The cone of light, the angle of incidence, and a burning mirror

Building the angle of incidence with compass and semicircle

Leonardo lays down the line a d, sets the compass foot at a to sweep the curve d f e, then draws a f to cut the circle near d and a parallel b f. Placing the compass at the cut f he strikes the semicircle d h g, transfers the measure d h onto i g, and so obtains the angle of incidence h f i standing exactly between the two equal angles d f h and g f i.

The cone of light narrows by a fixed part for each braccio

On the right-hand leaf the base a o is set at 10 braccia while the space a b is said to diminish by 1/100 of the base o p. Reasoning that the cone of light contracts by a fixed fraction with distance, he finds that at 20 braccia the eye's cone contracts by half, its whole base, so that m becomes the base of a pyramid one braccio wide.

A cone reversed to show two angles are one and the same

The pyramid a f g is turned upside down and set into g c m, with g held fixed and c m kept parallel to a d. Leonardo argues the angle c g m equals a g f precisely because it is one and the same angle simply reversed.

Three circles n: computing the power of the light-cone

Beside three circles labelled n drawn upside-down along the top margin, Leonardo computes that if n measures 1/12 of an inch while the great circle spans a braccio (12 inches), the small circle is 1/20736 of the greater and '20736 times more powerful.' He concludes the cone diminishes by a 144th of an inch for every inch of length, a nearby struck-through note adding that circle is to circle as square to square built on their diameters.

Why a concave mirror's rays do not meet at its center

Testing a concave mirror, Leonardo notes that if the rays n m had to pass through the center o they would reach only a b and never fill the whole concavity c a b d. Since experience shows otherwise, he concludes the rays do not in fact intersect at the center o.

A column of household expenses in another hand

Down the left of the verso, in ordinary (non-mirror) script and a different hand, runs a short reckoning of outlays: a pan, hay, candles, wine, bread, maioni, fodder and a garment, each with its sum in soldi and denari. The list is unrelated to the optical studies that surround it.

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Nella parte mediana del foglio, a sinistra della figura al centro, scritte non speculari di altra mano:

Al centro del foglio figura con lettere.

Sotto la figura:

Sul lato sinistro della figura:

Nella metà superiore del foglio, in alto a sinistra:

A sinistra della figura posta al centro del foglio, testo cassato:

In basso a destra, altro testo cassato:

Nella metà superiore del foglio, al centro sopra e di fianco ad alcune operazioni matematiche, capovolto, testo cassato:

Lungo il margine superiore, capovolti, figura di tre cerchi con lettera n affiancata dal testo cassato:

Nella metà superiore del foglio a sinistra lungo il margine, capovolti, testo cassato affiancato da una figura, e sopra verso il centro, figura con lettere a b c d e altri diagrammi seguiti da operazioni matematiche (cassate quelle lungo il margine):

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Figura con lettere e numeri.

A sinistra della figura:

A destra della figura:

Nel margine destro del foglio figura con lettere.

A lato della figura:

Nel margine destro, sotto la figura:

Nella metà inferiore del foglio, al centro, figura con lettere.

A sinistra della figura:

In the middle of the sheet, to the left of the central figure, non-mirror writing in another hand:

At the center of the sheet, a figure with letters.

Beneath the figure:

On the left side of the figure:

In the upper half of the sheet, at the top left:

To the left of the figure at the center of the sheet, struck-through text:

At the bottom right, another struck-through text:

In the upper half of the sheet, at the center above and beside some mathematical operations, upside down, struck-through text:

Along the upper margin, upside down, a figure of three circles with the letter n beside the struck-through text:

In the upper half at the left along the margin, upside down, struck-through text beside a figure, and above toward the center a figure with letters a b c d and other diagrams followed by mathematical operations (those along the margin struck through):

A figure with letters and numbers.

To the left of the figure:

To the right of the figure:

In the right margin of the sheet, a figure with letters.

Beside the figure:

In the right margin, beneath the figure:

In the lower half of the sheet, at the center, a figure with letters.