Conception. Among heavy bodies of equal thickness... Among heavy bodies that are alike in thickness, that one will be of greater weight which is of greater length.

Among waters passing through equal apertures, that one will be the more abundant in an equal time which enters its aperture with the greater velocity; and so it happens with the mouths that are near Abbia. Of water of equal depth, width and slope, that part is swiftest which is nearest the surface. And this happens because the water above borders on the air, which is of little resistance, being lighter than water, while the water below borders on the earth, which is of great resistance, being immovable and heavier than water. It follows that the part farthest from the bed is of less resistance than the part above, which borders on the light and mobile air. Therefore the little mouths near the surface of the water do not lose that quantity of water that... That water is the swifter which descends by a more sloping line. That aperture pours out its water most abundantly which receives the water with the greater velocity. Among waters that in equal time pass through equal apertures, that one will be the most abundant which passes through its aperture with the greater velocity. It is proved in the first book of De ponderibus that among heavy bodies of equal thickness the proportion of the velocity and of the length of their motions is the same as that which the moving weights have among themselves. That is, if there be two heavy bodies of equal thickness and of double weight, and they are let fall through the air in one instant, I say that, the weights being in double proportion, their motion will be in the same proportion, and likewise the velocity. For weights of equal thickness the proportion of the velocity and of the weight is alike.

e - b f o a - d n p c - f q e. a b c d is the thickness of a crystal; o is mirrored at p on the surface c d, and appears as far on this side of that surface as o itself is on the far side; the eye e, which sees it at n, perceives it at q, and likewise at f, and consequently along the whole line n f, were there many surfaces. And this you will see by the light of the sun or of a candle, when the bottom of the crystal or of the water is seen to shine, having the object at its surface. That part of a dark object, of uniform thickness and color, will show itself thinner when seen against a more luminous ground. And the part of a luminous body, of uniform thickness and brightness, will appear thicker when seen against a darker ground.

Divide the base into ninety and cut the pyramid at 100 braccia from the base, and make it narrow by 1/90, and say: if in 100 braccia it narrows for me by 1/90, by how much will it narrow in 9000?

20 ¼ 16 / 45. If 10000 comes from 1/100, what will come from 9000? [with columns of figures: 10000, 100, 1/90, 9000, 90, 1000, 10]

124 / 6744 / £37 soldi 4 / 13 / 7 / 9 1 (a monetary reckoning).