When two curved lines meet: parallel arcs and "curved pyramids"
Concentric arcs c b and o l, and tangent circles centred a and r, with cuts made equidistant from a circle.
Two nearly concentric arcs, one marked c and b and the other o and l, prompt the question of how far apart they run before they would join. Below, a small circle sits tangent inside a larger one, divided by the line f g through the point n, with centres a and r and extra arcs S t and m in the crescent between them. Leonardo asks whether two given curved lines are parallel and, if not, whether they compose "pyramids" and at what distance from the base their curved sides would meet, cutting equidistant from the lower circle using its centre r, or from the upper using centre a, and then proceeding as for the straight pyramid.
On this page
At what distance do two equal-curvature arcs join?
The upper figure shows two arcs, c and b against o and l, drawn with the same curvature, and Leonardo asks at what distance the two lines would join.
Cutting equidistant from a circle using its centre
If you cut above, cut equidistant from the circle below, using its centre r; if you cut below, cut equidistant from the circle above, using its centre a. The figure shows the small circle tangent within the large one, split by the line f g through n.
Whether curved lines are parallel or compose pyramids
Leonardo asks whether two given curved lines are parallel and, if not, whether they will compose pyramids and at what distance their sides join. A detached piece must be the same fraction of the base as it is of the side, taken from above or below.