1600-1699: Measurement and theory
Among the most important problems of the 17th century were those concerned with physical measurement- of time, distance, and space- for astronomy, surveying, map making, navigation and territorial expansion. This century saw great new growth in theory and the dawn of practice- the rise of analytic geometry, theories of errors of measurement and estimation, the birth of probability theory, and the beginnings of demographic statistics and "political arithmetic".
By the end of this century, the necessary elements were at hand- some real data of significant interest, some theory to make sense of them, and a few ideas for their visual representation. Perhaps more importantly, one can see this century as giving rise to the beginnings of visual thinking.
Tables of empirical data, published tables of numbers begin to appear. "Die Tabellen-Statistik," as a branch of statistics devoted to the numerical description of facts- Germany.
Tables of empirical data, published tables of numbers begin to appear. "Die Tabellen-Statistik,'' as a branch of statistics devoted to the numerical description of facts
The pantograph was invented for mechanically copying a figure on an enlarged or reduced scale
Invention of logarithms, and the first published tables of logarithms.
In 1617, the year of his death, Napier invented a calculating device, called "Napier's Bones," based on logarithms to facilitate multiplication and division. Napier was also the first to describe the systematic use of the decimal point in representing the result of long division.
First use of Frisius' method of trigonometric triangulation to produce locations of major cities in Holland; foundation of geodesy
In 1621, Willibrord Snell, in Cyclometricus, discovered the law of refraction which says that the ratio of the sines of the angles of incidence and refraction is a constant and the index of refraction varies from one transparent substance to another. This law implies that the velocity of light in a medium is inversely proportional to its refractive index. Cyclometricus was published after Snell's death by Rene' Descartes.
Invention of a mechanical device, containing a logarithmic scale of equal parts and trigonomic functions which, with the aid of a pair of calipers, could be used as a slide rule. This device, called "Gunter's scale,'' or the "gunter'' by seamen, was soon replaced by a true slide rule, containing two parallel logarithmic scales
The first known adding machine, a mechanical calculator called the "Calculating Clock.'' It could add and subtract up to six-digit numbers, based on the movement of six dented wheels geared through a "mutilated" wheel which with every full turn allowed the wheel located at the right to rotate 1/10th of a full turn
Coordinate system reintroduced in mathematics, analytic geometry; relationship established between graphed line and equation
About 1629, Pierre de Fermat discovered that the equation $f(x,y)=0$ represents a curve in the xy-plane. This is the fundamental principle of analytic geometry, and was first published by Descartes in 1637. He also formulated a method for determining the maximim and minimum values which give single solutions for problems which in general have two solutions. This procedure is "almost precisely that now given in the differential calculus''" ''(Boyer 1949:156).
First visual representation of statistical data: variations in determination of longitude between Toledo and Rome
Invention of the first projection lantern (the magic lantern). [Images were painted on glass and projected on walls. Kirscher, a Jesuit priest, was the last recorded ordained priest openly to concern himself with optics. Henceforth, the art of projecting images was classified as an entertainment and curtailed.]
The first large scale attempt at a scientific, economic survey (of the Irish estates confiscated by Oliver Cromwell), perhaps the first econometric study, leading to development of political arithmetic
First text on probability
Founding of demographic statistics: Development of the idea that vital statistics (records of christenings and burials in London) could be used to construct life tables. The average life expectancy in London was 27 years, with 65\% dying by age 16
Graunt's work of 1662 is often ascribed to Sir William Petty. The authorship questionhas been discussed by Wilcoxwho concludes that although a portion ofthe work was by Petty, the majority is due to Graunt.
References:Graunt:1662 Petty:1665 Sutherland:1963 Wilcox:1937
First modern complete demographic census, a record of each individual by name of the 3215 inhabitants of New France
E. H. Godfrey says that this is "a date prior to any modern census, whether European or American'', seeThe returns were fairly complete, giving data on population, sexes, families, conjugal condition, age, profession and trades, and they filled 154 pages. The original copy is now in the Archives of Paris, and a transcript in the Archives of Ottawa.
First graph of a continuous distribution function, a graph of Gaunt's life table, and a demonstration of how to find the median remaining lifetime for a person of given age
Source: correspondence between Huygens and his brother Lodewijk.
First attempt to determine scientifically what should be the purchase price of annuities, using mortality tables
A map of England showing distances between cities arranged for the use of travellers.
Bivariate plot of a theoretical curve derived from observations (barometric pressure vs. altitude), graphical analysis based on empirical data
First known weather map, showing prevailing winds on a geographical map of the Earth