Military architecture embraces fortification and field works, which,
with their bastions, curtains, hornworks, redoubts, &c. are based on a
technical combination of lines and angles. These are adapted to offence
and defence, with and against the effects of bombs, balls, escalades,
he. But lines and angles make the sum of elementary geometry, a branch
of pure mathematics: and the direction of the bombs, balls, and other
projectiles, the necessary appendages of military works, although no
part of their architecture, belong to the conic sections, a branch of
transcendental geometry. Diderot and D'Alembert, therefore, in their
_Arbor scienciae_, have placed military architecture in the department
of elementary geometry. Naval architecture teaches the best form and
construction of vessels; for which best form it has recourse to the
question of the solid of least resistance; a problem of transcendental
geometry. And its appurtenant projectiles belong to the same branch as
in the preceding case. It is true, that so far as respects the action of
the water on the rudder and oars, and of the wind on the sails, it may
be placed in the department of mechanics, as Diderot and D'Alembert
have done; but belonging quite as much to geometry, and allied in its
military character to military architecture, it simplified our plan to
place both under the same head. These views are so obvious, that I am
sure they would have required but a second thought to reconcile the
reviewer to their location under the head of pure mathematics.
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