Geometric constructions with compass and straightedge
Tangents, equal segments, the squared circle and right-triangle problems
Both leaves are crowded with compass-and-straightedge constructions, triangles, circles and squares interleaved with explanatory text. Leonardo poses a series of problems: drawing from a given point outside a line a second line that becomes the semidiameter of a required circle; cutting off from a line a part equal to a drawn line; finding a third line equal to two given equal lines; and completing constructions that touch on the thickness of the squared circle and on right-triangle and hypotenuse relations. Several captions labelled only as figures with letters mark diagrams whose own text was not transcribed.
On this page
A line from an external point as the semidiameter of a circle
The first problem asks that from a given point outside a line a second line be drawn to the contact of the first, this second line being the semidiameter of a required circle. It sets the theme of the page: constructions that generate a circle or an equal length from a point lying off a given line.
Cutting off an equal segment and finding a third equal line
From the point c outside line a b, Leonardo draws c q and cuts from a b a part equal to c q, which may be a q or q b. He then poses the companion problem: with two given lines of equal length, find a third line equal to each of the two.
Compass construction and the thickness of the squared circle
With c outside line a K, he draws K c, sets the compass foot at a to strike circle h e, then at c to strike circle m f, and joins the intersections n g; where n g cuts K c at d the junction of two equal lines is made. These are the semidiameter of the required circle, which meets the third semidiameter d b with the part b K, the part called the thickness of the squared circle.
A circle through two points and right-triangle problems
The last group asks to draw from two given points two lines meeting at a third point equidistant from both, and to draw the circumference of a circle upon two given points. A right-triangle problem is repeated: from the extreme of the lesser side of a right angle, produce a line to the opposite side so that its excluded remainder equals that line.