Constructing a Triangle from Three Given Lines
Segments a, b, c marked on a line, with two circles meeting to fix the apex
This folio sets and solves the problem of building a triangle from three given segments a, b and c, provided any two together exceed the third. A line of indefinite length d e is drawn, the three lengths laid off along e f at the points c, b and a, and two overlapping circles are struck whose intersection fixes the apex. The captions cite 'the third of the first' and note that the circles cut each other, so it is proved to be a triangle by the definition of the circle.
On this page
The three given lines a, b, c
Three segments of different sizes are labelled a, b and c. Leonardo states the aim: to make a triangle of the three lines, arranged so that any two joined together are larger than the third, single line.
A base line d e of indefinite length
A horizontal segment d e is drawn across the page as a line of indefinite quantity, to be measured off. The caption cites 'the third of the first' as the governing rule.
Two circles cut to fix the apex
On the marked segment e f (points c, b, a, f) two overlapping circles meet, and a triangle is inscribed in the overlap with its apex at their intersection. Because the circles cut each other, it is proved to be a triangle by the definition of the circle.