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.

early 1600s

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.

1600
Empirical data tables

References:
1603
1st world map with isogons

Le Nautonier's geomagentic map

Modern re-creation of the magnetic equator after Le Nautonier

Le Nautonier portrait

References:
Nautonier:1602 MandeaMayaud:2004
1603
Pantograph

Scheiner's pantograph

1610
Astronomical pictures

Page 9v: craters on the moon

Cover page from Sidereus Nuncius

References:
Galilei:1610
1614
Logarithmic tables

Two pages from Napier's table of logarithms

Diagram of spherical triangles from

Napier portrait

Linear and logarithmic scales

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.
References:
Napier:1614
1617
Trigonometric triangulation

Snellius portrait

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.
References:
Snell:1617
1620 to 1628
Gunter's scale

Gunter's scale image

Gunter's log scale

Oughtred's dual log scale

References:
Gunter:1624 Babcock:1994
1623

reproduction of Schickard's calculating clock

References:
1626
Sunspots

Apparatus for recording sunspots

Scheiner sunspot image

Scheiner:1626
1632
Least deviations

Galileo portrait

References:
Galileo:1632 Hald:1990
1637
Coordinate system

Descartes portrait

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).
Descartes:1637
1644
1st data graph

Langren image

References:
Langren:1644
1646
Image projection

Althanasius Kircher portrait

References:
Kirscher:1646
1654
Theory of probability

Pascal portrait

References:
Ball:1908
1654
1st econometric survey

William Petty portrait

References:
Petty:1665 Petty:1690
1657
1st text on probability

Huygens portrait

References:
Huygens:1657 Ball:1908
1662
Demographic statistics

Mortality table, from

Graunt portrait

Cover page of "Natural and Political Observations..."

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
1663
Weather clock

Wren portrait

References:
Wren:1750 Bennett:1982
1666
1st complete census

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.
References:
Godfrey:1918 JohnsonKotz:97
1669
Life table

Huygens graph

Source: correspondence between Huygens and his brother Lodewijk.
Boyer:1947
1671
Mortality table

de Witt portrait

References:
deWitt:1671
1679
Network diagram on a map

References:
1686
Bivariate plot

Halley's graph of change in barometric pressure

References:
Halley:1686
1686
1st weather map

Halley's wind map, section 1 detail

Halley's wind map, 1686

Halley portrait

References:
Halley:1686a
1687
International statistics

Petty portrait

References:
Petty:1687b Petty:1687a
1693
1st mortality tables

References:
Halley:1693
1693
rectangles for probabilities