Two chords crossing off-centre inside a circle
'It is impossible that they pass through the centre' — a refutation with points a, b, c
Drawn in pen circles over faint pencil, the page argues about two straight lines that cross inside a circle without passing through its centre (points c, a, b). Leonardo states that 'it is impossible that they pass through the centre' and answers an imagined 'adversary' who claims that ba equals ac. A companion figure joins the centre to the point of intersection, justified 'by the first,' and a further circle shows a diameter cutting a chord. The sequence is a small dialectical proof about chords and the centre.
On this page
Two lines crossing without passing through the centre
Two straight lines cross inside a circle at points c, a, b, and the note insists 'it is impossible that they pass through the centre.' An imagined adversary objects that ba is equal to ac. The figure sets up the contradiction the proof will resolve.
Centre joined to the point of intersection
In analogous figures the centre of the circle is joined to the point where the two lines intersect, supported 'by the first.' Drawing this line is the key step against the adversary's claim. It carries the argument toward its conclusion.
A diameter cutting a chord
A final circle shows a diameter that cuts across a chord. It illustrates the correct case in which a line does pass through the centre. The figure rounds out the study of crossing lines within a circle.