The New Science

A scientific diagram illustrates a gunner's quadrant or surveying tool. It consists of two straight arms meeting at a right-angled vertex labeled A. A curved arc, or quadrant, connects the two arms and is divided into segments, with labels E at the left end, G in the center, and F at the right end. A plumb line is suspended from a point H just below the vertex, passing directly through the midpoint G of the arc and ending in a spherical plumb bob labeled D. The ends of the straight arms are labeled B and C respectively, with arm AB shown as significantly longer than arm AC.

...ly) into two equal parts (that is, at point G). At that point, it shall be said that the said
piece the cannon or artillery engine will look straight at 45 degrees above the horizonoriginal: "orizonte"; the horizontal line where the earth meets the sky, used here as the base reference for the angle of fire.. Because
(Most Illustrious Lord) the curved side E-G-F of the quadrantoriginal: "quadrante"; a mathematical instrument used to measure angles of elevation. (according to the astronomersoriginal: "astronomi"; Tartaglia refers to the authority of scientists who studied celestial measurements.)
is divided into 90 equal parts, and each of those they call a degreeoriginal: "grado".. Therefore
the half of it (that is, G-F) would come to be 45 degrees. But to harmonize
(Most Invincible Lord) with what remains to be said, we have divided it
into 12 equal parts; and so that Your Most Illustrious Lordship
might see in a figure what we have depicted above with words, we
have designed here below the piece with the squareoriginal: "squara"; a gunner's quadrant, often shaped like a carpenter's square with an added arc, used to set the elevation of a gun. set in its mouth, positioned
according to the resolution concluded by us for our said friend. Which
conclusion seemed to him to have some consistency, yet he doubted
it somewhat, it appearing to him that such a piece looked too high. Which
proceeded from him not being capable of [understanding] our reasons, nor in Mathematicsoriginal: "Mathematice".
well-strengthened; nonetheless, with several particular experiments,
it was finally verified to be totally thus.