Mathematical Treasures - Nicolo Tartaglia's Nova Scientia

This is the title page of the Nova Scientia (1537) of Nicolo Tartaglia (1499-1557).  In this work, Tartaglia discussed the mathematics of artillery and developed methods for determining the range of a cannon. The caption below the illustration reads,

The Mathematical sciences speak:  Who wishes to know the various causes of things, learn about us.  The way is open to all. 

The illustration itself depicts a walled compound, the compound of knowledge.  The high wall keeps out the man who attempts to scale it and enter improperly.  Entrance into the compound is through a single door opened by Euclid.  In the first courtyard, a crowd comprised of Tartaglia and the muses of the seven liberal arts watch a demonstration of Tartaglia's new knowlege, a theory of trajectories.  Beyond the first courtyard is a second smaller, more exclusive and highly elevated one.  Its entrance is manned by Aristotle and Plato.  Plato holds a banner proclaiming,

No one can enter who does not know geometry. 

Enthroned at the rear of this compound, in the highest position of all, is philosophy.

Above: On this page (folio 29v), we see a method of determining the height of a distant object using a quadrant, or set-square.

Editor's note: The images above, from Columbia University Library's David Eugene Smith and George Arthur Plimpton collections, were posted on 5/14/2008. The images below, obtained through the courtesy of the Dibner Library of Science and Technology, Smithsonian Libraries, were added on 5/14/2017.

Tartaglia established that the trajectories of projectiles follow a (somewhat) parabolic path:

The range of a cannon is determined by the elevation of the barrel. Tartaglia designed a set-square, or quadrant, that would help gauge cannon barrel elevation:

Index to the Collection of Mathematical Treasures from the David Eugene Smith and George Arthur Plimpton collections, Columbia University Library

Index to the Convergence Collection of Mathematical Treasures