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 |
Inni boken
Resultat 1-5 av 12
Side 13
... appears , 1. That the tangent is a fourth proportional to the co - fine , the fine , and radius . 2. That the fecant ... appears moreover ( because AT : AC :: CD ( AC ) : DH ) , that the rectangle of the tangent and co - tangent is equal ...
... appears , 1. That the tangent is a fourth proportional to the co - fine , the fine , and radius . 2. That the fecant ... appears moreover ( because AT : AC :: CD ( AC ) : DH ) , that the rectangle of the tangent and co - tangent is equal ...
Side 24
... 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 .. C B E A 3 ...
... 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 .. C B E A 3 ...
Side 41
... appears from the preceding Prop . that 1 + L L2 L ' --- + & c . is N therefore , if x + 1 be . 2.3 putN , we shall have L L ' L3 L + + + + 2 2.3 2.3.4 & c . x ; and confequently , by reverting the fe- ries , L x3 + + 3 & c . 2. E. I. ...
... appears from the preceding Prop . that 1 + L L2 L ' --- + & c . is N therefore , if x + 1 be . 2.3 putN , we shall have L L ' L3 L + + + + 2 2.3 2.3.4 & c . x ; and confequently , by reverting the fe- ries , L x3 + + 3 & c . 2. E. I. ...
Side 51
... appear to be 9,7621775 ; to which add 4,2530956 , the log . of 17910 , and from the fum ( 14,0152731 ) take 10 , the log . of radius , and there refults 4,0152731 the log . of BC ; which , in the tables , anfwers to 10358 , the length ...
... appear to be 9,7621775 ; to which add 4,2530956 , the log . of 17910 , and from the fum ( 14,0152731 ) take 10 , the log . of radius , and there refults 4,0152731 the log . of BC ; which , in the tables , anfwers to 10358 , the length ...
Side 54
... appears , that the Square of the fine of half any arch , or angle , is equal to a rectangle under half the radius and the verfed fine of the whole ; and that the fquare of its co - fine is equal to a rectangle under half the radius and ...
... appears , that the Square of the fine of half any arch , or angle , is equal to a rectangle under half the radius and the verfed fine of the whole ; and that the fquare of its co - fine is equal to a rectangle under half the radius and ...
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