Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S.F. Wingrave, successor to Mr. Nourse, 1799 - 79 sider |
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Side 17
... also very eafily demonftrated ; yet , as the first fine , from whence the rest are all derived , must be carried on to a great number of places , to render the nume rous deductions from it but tolerably exact ( because in every ...
... also very eafily demonftrated ; yet , as the first fine , from whence the rest are all derived , must be carried on to a great number of places , to render the nume rous deductions from it but tolerably exact ( because in every ...
Side 24
... also appears ( from Def . 2. ) that all great- circles , paffing through the pole of a given circle , cut that circle at right - angles ; because they pafs through , or coincide with the axis , which is per- pendicular to it . i ...
... also appears ( from Def . 2. ) that all great- circles , paffing through the pole of a given circle , cut that circle at right - angles ; because they pafs through , or coincide with the axis , which is per- pendicular to it . i ...
Side 37
... also known . As rad . co - fine AC ; : tang . A : co - tang . ACD ( by Theor . 5. ) and as co - fine A ; co - fine B :: fine ACD fine BCD ( by Cor . to Theor . 3. ) whence ACB is alfo know !! . As tang : AB ; tang . AC - BC AC + BC 2 ...
... also known . As rad . co - fine AC ; : tang . A : co - tang . ACD ( by Theor . 5. ) and as co - fine A ; co - fine B :: fine ACD fine BCD ( by Cor . to Theor . 3. ) whence ACB is alfo know !! . As tang : AB ; tang . AC - BC AC + BC 2 ...
Side 40
... also , 2 2 2 n Τ พ I n 2 have + ne + n .. .e2 . + n . 2 2 3 & c , N. But , because n ( from the nature of logarithras ) is here fuppofed indefinitely great , it is evident , fift , that the numbers connected to it by the fign , may be ...
... also , 2 2 2 n Τ พ I n 2 have + ne + n .. .e2 . + n . 2 2 3 & c , N. But , because n ( from the nature of logarithras ) is here fuppofed indefinitely great , it is evident , fift , that the numbers connected to it by the fign , may be ...
Side 45
... of 4 , which is the double thereof , will also be known . There- fore , taking a 2 , b = 3 , and 4 , we fhall , in this cafe , have x have × ( ; whence this Conftruction of Logarithms . 45 After the very fame manner the hyperbolic lo- ...
... of 4 , which is the double thereof , will also be known . There- fore , taking a 2 , b = 3 , and 4 , we fhall , in this cafe , have x have × ( ; whence this Conftruction of Logarithms . 45 After the very fame manner the hyperbolic lo- ...
Vanlige uttrykk og setninger
5th rem AB by Theor AC by Theor AC-BC AC+BC adjacent angle alfo alfo known alfo let alſo arch bafe baſe becauſe bifecting cafe chord circle co-f co-fecant co-fine AC co-tangent of half common logarithm confequently COROL COROLLARY diameter dius equal to half excefs fame fecant fecond feries fhall fides AC fince fines firft firſt fpherical triangle ABC fquare fubtracted fupplement fuppofed garithms gles great-circles half the difference half the fum half the vertical Hence hyperbolic logarithm hypothenufe interfect laft leffer leg BC likewife LUKE HANSARD moreover oppofite angle pendicular perpendicular plane triangle ABC progreffion PROP propofed proportion radius reafon refpectively right-angled spherical triangle right-line ſhall ſphere tang tangent of half THEOREM theſe thofe Trigonometry verfed vertical angle whence whofe