The American journal of science and arts . § o-a d 3 a. CO en and that 3 moi p 3nre o 5 ~ -sC^ K S3 ffun o (/J f*^ rj n) £ -r> ,_fc S.^s t. ^^ 3 § S o- o ocks sooften bof the s s 5o 3 o p tc M ^ » Cj X) a 3i C ?^ ^ 3; u H^ X* 3 3 TtJ^t; 4; S- ^ 5 Ss » 5, S5 3 W >D 38 Kectification of the Ellipse. Art. IV.—On the Rectification of the Ellipse ; by C. Wilder. Draw the indefinite right lines, AB and AB, intersecting in C,and between the lines AB and AB place the given right line DE,so that the point D may be in AB and the point E in AB; throughD and E draw DF and EF, parallel to AB and A
The American journal of science and arts . § o-a d 3 a. CO en and that 3 moi p 3nre o 5 ~ -sC^ K S3 ffun o (/J f*^ rj n) £ -r> ,_fc S.^s t. ^^ 3 § S o- o ocks sooften bof the s s 5o 3 o p tc M ^ » Cj X) a 3i C ?^ ^ 3; u H^ X* 3 3 TtJ^t; 4; S- ^ 5 Ss » 5, S5 3 W >D 38 Kectification of the Ellipse. Art. IV.—On the Rectification of the Ellipse ; by C. Wilder. Draw the indefinite right lines, AB and AB, intersecting in C,and between the lines AB and AB place the given right line DE,so that the point D may be in AB and the point E in AB; throughD and E draw DF and EF, parallel to AB and AB, then the locusof F is an ellipse, AABB^. Put a;=:CE=DF, ?/=CD=EF, DE equal to unity, and (p forthe obtuse angle ACB, then by trigonometry y^ —2 cos. (pxy-^-x- = 1;from this equation it is seen that x and y are positive in the directionCA and CA, and that cp is estimated from the line CB. Draw £?/! indefinitely near to DF, and through/ draw fe, parallelto FE, then without more words it is evident that we have gF +gf-^ ==Ff ;and at its limit dy^ —2dxdy cos. cp-^-dx^ =dz^, z being the arc, to the factors of the first member of y^ —2xy cos. (p+a;^ = l, and we have necessarily +zi ?/ —a?(cos. (p —sin. (pi/— i)=e and -z y — a?(cos. 9+ sin. (p-v/ — l)=6 e being the base of the Naperian system, and z a function of x and y to be determined. +z Differentiating and dy—dx{cos. cp — sin. (p-v/ — i) =^tdze~ dy — dx[cos. (p-\- sin. (p-v/ — i) =^^dze^ ?multiplying and dy~ ^2dxdy cos. (p-\-dx^ =? — dz^ ;integrating we have f^dy^ —2dxdy cos« (p-^dx^ =sv — 1 z=z. Rectification of the E
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Keywords: ., bo, bookcentury1800, bookpublishernewhavensconverse, bookyear1820
