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Mathematical economics is old enough to be respectable, but not all economists respect it. It has powerful supporters and impressive testimonials, yet many capable economists deny that mathematics, except as a shorthand or expository device, can be applied to economic reasoning. There have even been rumors that mathematics is used in economics (and in other social sciences) either for the deliberate purpose of mystification or to confer dignity upon common places as French was once used in diplomatic communications.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Margarita philosophica of Gregor Reisch
This is the title page of the Margarita philosophica (Pearl of Wisdom) of Gregor Reisch (1467 - 1525). The first edition was published in 1503. This work was used as a university textbook in the early sixteenth century. Among its twelve chapters are seven dealing with the seven liberal arts commonly taught at the universities: the trivium of logic, rhetoric, grammar and the quadrivium of arithmetic, music, geometry, and astronomy. There are also several chapters on more advanced topics. Most of the chapters have engravings dealing with the chapter's subject matter, some of which are included below.
This is the engraving depicting Grammar, often called the Tower of Learning. Reisch depicts Grammar, the foundation of all learning, as Nicostrata (legendary inventor of the alphabet) holding a hornbook and key and introducing a child into a tower of learning with six levels. Toward the top of the tower are portraits representing the subjects of the trivium and the quadrivium.
This is the classic engraving of Arithmetica (or the Allegory of Arithmetic) supervising a contest between Boethius, representing written calculation using Hindu-Arabic numbers, and Pythagoras, represented as using a counting board.
Here is an illustration from the geometry chapter (Allegory of Geometry) illustrating various geometric figures as well as geometric instruments.
At the beginning of the astronomy chapter is the Allegory of Astronomy, that is, the image of Astronomia instructing Ptolemy on measuring the heavens by the use of the quadrant.
Also, in the astronomy chapter, there is an image of the Ptolemaic (and also the medieval) version of the geocentric universe. Note that man is in the center of the universe.