A Line Equidistant from Two Given Points
Compass construction of the perpendicular bisector via the definition of the circle
This spread is devoted to a compass-and-straightedge construction: given two points a and b, Leonardo finds a third point, and indeed a whole line, every part of which is equidistant from both. He draws circles o m p and q n r centred on a and b, joins their intersections m and n and extends the line to f, and invokes 'the definition of the circle' to conclude that the resulting line c d lies midway between the two points. The right-hand folio (219r) carries the labelled circle diagrams; the left folio (222v) bears further untranscribed geometric figures.
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A line equidistant from two given points
Between two given points a straight line is drawn, every part of whose length is equidistant from each of them. Given the points a and b, the line c d lies midway between them, by the definition of the circles a o, e o b, a c and b c.
Compass construction of the third point
With the foot of the compasses at point a draw the circle o m p, and do the same at b with the circle q n r; draw the line m n through the two intersections of the circles as far as f. Place the third point anywhere on that line, say at c, and it lies midway between a and b, by the definition of the circle.
The condition rests on the definition of the circle
A line is placed so conditioned that every part of its length is equidistant from two given points, and a third point can be set below, in the middle or above the two, equally distant from each. The whole construction is grounded on the definition of the circle.
Untranscribed figures on folio 222v
The left folio carries further untranscribed drawings not covered by the transcription: rectangles crossed by diagonals and a column of lune-like semicircle figures.