Domed churches, columns, and a theorem on a divided line
Architectural and mechanical studies beside Euclid's rule for a line cut equally and unequally
The upper sheet is crowded with architectural studies of centrally planned domed churches, columns and entablatures, and arches, together with sketches of mechanical devices. The transcribed notes instead set out a geometric proposition: for a straight line divided both in half and into two unequal parts, the rectangle of the unequal parts plus the square on the difference equals the square on the half. A worked example with the numbers 4, 2 and 2 confirms the identity, giving 16 in both ways. Much of the sheet's mirror-script writing and the machine sketches remain untranscribed.
On this page
Centrally planned domed churches and columns
At the top stand two centrally planned domed churches seen in perspective, flanked and followed by studies of columns, entablatures and a springing arch. The forms belong to Leonardo's investigation of centralized church plans. The transcription does not cover these drawings.
Theorem on a line cut into equal and unequal parts
If a straight line is divided into two equal parts and into two unequal parts, the product of the lesser part by the greater, together with the square on the difference, equals the product of the equal part by itself. This is the geometric identity underlying the worked example beside it.
Worked example: 2 x 6 plus 4 equals 16
Taking a as the equal part and b c as 4, with the unequal part c equal to 2 and the difference square b equal to 2: 2 times the greater 6 makes 12, add the square of the difference 4 to make 16; and a multiplied by itself likewise makes 16. The two results agree.
Mechanical devices with cranked linkages
At the centre of the sheet are sketches of mechanical devices with cranked arms and hinged linkages. They are not described in the transcribed text and are recorded here only by their appearance.