The power of the voice, and constructing very large circles
Cone sections for voice and ear; finding the curvature of a circle 25–30 miles across
Under the heading 'On the power of the voice', Leonardo argues that because the sounding source a b is almost infinitely greater than f n, the voice striking the ear c d is amplified enormously; two cone-and-truncated-pyramid figures at upper right illustrate this. The rest of the leaf is geometry: a large sector reduced to a triangle, with four small circles and chords, is used to find the true curvature of a circle whose semidiameters are the two sides of a triangle, employing auxiliary circles, hexagon angles, and the compass. A marginal note explains how to lay out part of a circle 25 or 30 miles in diameter, drawing the circumferential line with a great lance of uniform thickness.
On this page
How the ear amplifies the voice
As much as the voice a b receives into itself the voice f n, so much more powerful is the ear c d, receiving more voice from a b than from f n. Because a b is almost infinitely greater than f n, the voice striking the ear c d becomes infinitely greater than if it were struck by f n.
Finding the true curvature of a very large circle
To find the curvature of a circle whose semidiameters are the two sides of a triangle, whose sides r n and v m do not reach the centre: make auxiliary circles centred at the ends n and m, take the equal spaces b c and b d, draw the diameters, join the centres n m, lay out hexagon angles h g S and x y z, then with the compass fixed at a and moving at m draw the sought circle p n m o.
Laying out a circle 25 or 30 miles in diameter
The two given lines are to be of equal obliquity. This is to make a part of a circle where there is neither periphery nor centre, a circle that would be 25 or 30 miles in diameter, whose circumferential line is drawn with a great lance of uniform thickness.
