Trigonometry, Plane and Spherical;: With the Construction and Application of Logarithms |
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Side 16
With the Construction and Application of Logarithms Thomas Simpson. PROP . III
. To find the fine of a very small arch ; suppose that of 15 ' LE U It is found , in p .
181. of the Elements , that the length of the chord of 75 % of the femi - periphery ...
With the Construction and Application of Logarithms Thomas Simpson. PROP . III
. To find the fine of a very small arch ; suppose that of 15 ' LE U It is found , in p .
181. of the Elements , that the length of the chord of 75 % of the femi - periphery ...
Side 63
D. PROP . XI . As the tangent of the vertical angle C of a plane triangle ABC , is to
radius , so is half the base AB to a fourth proportional ; and as half the base is to
the excess of the perpendicular above the said fourthproportional , so is the fine ...
D. PROP . XI . As the tangent of the vertical angle C of a plane triangle ABC , is to
radius , so is half the base AB to a fourth proportional ; and as half the base is to
the excess of the perpendicular above the said fourthproportional , so is the fine ...
Side 69
E. D. F PROP . XVIII . In any plane triangle ABC , it will be , as the perpendicular
is to the sum of the two sides , so is the tangent of half the angle at the vertex , to
the tangent of an angle ; and , as radius is to the tangent of balf this angle , so is ...
E. D. F PROP . XVIII . In any plane triangle ABC , it will be , as the perpendicular
is to the sum of the two sides , so is the tangent of half the angle at the vertex , to
the tangent of an angle ; and , as radius is to the tangent of balf this angle , so is ...
Side 71
but one , & c . we shall have , EF : 2AG ( AC - BC , fee Prop . 13. ) :: co - tang . EFI
: tang . Q ; and as radius : co - tang . Q :: AG : AE :: 2AG ( AC - BC ) : 2AE ( AB ) . 2
: E. D. PROP . XX . The hypothenuse AC , and the sum , or difference , of the ...
but one , & c . we shall have , EF : 2AG ( AC - BC , fee Prop . 13. ) :: co - tang . EFI
: tang . Q ; and as radius : co - tang . Q :: AG : AE :: 2AG ( AC - BC ) : 2AE ( AB ) . 2
: E. D. PROP . XX . The hypothenuse AC , and the sum , or difference , of the ...
Side 73
A : rad . co - f . A :: T. AC + T. AB : T. AC -- T. 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
. ) ...
A : rad . co - f . A :: T. AC + T. AB : T. AC -- T. 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
. ) ...
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Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1799 |
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 determine diameter difference divided drawn equal equal to half evident exceſs extremes fide AC fine fines firſt follows given gives gles greater half the ſum half their difference Hence hyperbolic logarithm hypothenuſe laſt logarithm manifeft meeting method minute moreover Note oppoſite parallel perpendicular plane triangle ABC preceding progreſſion PROP proportion propoſed radius rectangle reſpectively right-angled ſame ſecant ſee ſeries ſhall ſides ſince ſine ſpherical Spherical triangle ABC ſubtracted ſum ſuppoſed tang tangent of half Tbeor Theor THEOREM thereof theſe thoſe unity verſed vertical angle whence