Continuing with the example of the field mathematics, one would observe some 700 years of uninterrupted flourishing of a whole multiplicity of disciplines: algebra, algebraic geometry, theory of parallels, Diophantean analysis, numerology, computational techniques, methods of projection, geometric transformations, cartography,

mathematical geography, and so on.

28] In producing what would become for the sixteenth century the standard textbook of

mathematical geography, Peter Apian speaks in his dedicatory letter to the Archbishop of Salzburg, figuring as preface to his Cosmographicus liber of 1524, not only of the geographica disciplina but also of the geografica et cosmographica professio.

In Charting an Empire, Lesley Cormack divides geography into three different sorts, namely mathematical geography, "descriptive" geography, and chorography.

Mathematical geography was initially taught within the quadrivium, and after 1600 it was transformed with the development of trigonometry and triangulation.

SOLSTICE: AN ELECTRONIC JOURNAL OF GEOGRAPHY AND MATHEMATICS -- published by Sandra Lach Arlinghaus of the Institute of Mathematical Geography, a small, independent research organization in Ann Arbor, Mich.

At present, individuals wishing to see particular illustrations must obtain photocopies directly from the Institute of Mathematical Geography.

Arlinghaus is an Adjunct Professor of

Mathematical Geography and Population-Environment Dynamics in the School of Natural Resources and Environment, and in the College of Architecture and Urban Planning, at the University of Michigan, Ann Arbor.

Basing her arguments not only on formal curricula and anecdotal evidence of informal practices but also (and especially) on a careful examination of inventories of books owned by Oxford and Cambridge colleges and by individual masters and students and on a no less careful examination of the collective biographies of those book owners and producers, Cormack demonstrates that all three branches of geographical practice -

mathematical geography, descriptive geography, and chorography - commanded keen, persistent, and widespread university attention in the crucial forty years from 1580 to 1620 when the English began seriously thinking of theirs as an imperial nation.