The Image of the Sun in a Spherical Mirror
Catoptric constructions for the site and size of a mirror image, with a shop reminder and calculations
Two geometric constructions on this faded sheet tackle a problem of catoptrics: given a spherical mirror and the positions of the eye and an object, to find the site and size of the object's image — here the reflected image (simulacrum) of the sun m. Leonardo sets out a step-by-step procedure using a point on the mirror, an arc measured with compasses, the line o n to form the 'angle of contingence,' and the cathetus of the object to fix the image. A note at the top reminds him to 'see the shop that was Bartol the stationer's,' and columns of figures work through related calculations. The sheet is very faint and carries further untranscribed markings.
On this page
Finding the site and size of the sun's image in a spherical mirror
The problem is posed with lettered points c a K b, d n o, f h m g, e: to find the site and size of the image of the sun m. Given the spherical mirror and the positions of the eye and of the object, one is asked to determine the size and the site that the image of that object has within the mirror.
Construction of the image by the angle of contingence and cathetus
Set the circle of the spherical mirror and the site of the object, then a point upon the mirror; draw the straight line from the object to that point; make a circle upon point e; measure from d to a along the semicircle with compasses and lay that measure in c b. Then draw the line o n cutting b c to form the angle of contingence, and draw the cathetus of the object; of necessity the image's site is where the cathetus meets the line o n, thus establishing both site and size in the mirror.
A reminder about Bartolomeo the stationer's shop
At the top center a memorandum reads 'See the shop that was Bartol's, the stationer's' — a personal reminder to visit or inspect the former premises of a paper-seller.
Columns of calculation
Figures set below and beside the large circle work through numeric divisions and results (630, 15 120, 17 1/7, and related columns). They accompany the geometric optics without a stated context in the transcription.