Quadruple circles, with a timber frame and wheel
A geometric proof that in quadruple circles an eighth of one equals a half of the other, amid architectural and machine sketches.
The sheet mixes construction and machine sketches with a single geometric note. At upper left a timber frame of posts and beams is drawn in perspective, with a circular wheel-like device (concentric circles crossed by spokes) beside it and further rectilinear, wall-like structures below. The one transcribed passage, beside the lettered circle-and-triangle figure at lower left, argues that if two circles are quadruple one another, an eighth of the one equals a half of the other. Further untranscribed notes in mirror-writing appear above the timber frame and beside the wheel.
On this page
In quadruple circles, an eighth equals a half
Leonardo states that if two circles are quadruple one another, the eighth part of the one equals the half of the other. He adds that a portion cut from the quarter of the smaller circle has its half equal to the whole portion cut from the eighth of the larger, resting the proof on his knowledge that the quarter of the larger circle is quadruple the quarter of the smaller.
Timber frame of posts and beams
At upper left a heavy timber structure of uprights and cross-beams is drawn in receding perspective, suggesting a building frame, scaffold or truss. Related rectilinear, wall-like elements are sketched to the right and below. No text describing them is included in the bundle.
Wheel-like device of concentric circles
To the right of the timber frame Leonardo drew a round device: two or three concentric circles crossed by radial spokes, reading as a wheel, pulley or geared disc. It sits amid the construction sketches without accompanying transcribed text.