Perpendicular from a circle's centre onto a chord
Circle constructions citing 'the eighth of the first' and 'the fifth of the first'
The sheet, largely in faint pencil with a few pen circles, treats the relation of a chord to the centre of its circle. One figure drops a perpendicular from the centre onto a chord; another joins the centre to the ends of the chord, justified 'by the eighth of the first.' A third inscribes a triangle in the circle, citing 'the fifth of the first' and 'the definition of the circle.' The references are to earlier propositions Leonardo is building on.
On this page
Perpendicular dropped from the centre onto a chord
A circle is drawn with a chord, and a perpendicular is let fall from the centre onto that chord. The construction is the starting point for reasoning about how the centre relates to a chord. It heads the small group of circle figures on the page.
Joining the centre to the ends of the chord
The centre of the circle is joined to both ends of the chord, and the step is justified 'by the eighth of the first.' Drawing these radii sets up the isosceles triangle used in the argument. The citation points back to an earlier proposition.
Triangle inscribed in the circle
A triangle is inscribed within the circle, supported by 'the fifth of the first' and 'the definition of the circle.' The equal radii make the argument turn on the circle's defining property. It concludes the chord-and-centre sequence.