New Series of The Mathematical Repository, Volum 5W. Glendinning, 1830 |
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Resultat 1-5 av 100
Side
... roots may be in harmonical progression , and find those roots . IV . QUESTION 374 , by JULIUS . Exponential equations of the form xx = a , may be divided into three classes , viz . those having only one real root , those having two real ...
... roots may be in harmonical progression , and find those roots . IV . QUESTION 374 , by JULIUS . Exponential equations of the form xx = a , may be divided into three classes , viz . those having only one real root , those having two real ...
Side 150
... roots of which ' equation are x = ba • then a being known we have 1 + a 2 = ab g . Putry , then the first equation when divided By g " becomes r12 + ar ? ‡ zbr2 = : the roots of which are those of ra — úr3 ° . - b 3 ; r therefore is u2 ...
... roots of which ' equation are x = ba • then a being known we have 1 + a 2 = ab g . Putry , then the first equation when divided By g " becomes r12 + ar ? ‡ zbr2 = : the roots of which are those of ra — úr3 ° . - b 3 ; r therefore is u2 ...
Side 15
... root of such equation is unity ; and the equation must be depressed before the process commences : And if , in any case , c , beo ( see n ° IV . below ) the roots of the pro- posed equation must be either increased or diminished , pre ...
... root of such equation is unity ; and the equation must be depressed before the process commences : And if , in any case , c , beo ( see n ° IV . below ) the roots of the pro- posed equation must be either increased or diminished , pre ...
Side 16
... roots of x2 + 2x + 4 = 0 .. IV . 10 = 4x — 5x2 + 2x3 , and the roots of x2 + 2 = -- -- V 180-9r + 29x ? —x3 — x4 | 3 ; 4 ; S and - 5 ..... 49-2-1 012 1-10 -2116 6 0-1 1 20 0 .... -14460,20- 916 S 20 121 & c . VI . 24 = 16x --Sr " + 2x3 ...
... roots of x2 + 2x + 4 = 0 .. IV . 10 = 4x — 5x2 + 2x3 , and the roots of x2 + 2 = -- -- V 180-9r + 29x ? —x3 — x4 | 3 ; 4 ; S and - 5 ..... 49-2-1 012 1-10 -2116 6 0-1 1 20 0 .... -14460,20- 916 S 20 121 & c . VI . 24 = 16x --Sr " + 2x3 ...
Side 23
... roots are less by 1 than those of a given equation of n dimensions . RULE . Under the second coefficient write the first , n times repeated . Under the third , the successive sums of the second and the several numbers beneath it ...
... roots are less by 1 than those of a given equation of n dimensions . RULE . Under the second coefficient write the first , n times repeated . Under the third , the successive sums of the second and the several numbers beneath it ...
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abscissa axis bisected centre chord circle co-ordinates coefficients cone conic section conjugate consequently constant cos² cubic equation CUNLIFFE curve denote determine diamedral diameter direction divisor draw drawn dx² ellipse equal equation expression force formula fraction given by position given point given ratio Hence inscribed integral intersection JOHN BAINES Mathematical method motion multiplying obtain ordinate PALABA parabola parallel perpendicular Porism problem projection quantities QUESTION quotient radius rectangle reduced respectively right angles roots second order SECOND SOLUTION shew sides similar triangles sin² sin³ sphere square straight line substituting suppose surface tang theorem tion transformation triangle velocity vertical whence