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 15
From whence , and the preceding corollary , we have these two useful theorems .
1. If the fine of the mean , of three equidifferent arches ( supposing radius unity )
be multiplied by twice the co - line of the common difference , and the line of ...
From whence , and the preceding corollary , we have these two useful theorems .
1. If the fine of the mean , of three equidifferent arches ( supposing radius unity )
be multiplied by twice the co - line of the common difference , and the line of ...
Side 39
These are the properties of the indices of a geometrical progression ; which
being universally true , let the common ratio be now supposed indefinitely near to
that of equality , or the excess of a above unity , indefinitely little ; so that some
term ...
These are the properties of the indices of a geometrical progression ; which
being universally true , let the common ratio be now supposed indefinitely near to
that of equality , or the excess of a above unity , indefinitely little ; so that some
term ...
Side 41
ra various it is evi . efpect to in re , f them es and number of terms being
indefinitely small in comparison of n : it is also evident , that they ' may be rejected
in all the rest of the terms of the feries ; because these terms ( by reason of the
indefinite ...
ra various it is evi . efpect to in re , f them es and number of terms being
indefinitely small in comparison of n : it is also evident , that they ' may be rejected
in all the rest of the terms of the feries ; because these terms ( by reason of the
indefinite ...
Side 64
But DC = OC ? + OD ' + 200 x OF ( by 11. 2. ) = OA ' + OD ? + 2ODxDF --UD - OA '
- OD ' + 2OD X DF = AD + 2OD * DF ( by 7.2 . ) ;, whence , by taking away AD
from the first and last of these equal quantities , we have DCP - AD : - 20DXDF ...
But DC = OC ? + OD ' + 200 x OF ( by 11. 2. ) = OA ' + OD ? + 2ODxDF --UD - OA '
- OD ' + 2OD X DF = AD + 2OD * DF ( by 7.2 . ) ;, whence , by taking away AD
from the first and last of these equal quantities , we have DCP - AD : - 20DXDF ...
Side 71
... to determine the triangle . Let AE be the fum , and AF the difference of the two
legs . Because , radius : CO - s . AB :: Co - f . BC : Co - s . B AC ( by Theor . 2. )
therefore , co - f . AB x co - f . BC = rad . X.co.f. AC ; but the former of these is = {
rad .
... to determine the triangle . Let AE be the fum , and AF the difference of the two
legs . Because , radius : CO - s . AB :: Co - f . BC : Co - s . B AC ( by Theor . 2. )
therefore , co - f . AB x co - f . BC = rad . X.co.f. AC ; but the former of these is = {
rad .
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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 |