Trigonometry, Plane and Spherical;: With the Construction and Application of LogarithmsJ. Nourse, bookseller in ordinary to his Majesty., 1765 - 79 σελίδες |
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Σελίδα 41
... feries ; because these terms ( by reafon of the in- definite fmallness of e ) bear no affignable propor- tion to the preceding ones . Hence we have i + n4e4 & c . N : but ne is n2e2 ne + + n3 e3 — + 2 2.3 2.3.4 ( L ) the hyperbolic ...
... feries ; because these terms ( by reafon of the in- definite fmallness of e ) bear no affignable propor- tion to the preceding ones . Hence we have i + n4e4 & c . N : but ne is n2e2 ne + + n3 e3 — + 2 2.3 2.3.4 ( L ) the hyperbolic ...
Σελίδα 42
... feries , tho ' indeed the most easy and natural , is of little ufe in determining the loga- rithms of large numbers ; fince , in all such cases , it diverges , inftead of converging . It will be proper , therefore , to give , here , the ...
... feries , tho ' indeed the most easy and natural , is of little ufe in determining the loga- rithms of large numbers ; fince , in all such cases , it diverges , inftead of converging . It will be proper , therefore , to give , here , the ...
Σελίδα 43
... feries , it is manifeft , will always converge , let the value of I I - x be ever so great ; because x will be always lefs than unity . But it is further obfervable that this feries has exactly the fame form ( except in its figns ) with ...
... feries , it is manifeft , will always converge , let the value of I I - x be ever so great ; because x will be always lefs than unity . But it is further obfervable that this feries has exactly the fame form ( except in its figns ) with ...
Σελίδα 44
... feries 2x + 2x3 2x5 3333 + & c . will give the hyperbolic logarithm 5 of the respective number . Example . Let it be propofed to find the hyper- bolic logarithm of the number 2 . Here x being 2 -- I , and x ; we fhall have 2+ I x x3 205 ...
... feries 2x + 2x3 2x5 3333 + & c . will give the hyperbolic logarithm 5 of the respective number . Example . Let it be propofed to find the hyper- bolic logarithm of the number 2 . Here x being 2 -- I , and x ; we fhall have 2+ I x x3 205 ...
Σελίδα 47
... feries 2x + 2 ** 2x5 3 + · & c . x 0,434294481 & c . which expreffes 5 x the common logarithm of1 + ( by what has been I X already fhewn ) , and which , by making R = , 868588963 & c . will stand more commodiously Rx3 Rx5 Rx7 thus , Rx ...
... feries 2x + 2 ** 2x5 3 + · & c . x 0,434294481 & c . which expreffes 5 x the common logarithm of1 + ( by what has been I X already fhewn ) , and which , by making R = , 868588963 & c . will stand more commodiously Rx3 Rx5 Rx7 thus , Rx ...
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4th rem AC by Theor AC-BC AD² adjacent angles AE² alſo known arch baſe becauſe bifecting cafe chord circle co-fecant co-fine AC co-tangent of half common logarithm confequently COROL COROLLARY defcribed diameter dius E. D. PROP equal to half excefs exceſs faid fame fecant fecond feries fhall fides AC fince fines firft firſt fpherical triangle ABC fquare fubtracted fupplement fuppofed garithms gent of half given gles great-circles half the bafe half the difference half the fum half the vertical Hence hyperbolic logarithm hypothenufe interfect itſelf laft leffer leg BC likewife moreover pendicular perpendicular plane triangle ABC progreffion propofed proportion radius refpectively right-angled Spherical triangle right-line ſhall ſphere ſpherical tang tangent of half THEOREM thofe thoſe Trigonometry verfed vertical angle whence whofe