Christoph Clavius · 1611
Read the translation (PDF) · Editorial footnotes (PDF)
Tomus II collects Clavius’s practical mathematics: the mathematics meant to be used rather than contemplated, and the volume closest to what a student in a Jesuit college would actually have been drilled in.
The Geometria Practica treats measurement and surveying — areas, volumes, heights and distances — and it is as much about instruments as about geometry. Its first book opens with the parts of the instrument, their construction and use, and quickly turns into a working table of the quadrant, running division by division across dozens of printed pages so that a surveyor could read off what he needed. The prose then returns for problems of rectilinear triangles, right-angled and oblique, followed by a second book on measuring straight lines with the astronomical quadrant.
The Arithmetica Practica is a full course in computation: the operations, fractions, proportion, the rule of three, roots, worked through many numeric examples. The Algebra presents the cossist symbolic method — the res, census and cubus unknowns — for solving equations.
The Jesuit colleges were among the most systematic mathematical educators in Europe, and this volume is the curriculum they used. Its character is worth noticing: page after page of tables, instrument diagrams and worked examples, aimed at someone who had to measure a field, compute an interest, or lay out a building. Set beside the Euclid of Tomus I, it shows Clavius deliberately covering both the demonstrative and the practical faces of mathematics, and treating the second as no less deserving of a proper textbook.
The translated source is the Mainz printing of 1611.