Analytical Institutions in Four Books Originally Written in Italian
Analytical Institutions in Four Books Originally Written in Italian
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ia8a 8 After another manner, thus. In the formula • — - — r=~= — —, if we make avaa — xx -, the two radicals being re- hi —•*{?—— cc, fo that it may be . \yV - folved into feries, it will be — t^^-LJL aw aa — xx c*x* C 4 X* C 6 * 6 CC S X* nto a" - — jr-^ r-^ — ■ „, &c.
C 2 X* 20 1 8a 6 c*x 6 16^1 128a 1 * X 2 . V* X*> %a 8a 3 i6a s S*' 128a?
, &c.
; and aftually making the divifion of the numerator by the denominator, after a very long calculation we fhall find another feries, which, being int...egrated, and the value of cc rcftored in it's place, will give us the fame feries as above, which exprefles the value of the arch DO.
EXAMPLE XXI.
Fig. 125, £ B c 113. Let BD be an hyperbola with tranf- verfe lemiaxis AB zz a, conjugate femiaxis AE p b, CD ss y, AC zz x; the equation will be xx — aa S= ~^ . Then, by taking the fluxions, it will be x ZZ bvbb + yy whence ^FTJy = yj > + ^ = ^* ^f^- Therefore, this being reduced into a feries, after either of the ways before made ufe of for the ellipfis, we (hall find it's integral, or the arch BD zz y -f- —• — 4 *, 8 — y* 8..
What to read after Analytical Institutions in Four Books Originally Written in Italian?
You can find similar books in the "Read Also" column, or choose other free books by Maria Gaetana Agnesi to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
ia8a 8 After another manner, thus. In the formula • — - — r=~= — —, if we make avaa — xx -, the two radicals being re- hi —•*{?—— cc, fo that it may be . \yV - folved into feries, it will be — t^^-LJL aw aa — xx c*x* C 4 X* C 6 * 6 CC S X* nto a" - — jr-^ r-^ — ■ „, &c.
C 2 X* 20 1 8a 6 c*x 6 16^1 128a 1 * X 2 . V* X*> %a 8a 3 i6a s S*' 128a?
, &c.
; and aftually making the divifion of the numerator by the denominator, after a very long calculation we fhall find another feries, which, being int...egrated, and the value of cc rcftored in it's place, will give us the fame feries as above, which exprefles the value of the arch DO.
EXAMPLE XXI.
Fig. 125, £ B c 113. Let BD be an hyperbola with tranf- verfe lemiaxis AB zz a, conjugate femiaxis AE p b, CD ss y, AC zz x; the equation will be xx — aa S= ~^ . Then, by taking the fluxions, it will be x ZZ bvbb + yy whence ^FTJy = yj > + ^ = ^* ^f^- Therefore, this being reduced into a feries, after either of the ways before made ufe of for the ellipfis, we (hall find it's integral, or the arch BD zz y -f- —• — 4 *, 8 — y* 8..
What to read after Analytical Institutions in Four Books Originally Written in Italian?
You can find similar books in the "Read Also" column, or choose other free books by Maria Gaetana Agnesi to read onlineMoreLess
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