Constructions from a Point Outside a Line
Drawing a tangent as a circle's radius, cutting off an equal segment, and passing a circle through given points.
A page of compass-and-straightedge problems, each phrased as a task. From a point set outside a given line Leonardo draws a second line that serves as the radius of a sought circle, and shows how to cut off from a line a part equal to a drawn segment c q. A worked construction uses the point c outside line a K, two circles h e and m f struck from a and c, and their intersections n g to locate point d. The right leaf continues with drawing two lines from two points that meet at a third equidistant point, and passing a circle's circumference through two given points.
On this page
A tangent line as the radius of a sought circle
From a given point outside a line, a second line is drawn to touch the first, and this line is taken as the radius of a circle to be constructed. The task opens the sheet as a general problem.
Cutting off from a line a part equal to c q
With the given point c outside line a b, Leonardo draws the line c q and requires that a part of a b be cut off equal to c q, either a q or q b. He then sets the further task of finding a third line equal to two given lines of equal length.
Compass construction with circles h e and m f
Point c lies outside line a K; the line K c is drawn, then a circle h e is struck from a and a circle m f from c. The straight line through their two intersections n g cuts K c at point d, joining two equal lines that serve as the radius of the sought circle.
A circle through two given points
On folio 240r, two lines are drawn from two given points to meet at a third point equally distant from both, and a circle's circumference is passed over the two given points. A further note produces a line from the shorter side of a right angle so that its remainder equals it.