A Treatise of Algebra Wherein the Principles Are Demonstrated And Applied in M
A Treatise of Algebra Wherein the Principles Are Demonstrated And Applied in M
Thomas Simpson
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V — lay -if Ittu -f- 2 ?/;; — ^yy::^ by and £?; — uu — uy -f j'j; zz o. To the former of which add the 'double of the latter fo fhall aa — 2au -zz b ; and therefore u — 1^ _A . _J 2 2a From whence, and yy - f « --.^^ X >• = z»7/, the value of;' f = Y «« + • iE]± _ lirif ) is likevvife given. 4 2 ' ^ , ... Y, ^. , PROBLEM LXXII. r% /V^^, ' % ^ The fum [a\ ihe fum of the fquares (/>), and the ju?n if 3^ '5_ ^^ /;^^ cubes (c)^ of any four amnbers in geometrical proportion ♦ hei}ig given ; /^ find ...the nurnbers. Let half the fum of the two means be x^ and half their (difference y ; aifo let half the fum of the two extremes be z, and half their diiFr-rcnCe v^ and then the numbers themfelves will be exprefled thus, z — v^ x — >', x -f y^ z -f V : whence, by the conditions of the problem, wc have ><-< > 7 ^ — ■yXz+'z/zzA-— y X A- + y (Theor. I, p. 72)1 / * f, j which, contracl:ed, arc, l^^-i^^Cj - i^ 22: + 2;^ ~ ^, ^ 2z3 -J- 6z7;^+ 2a:^ + bxy'^z=.
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