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
Hence it appears , 1. That the tangent is a fourth proportional to the co - fine , the
sine , and radius . 2. That the secant is a third - proportional to the co - fine and
radius . 3. That the co - tangent is a fourth proportional to the fine , co - fine , and ...
Hence it appears , 1. That the tangent is a fourth proportional to the co - fine , the
sine , and radius . 2. That the secant is a third - proportional to the co - fine and
radius . 3. That the co - tangent is a fourth proportional to the fine , co - fine , and ...
Side 41
N. 2.3 2.3.4 2.3.4.5 2. E.I. che inof all , 2 2.3 cers L + + + + the PROP . II . To
determine the byperbolic logarithm ( L ) of any given number ( N ) . It appears
from the preceding Prop . that itt L L } & c . is = N : therefore , if x + i be . " 2.3 L '
L L + put ...
N. 2.3 2.3.4 2.3.4.5 2. E.I. che inof all , 2 2.3 cers L + + + + the PROP . II . To
determine the byperbolic logarithm ( L ) of any given number ( N ) . It appears
from the preceding Prop . that itt L L } & c . is = N : therefore , if x + i be . " 2.3 L '
L L + put ...
Side 71
... it appears , that , if from twice the co - fine of the hypothenuse , the co - fine of
the given jum , or difference , of the legs , be subtraited , the remainder will be the
co fine of an arch , wbich added to the said fum , or difference , gives the double ...
... it appears , that , if from twice the co - fine of the hypothenuse , the co - fine of
the given jum , or difference , of the legs , be subtraited , the remainder will be the
co fine of an arch , wbich added to the said fum , or difference , gives the double ...
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 ...
Side 76
Prop . 1. ) which last being substituted for its equal , we shall have , S. CA X S. CB
x co - f . C CO - 1 . AB x rad . = rad . + Co - f . AC x co - f . BC ; from whence , if
each term be multiplied by radius , the truth of the proposition will appear manifeft
.
Prop . 1. ) which last being substituted for its equal , we shall have , S. CA X S. CB
x co - f . C CO - 1 . AB x rad . = rad . + Co - f . AC x co - f . BC ; from whence , if
each term be multiplied by radius , the truth of the proposition will appear manifeft
.
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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 |