T. Sundara Row's Geometric Exercises in Paper Folding;
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To quickly assess the difficulty of the text, read a short excerpt:
iVand N' coincide when PFP is the latus rectum.
As N' recedes from F to O, Amoves forward from F to infinity.
At the same time, T'moves toward O, and T\OT'= ON) moves in the opposite direction toward infinity.
242. To find the area of a parabola bounded by the axis and an ordinate.
Complete the rectangle ONPK. Let OK be di- 120 GEOMETRIC EXERCISES vided into n equal portions of which suppose Om to contain r and mn to be the {r-\- 1)' A Draw mp, nq at right angles to OK meeting the curve in p, q..., and pri at right angles to nq. The curvilinear area OPK is the limit of the sum of the series of rectangles con- structed as mn' on the portions corresponding to mn.
But nnpn : C3 NK=pm • mn : PK- OK, and, by the properties of the parabola, pm : PK= On? : OK* = ;- 2 : « 2 and mn : 0K= 1 : n.
. ■ . pm • mn:PK- 0K= r 2 : n 3 .
.-. cnpn = -.^uzlNK.
w Hence the sum of the series of rectangles _ 1-3 -f 2 2 + 3 2 ■ ■ .. + (»_ I) 2 n° XC3NK (« — 1)«(2«— 1) 2n s — 3n* + n 1-2-3-J XD^A 1 1 1 \ 3-2^ + 6^Jx a ^ = -j of □ iV.A'in the limit, i.
What to read after T. Sundara Row's Geometric Exercises in Paper Folding;?
You can find similar books in the "Read Also" column, or choose other free books by T Tandalam Sundara Rao to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
iVand N' coincide when PFP is the latus rectum.
As N' recedes from F to O, Amoves forward from F to infinity.
At the same time, T'moves toward O, and T\OT'= ON) moves in the opposite direction toward infinity.
242. To find the area of a parabola bounded by the axis and an ordinate.
Complete the rectangle ONPK. Let OK be di- 120 GEOMETRIC EXERCISES vided into n equal portions of which suppose Om to contain r and mn to be the {r-\- 1)' A Draw mp, nq at right angles to OK meeting the curve in p, q..., and pri at right angles to nq. The curvilinear area OPK is the limit of the sum of the series of rectangles con- structed as mn' on the portions corresponding to mn.
But nnpn : C3 NK=pm • mn : PK- OK, and, by the properties of the parabola, pm : PK= On? : OK* = ;- 2 : « 2 and mn : 0K= 1 : n.
. ■ . pm • mn:PK- 0K= r 2 : n 3 .
.-. cnpn = -.^uzlNK.
w Hence the sum of the series of rectangles _ 1-3 -f 2 2 + 3 2 ■ ■ .. + (»_ I) 2 n° XC3NK (« — 1)«(2«— 1) 2n s — 3n* + n 1-2-3-J XD^A 1 1 1 \ 3-2^ + 6^Jx a ^ = -j of □ iV.A'in the limit, i.
What to read after T. Sundara Row's Geometric Exercises in Paper Folding;?
You can find similar books in the "Read Also" column, or choose other free books by T Tandalam Sundara Rao to read onlineMoreLess
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