Christoph Clavius · 1612
Read the translation (PDF) · Editorial footnotes (PDF)
Tomus IV is Clavius’s Gnomonices — the most exhaustive Renaissance treatise on gnomonics, the science of sundials and shadow-casting.
Across eight books it develops the geometry of the gnomon’s shadow and shows how to lay out sundials of every kind: horizontal, vertical, inclined, on any plane and for any latitude. The first book begins where a reader would expect a technical manual not to — with timepieces in general, their necessity and their invention — before turning to sciotheric dials and their various kinds.
What follows is the underlying spherical-astronomical theory of hour-lines, carried through in construction diagrams and in tables of shadow lengths and hour-line positions. The volume closes with a description of an instrument for drawing the lines mechanically, so that a dial could be laid out without recomputing its geometry from scratch.
Sundials were the period’s public clocks, and putting one on an arbitrary wall facing an arbitrary direction at an arbitrary latitude is a genuinely hard problem in spherical astronomy. That is what makes the Gnomonices more than a craftsman’s manual: it is applied celestial geometry, worked out to a degree of completeness no one had attempted, by the man who had just reformed the calendar. The same command of the Sun’s apparent motion underlies both projects.
The translated source is the Mainz printing of 1612, the year of Clavius’s death, dedicated like the other volumes to Prince Johann Gottfried.