Geometry: proportional division and circle contact points
Semicircles and inscribed triangles; a note that dividing all extremes equally keeps the proportion
The sheet is covered with faint geometric constructions: semicircles crossed by radiating chords, inscribed triangles, and at lower centre a circle with an inscribed triangle. A marginal note states that all the extremes of any proportion, when divided equally, remain in the same proportion as before. Two further figures explore the point where a descending chord a c touches a circle, which Leonardo calls the angle of incidence of the two points a b upon circle d. Faint additional writing along the right edge is present on the sheet but is not part of the transcription.
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Equal division preserves proportion
A marginal rule states that all the extremes of any proportion, when partitioned equally, remain in the same proportion as before. The accompanying figures 12, 4, 6 and 2 illustrate the claim.
The angle of contact of a chord on a circle
When the segment a b descends with equal motion until the chord a c reaches the point of contact of the circle, that contact point is precisely what Leonardo calls the angle of incidence of the two given points a b upon circle d. A companion figure lets a b and c d be of any proportion.