"By [diagrams] it is possible to present at a glance all the facts which could be obtained from figures as to the increase, fluctuations, and relative importance of prices, quantities, and values of different classes of goods and trade with various countries; while the sharp irregularities of the curves give emphasis to the disturbing causes which produce any striking change." (Arthur L Bowley, "A Short Account of England's Foreign Trade in the Nineteenth Century, its Economic and Social Results", 1905)
"Mathematicians, however, are well aware that it is childish to try to show by drawing curves that every continuous function has a derivative. Though differentiable functions are the simplest and the easiest to deal with, they are exceptional. Using geometrical language, curves that have no tangents are the rule, and regular curves, such as the circle, are interesting but quite special." (Jean-Baptiste Perrin, 1906)
"Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions. […] A curve is the totality of points, whose coordinates are functions of a parameter which may be differentiated as often as may be required." (Felix Klein, "Elementar Mathematik vom hoheren Standpunkte aus" Vol. 2, 1909)
"But it is a third geometry from which quantity is completely excluded and which is purely qualitative; this is analysis situs. In this discipline, two figures are equivalent whenever one can pass from one to the other by a continuous deformation; whatever else the law of this deformation may be, it must be continuous. Thus, a circle is equivalent to an ellipse or even to an arbitrary closed curve, but it is not equivalent to a straight-line segment since this segment is not closed. A sphere is equivalent to any convex surface; it is not equivalent to a torus since there is a hole in a torus and in a sphere there is not. Imagine an arbitrary design and a copy of this same design executed by an unskilled draftsman; the properties are altered, the straight lines drawn by an inexperienced hand have suffered unfortunate deviations and contain awkward bends. From the point of view of metric geometry, and even of projective geometry, the two figures are not equivalent; on the contrary, from the point of view of analysis situs, they are." (Henri Poincaré, "Dernières pensées", 1913)
"The number was first studied in respect of its rationality or irrationality, and it was shown to be really irrational. When the discovery was made of the fundamental distinction between algebraic and transcendental numbers, i. e. between those numbers which can be, and those numbers which cannot be, roots of an algebraical equation with rational coefficients, the question arose to which of these categories the number π belongs. It was finally established by a method which involved the use of some of the most modern of analytical investigation that the number π was transcendental. When this result was combined with the results of a critical investigation of the possibilities of a Euclidean determination, the inferences could be made that the number π, being transcendental, does not admit of a construction either by a Euclidean determination, or even by a determination in which the use of other algebraic curves besides the straight line and the circle are permitted." (Ernest W Hobson, "Squaring the Circle", 1913)
"Human knowledge is not" (or does not follow) a straight line, but a curve, which endlessly approximates a series of circles, a spiral. Any fragment, segment, section of this curve can be transformed" (transformed one-sidedly) into an independent, complete, straight line [...]" (Vladimir I Lenin, "On the Question of Dialectics", 1915)
"The practice of drawing several curves on the same sheet is not to be commended except in cases where the curves will not intersect. A crowded chart on which the curves frequently intersect resembles a Chinese puzzle more than a graphic record, and a report submitted in figures is to be preferred to a chart of this kind. Even when the curves do not intersect, they should be made in different colors in order that they may be readily distinguished, one from the other." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)
"The principles of charting and curve plotting are not at all complex, and it is surprising that many business men dodge the simplest charts as though they involved higher mathematics or contained some sort of black magic. [...] The trouble at present is that there are no standards by which graphic presentations can be prepared in accordance with definite rules so that their interpretation by the reader may be both rapid and accurate. It is certain that there will evolve for methods of graphic presentation a few useful and definite rules which will correspond with the rules of grammar for the spoken and written language." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)
"Under certain conditions, however, the ordinary form of graphic chart is slightly misleading. It will be conceded that its true function is to portray comparative fluctuations. This result is practically secured when the factors or quantities compared are nearly of the same value or volume, but analysis will show that this is not accomplished when the amounts compared differ greatly in value or volume. [...] The same criticism applies to charts which employ or more scales for various curve. If the different scale are in proper proportion, the result is the same as with one scale, but when two or more scales are used which are not proportional an indication may be given with respect to comparative fluctuations which is absolutely false." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)
"The chief problems in the technique of historigram [aka histogram] plotting are those of base line scales, types of lines to use for the graphs and methods of and purposes of smoothing these curves. The size of page, ability of grasp by the eye, subsequent treatment of the illustration, etc., are determining factors. The variable factor is usually plotted from a base line along the ordinate axis. Spacing and rules for scales apply as in frequency diagrams." (William C Marshall, "Graphical methods for schools, colleges, statisticians, engineers and executives", 1921)
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