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).
a<0
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Notes
For the solution of the cubic equation see pp. 161–163.
For degree of a curve see p. 239.
For solution of the algebraic equation of the n-th degree see pp. 164–167 and pp. 169–171.
For the definitions and formulas see pp. 223–225.
For theoretical discussion of hyperbolic functions see pp. 229–230; for the tables see pp. 61–65.
For theoretical discussion see pp. 232–233.
In the following M will denote an arbitrary point of the curve with the coordinates x, y.
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.
For solution of such equations see pp. 161–162.
See footnote on p. 119.
For solution of such equations see pp. 168–169.
The constant denoted on p. 120 by a is here denoted by 2λa and l denoted the diameter 2a. The coordinate system has been changed.
For the involute see p. 294.
For solution of such equations see pp. 168–169.
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).
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© 1973 Verlag Harri Deutsch, Zürich
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Bronshtein, I.N., Semendyayev, K.A. (1973). Graphs. In: A Guide Book to Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6288-3_2
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DOI: https://doi.org/10.1007/978-1-4684-6288-3_2
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