Ars magna, or, The rules of algebra by Girolamo Cardano

By Girolamo Cardano

CARDANO, G.: ARS MAGNA OR the foundations OF ALGEBRA. TRANSLATED by means of T. R. WITMER [1968, REPRINT]. manhattan, manhattan, 1993, xxiv 267 p. figuras.Encuadernacion unique. Nuevo.

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General form TECHNOLOGY PITFALL The slope of a line will appear distorted if you use different tick-mark spacing on the x- and y-axes. 21(b) both show the lines given by y ϭ 2x 1 y ϭ Ϫ 2x ϩ 3. and Because these lines have slopes that are negative reciprocals, they must be perpendicular. 21(a), however, the lines don’t appear to be perpendicular because the tick-mark spacing on the x-axis is not the same as that on the y-axis. 21(b), the lines appear perpendicular because the tick-mark spacing on the x-axis is the same as on the y-axis.

Copper Wire The resistance y in ohms of 1000 feet of solid copper wire at 77ЊF can be approximated by the model yϭ (b) Prove that if a graph is symmetric with respect to one axis and to the origin, then it is symmetric with respect to the other axis. CAPSTONE 82. Match the equation or equations with the given characteristic. (i) y ϭ 3x3 Ϫ 3x (ii) y ϭ ͑x ϩ 3͒2 (iii) y ϭ 3x Ϫ 3 3 x (iv) y ϭ Ί (v) y ϭ 3x2 ϩ 3 (vi) y ϭ Ίx ϩ 3 (b) Three x-intercepts (c) Symmetric with respect to the x-axis (d) ͑Ϫ2, 1͒ is a point on the graph (e) Symmetric with respect to the origin (f) Graph passes through the origin True or False?

The zero polynomial f ͑x͒ ϭ 0 is not assigned a degree. It is common practice to use subscript notation for coefficients of general polynomial functions, but for polynomial functions of low degree, the following simpler forms are often used. ͒ Zeroth degree: First degree: Second degree: Third degree: ■ FOR FURTHER INFORMATION For more on the history of the concept of a function, see the article “Evolution of the Function Concept: A Brief Survey” by Israel Kleiner in The College Mathematics Journal.

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