Proportional figures, an instrument for refraction and a cutting tool
Geometry of narrowing and doubling squares, with a glass refraction gauge and a test of pyramid-shaped points
The sheet is crowded with geometry on the proportional narrowing and doubling of squares, worked through the labelled figures r x m n and a b, c d, together with trapezoids, an octagonal figure and inscribed triangles. At upper left an optical instrument is described for measuring the rectitude of refraction through glass, with the visual line passing through a hole h in the middle of the device. At lower left a cutting instrument on a copper base prompts a test of two pyramids of equal base and decuple length, to see whether their points have equal power and whether a point weakens at a distance. Much further writing runs down the right-hand column beyond the passages transcribed here.
On this page
Narrowing and doubling of a square
Using the letters r x m n, a b and c d, Leonardo argues that as n m grows narrower than n r, so v x rises higher than s n, and that a doubled square lowers in height in the same proportion. He directs that when a square is doubled from above, one keeps half o n m and removes the other half n m p so the figure fits the proposition.
Instrument to measure the refraction of light through glass
Labelled with the word 'glass' and the letters a c b d e f, the note keeps the instrument that measures distance separate from the one that measures the rectitude of refraction along the line d c. The visual line passes through a hole h made in the middle of the instrument.
Testing the power of pyramid-shaped points
On a copper base, Leonardo proposes to test two pyramids of equal base and decuple length, to see whether, cut equally at the point, they are of equal power. He also asks whether at a long distance such a point weakens even when the cutting edge is of equal thickness.
Cutting instrument and mechanical sketches
A cutting instrument is drawn at lower left over a copper base, together with beam-and-joint mechanisms, an upright cylinder and various pointed tools scattered across the sheet. The instruments accompany the geometric and optical notes.