
Side 30
... the tangent of balf the sum of those arches to the tangent of balf their difference
: and , as the sum of the co - fines is to their difference , so is the co - tangent of
half the sum of the arches to the tangent of half the difference of the Jame arches
.
... the tangent of balf the sum of those arches to the tangent of balf their difference
: and , as the sum of the co - fines is to their difference , so is the co - tangent of
half the sum of the arches to the tangent of half the difference of the Jame arches
.
Side 31
In any spherical triangle ABC it will be , as the to - tangent of balf the sum of the
two fides is to the tangent of half their difference , so is the co - tangent of balf the
base to the tangent of the distance ( DE ) of the perpendicular from the middle of
...
In any spherical triangle ABC it will be , as the to - tangent of balf the sum of the
two fides is to the tangent of half their difference , so is the co - tangent of balf the
base to the tangent of the distance ( DE ) of the perpendicular from the middle of
...
Side 60
WABC . 2. E. D. PROP . VI . In any plane triangle ABC , it will be , as the base plus
the difference of the two sides , is to the base ininus the same difference , so is
the tangent of half the greater angle at the base , to the tangent of balf the lefser .
WABC . 2. E. D. PROP . VI . In any plane triangle ABC , it will be , as the base plus
the difference of the two sides , is to the base ininus the same difference , so is
the tangent of half the greater angle at the base , to the tangent of balf the lefser .
Side 72
tang : :: Co - tang : AC + AB AC - AB that is , As the cotang . of balf the given leg ,
is to its tangent ; so is the co - tang . of balf the sum of the hypothenuse and the
other leg , to the tangent of half their difference . 2 2 2 : tang PROP . XXII .
tang : :: Co - tang : AC + AB AC - AB that is , As the cotang . of balf the given leg ,
is to its tangent ; so is the co - tang . of balf the sum of the hypothenuse and the
other leg , to the tangent of half their difference . 2 2 2 : tang PROP . XXII .
Side 74
30. and equaDE + BC DE - BC lity ) tang AE + AC AE- AC : tang . : that is , As the
tan2 gent of balf the sum of the two perpendiculars , is to the tangent of half their
difference ; so is the tangent of balf the sum of the two hypot benufeș , to the ...
30. and equaDE + BC DE - BC lity ) tang AE + AC AE- AC : tang . : that is , As the
tan2 gent of balf the sum of the two perpendiculars , is to the tangent of half their
difference ; so is the tangent of balf the sum of the two hypot benufeș , to the ...
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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 |