Polygons in circles, spiral, and area equivalences
Geometric studies toward squaring the circle, with untranscribed notes at upper right.
The sheet is filled with geometric figures exploring the quadrature of the circle: a pentagon and a square inscribed in circles, a hatched disk, a tight spiral, and small lune-and-sector diagrams whose areas Leonardo equates with one another. The transcribed notes state a Euclidean common notion—'if from equal things you take away equal parts'—and label several figures so that one shaded portion 'is worth' another (a b vale c; n vale m), ending with a triangle transformed into a rectangle. Further mirror-script that is not transcribed here runs at the upper right; the Ambrosiana catalogue also associates the sheet with notes on compressibility, the sound of struck iron, and two ways of seeing an object.
On this page
Polygons inscribed in circles and a Euclidean common notion
At the top of the sheet a pentagon and a square are inscribed in circles, beside a hatched disk and a tight spiral. The note states the axiom that 'if from equal things you take away equal parts' the remainders stay equal, the principle Leonardo uses throughout to equate the areas of circular figures.
Lune-and-sector equivalences: a b vale c; n vale m
Small crescent and sector figures are each lettered so that one shaded portion equals another: 'a b is worth c' and 'n is worth m.' At the lower edge a triangle is redrawn as a rectangle (6—4), converting a triangular area into an equal rectangle.
Untranscribed mirror-script at upper right
Several lines of Leonardo's mirror-script run across the top right of the sheet and are not included in the transcription. The Ambrosiana catalogue associates this sheet with notes on compressibility and on the sound of iron when struck.