## Abstract

**Linear function**:

*y*=

*ax*+

*b*(Fig. 2a). The graph—

*a straight line*. The function increases monotonically for

*a*> 0 and decreases monotonically for

*a*< 0; it is constant for

*a*= 0. Intersections with the axes: \(A\left ( -\frac{a}{b},0 \right )\),

*B*(0,

*b*). For details see p. 239. For

*b*= 0, it represents a

*direct proportionality*:

*y*=

*ax*; the graph is a straight line passing through the origin (Fig. 2b).

## Keywords

Parametric Form Tangent Line Double Point Sine Curve Irrational Function
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## Notes

- (1).For the solution of the cubic equation see pp. 161–163.Google Scholar
- (1).For degree of a curve see p. 239.Google Scholar
- (2).For solution of the algebraic equation of the
*n*-th degree see pp. 164–167 and pp. 169–171.Google Scholar - (1).For the definitions and formulas see pp. 223–225.Google Scholar
- (1).For theoretical discussion of hyperbolic functions see pp. 229–230; for the tables see pp. 61–65.Google Scholar
- (1).For theoretical discussion see pp. 232–233.Google Scholar
- (1).In the following
*M*will denote an arbitrary point of the curve with the coordinates*x*,*y*.Google Scholar - (1).In general, the
*conchoid*of a curve is the curve obtained from the given one by increasing or decreasing the radius vector of the curve by a constant segment*l*. If the equation of the given curve in the polar coordinates is ϱ =*f*(φ), then the*equation of its conchoid*is ϱ =*f*(φ) ±*l*. The conchoid of Nicomedes is the conchoid of the straight line.Google Scholar - (1).For solution of such equations see pp. 161–162.Google Scholar
- (2).See footnote on p. 119.Google Scholar
- (1).For solution of such equations see pp. 168–169.Google Scholar
- (1).The constant denoted on p. 120 by
*a*is here denoted by 2λ*a*and*l*denoted the diameter 2*a*. The coordinate system has been changed.Google Scholar - (1).For the involute see p. 294.Google Scholar
- (2).For solution of such equations see pp. 168–169.Google Scholar
- (1).In other words: If one end point of a non-expansible thread of a given length
*a*is fastened to a material point*M*and the other end point*P*is dragged along a straight line (*Ox*), then the point*M*draws the tractrix (whence comes the name of the curve;*tractus*, in Latin, means dragged).Google Scholar

## Copyright information

© Verlag Harri Deutsch, Zürich 1973