A Treatise On Algebra
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In our eReader you can find the full English version of the book. Read A Treatise On Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Treatise On Algebra
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To quickly assess the difficulty of the text, read a short excerpt:
Because, substitating this value of x in each term of [e], we have, X" z= (u — »y/^T.)" = m' — «' n/— T-i Ai»-i = A(« — t)v^^^l)»-' = «" — t)"v'— 1.
Bar»-' = = !4'" — t)"V— T^. &o.
E = K.
And therefore, x» 4- Aa^-'+ + K = U — Vv''^.
But when a; ^ « + "v'— 1 is a root of [e] = 0, U and V are sepa- rately each equal to zero; hence, U — V^ — 1, as well as U 4- V y/ — 1, is equal to zero. But U — V^ — 1 is that which [e] becomes when « — »y/ — 1 is substituted for x ; hence, x = u — v^ — 1 is a roo...t of [«] = 0. Therefore, when one of the conjugate radical ex- pressions is a root of the equation, the other also is necessarily a root of the same equation.
From this connection it follows, first, that the number Corollaries.
of the roots of the imaginary form (o ± b^ — 1) must necessarily be even.
Secondly, since whatever be the roots of [«] = 0, we have always [«] = (x — h)(x — i) (x — s)(x — t).
Supposing that the first two, or four, or eight and so on, are imagi- nary, we will have for example, A = a -f- b-^/^^l, i= a — 6y/-^^ ; hence, (x—h)(x—i) = {x — a—b^—l)(x — a+b^^^) == (a; — o)'+ 6^, and, consequently, W = l(x-af + i^](x-l) (x-t).
What to read after A Treatise On Algebra?
You can find similar books in the "Read Also" column, or choose other free books by Sestini, Benedict, 1816-1890 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Because, substitating this value of x in each term of [e], we have, X" z= (u — »y/^T.)" = m' — «' n/— T-i Ai»-i = A(« — t)v^^^l)»-' = «" — t)"v'— 1.
Bar»-' = = !4'" — t)"V— T^. &o.
E = K.
And therefore, x» 4- Aa^-'+ + K = U — Vv''^.
But when a; ^ « + "v'— 1 is a root of [e] = 0, U and V are sepa- rately each equal to zero; hence, U — V^ — 1, as well as U 4- V y/ — 1, is equal to zero. But U — V^ — 1 is that which [e] becomes when « — »y/ — 1 is substituted for x ; hence, x = u — v^ — 1 is a roo...t of [«] = 0. Therefore, when one of the conjugate radical ex- pressions is a root of the equation, the other also is necessarily a root of the same equation.
From this connection it follows, first, that the number Corollaries.
of the roots of the imaginary form (o ± b^ — 1) must necessarily be even.
Secondly, since whatever be the roots of [«] = 0, we have always [«] = (x — h)(x — i) (x — s)(x — t).
Supposing that the first two, or four, or eight and so on, are imagi- nary, we will have for example, A = a -f- b-^/^^l, i= a — 6y/-^^ ; hence, (x—h)(x—i) = {x — a—b^—l)(x — a+b^^^) == (a; — o)'+ 6^, and, consequently, W = l(x-af + i^](x-l) (x-t).
What to read after A Treatise On Algebra?
You can find similar books in the "Read Also" column, or choose other free books by Sestini, Benedict, 1816-1890 to read onlineMoreLess
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