Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . the Unit Measure of an Elliptic Elbow of any given Angle. C = circumference of angle of elbow in =z conjugate diameter of — C-—n=conjugate axis of e = ^C(7r—2)^-nz=z^ird — D = a = \ circumference of ellipse.\c _|cX cos £Vsin h V~ A C=b tan£F db t = — [$d -j- ^(a3 + 4^2)] = transverse axis of hyperbola. x = j ^(\d2 -f- y~) — \t •= abscissa from \/(tx-\- or) ==
Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . the Unit Measure of an Elliptic Elbow of any given Angle. C = circumference of angle of elbow in =z conjugate diameter of — C-—n=conjugate axis of e = ^C(7r—2)^-nz=z^ird — D = a = \ circumference of ellipse.\c _|cX cos £Vsin h V~ A C=b tan£F db t = — [$d -j- ^(a3 + 4^2)] = transverse axis of hyperbola. x = j ^(\d2 -f- y~) — \t •= abscissa from \/(tx-\- or) == ordinate. 360 PATTERN CUTTING. Prob. 14. — To construct (lie Quadrant of a given Circle by inter-secting lines. Rule Construct a square, A B C D, making each side equal to the radius of the proposed circle, and make A e equal to the di-ameter of the circle ; thence by rule, Prob. 8. Prob. 15. — To construct the Quadrant of a given Ellipse by in-tersecting lines. Rule.—Constructa rectangle, A BCD,making A B equal tohalf the transversediameter, and A 1)equal to half the con-jugate. Make A eequal to the conju-gate ; thence by rule,Prob. Prob. 16.— To apply the Quadrant of a Circle, or Quadrant of anEllipse, to the Construction of the Circle or Ellipse. Rule. — Draw a guide-line of sufficient length ; then, with A Bof the quadrant in that line, in the four requisite positions, scribeto the curve and to B C, as required. Prob. 17.— To construct the Quadrant of a Cycloidal Ellipse byintersecting lines. Rule. — Construct a rectangle, A B C D, making the trans-verse diameter to the conjugate as tt to 2; in all other respectsproceed by rule, Prob. 15. Prob. 18.— To describe an Ellipse of given diameters, by meansof two Posts, a Pencil, and a String. Let A B be the transverse diameter, and C D the , — Lay down the given diameters at right angles to each PATTERN CUTTING. 361 other, and bisecting each other, as in o. Next, with half A B i
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectmathematics, bookyear
