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2 Projective Plane
3 Projective (Collineation) Transformations
4 Analytical Representation of a Projective Transformation
5 Rectilinear Coordinates. Correlation
II. Equations with Two Variables
6 Graph of a Function
7 Functional Scale
8 Logarithmic Scale
9 Projective Scale
III. Equations with Three Variables
I. Collineation Nomograms
10 Equations of the Form f1(u)+f2(v)+f3(w) = 0. Nomograms with Three Parallel Scales
11 Equations of the Form 1/f1(u)+1/f2(v)+1/f3(w) = 0. Nomograms with Three Scales Passing Through a Point
12 Equations of the Form f1(u)f2(v)=f3(w). Nomograms of the Letter N Type
13 Equations of the Form f1(x)f2(y)f3(z)=1. Nomograms with Scales on the Sides of a Triangle
14 Nomograms with Three Rectilinear Scales
15 Nomograms with Curvilinear Scales
16 The Cauchy Equation
17 The Clark Equation
18 The Soreau Equation of the First Kind
19 The Soreau Equation of the Second Kind
20 An Arbitrary Equation with Three Variables. Nomograms Consisting of Two Scales and a Family of Envelopes
II. Lattice Nomograms
21 General Form of Lattice Nomograms
22 Rectilinear Lattice Nomograms
IV. Equations with Many Variables
23 Collineation Nomograms of Many Variables
24 Elementary Geometrical Methods of Joining Nomograms
25 Systems of Equations. Nomograms Consisting of Two Parts to be Superimposed on Each Other
V. Problems of Theoretical Nomography
26 The Massau Method of Transforming Nomograms
27 Curvilinear Nomograms for the Equations f1(u)f2(v)f3(w) = 1, f1(u)+f2(v)+f3(w) = 0, f1(u)f2(v)f3(w) = f1(u)+f2(v)+f3(w)
28 The Nomographic Order of an Equation. Kind of Nomogram. Critical Points
29 Equations of the Third Nomographic Order
30 Equations of the Fourth Nomographic Order
31 Criteria of Nomogrammability of a Function
32 Criterion of Saint Robert
Nomography deals with geometrical transformations, particularly projective transformations of a plane. The book reviews projective plane and collineation transformations in geometrical and algebraical terms. The geometrical approach aims at permitting the use of elementary geometrical methods in drawing collineation nomograms consisting of three rectilinear scales. The algebraical treatment concerns nomograms containing curvilinear scales. The text explains functional scales that include the graph of a function and a logarithmic scale. The book explores equations which can be represented by elementary methods without the use of a system of coordinates, some equations that require algebraic calculations, as well as nomograms with a binary field (lattice nomograms). The text investigates collineation monograms of many variables, elementary geometrical methods of joining nomograms, and also of nomograms consisting of two parts to be superimposed on each other. In addition to the Massau method and the criterion of Saint Robert, the book also applies the criteria of nomogrammability of a function to address mathematical problems related to the analysis of the methods in constructing nomograms. The book can be useful for mathematicians, geometricians, engineers, and researchers working in the physical sciences who use graphical calculations in their work.
- No. of pages:
- © Pergamon 1963
- 1st January 1963
- eBook ISBN:
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