[STAIRCASE. — WATER (CARRIED OBJECTS. — VORTICES)].

3. — [1^st figure:] I 2 C
— [at the top, in red pencil:] brick staircase
— OF OBJECTS CARRIED BY WATER, THAT WHICH IS OF SMALLER SHAPE WILL UNDERGO GREATER REVOLUTION original: "revolutione" — here referring to the spinning or swirling motion caused by eddies..
This happens because the large revolutions of vortices original: "retrosi" — Leonardo's term for back-currents or whirlpools. are rare in the courses of rivers, while small vortices are almost innumerable; large objects are only turned by large vortices and not by small ones, whereas small objects are turned by both small and large vortices Leonardo is observing that smaller objects are more "obedient" to the chaotic movements of water because they fit within even the tiniest eddies..
— OF OBJECTS CARRIED BY THE WATER'S COURSE THAT ARE EQUAL IN LENGTH AND WIDTH, THOSE WHICH SINK DEEPER WILL UNDERGO FEWER REVOLUTIONS.
This occurs because these revolutions vary greatly from the surface to the bottom of the water; in the water, depths generate as many revolutions as there are depressions in their causes The "causes" refers to the unevenness of the riverbed or obstacles.. Therefore, by necessity, an object carried by water that sinks deeply is buffeted by many different heights of revolutions; for this reason, it remains hesitant original: "dubbiosa" — literally "doubtful," describing an object that doesn't move decisively in one direction because it is being pulled multiple ways., and frequently it obeys none of them, and if it does obey, it obeys the most powerful one.
Of objects equal in shape and quantity, the one that sinks deeper obeys the revolutions of the water less.

Editorial notes from the transcription: Numbers 1, 2, and 4 in the source also appear in red pencil as drafts beneath the main writing. The text begins with "Of objects carried by water..." and ends with "many tiny revolutions." These observations on water are also found in the "Cardinali" collection, Book 7, Chapters 44 and 45.

[LEVERS AND WEIGHTS (PROPORTIONS). — “JUDICIAL” SCALES].

[Figure:] c f g a e b 2 [under e] 4 [under d] 8 [under 4] 8 [under f]
The adversary says here that one must understand the weights of the arms of the scale together with the weight of the bodies joined to those arms; and that by considering this, the opposite centers of these combined weights will have distances proportioned to the pole original: "polo" — the fulcrum or pivot point of the scale. of the scale in the same proportion as those combined weights. To which the answer is yes, and it is proven thus: If each arm of the scale is 4 pounds, that is a-b and a-c, I will attach to the middle of a-b a weight of 4, which will make 8 between the attached weight and the weight of the arm; that is, the combination of the 2 weights is 8, and the center of gravity of this 8 is in the middle of that arm, at point e. On the opposite arm, at the extremity of that arm, I will place 2 against the 4 of the other arm Leonardo is calculating how to balance a scale when the weight of the arm itself is factored in alongside added weights., and since the distances of the attached weights are doubled as are their weights, I will now make the "judicial" scale original: "bilaca guditiale" — likely referring to a precision balance or a specific diagrammatic arrangement used for legal or scientific judgment. e-f-g. [The continuation is on folio 4 recto.]

This page was originally written in red pencil. The numbers 2 and 3 in the diagram were written from left to right, contrary to Leonardo's usual mirror-writing.