Geometry sketches: triangles, a rhombus, and nested figures
Rapid Euclidean studies keyed to numbered propositions
This page of Notebook M is filled with rapid geometric sketches: a segment joining two points a and b, several triangles built on a common base, and a rhombus shown divided by each of its diagonals. Marginal captions such as 'Proof' and 'It follows that the part is greater than the whole' accompany demonstrations about triangles and lines that meet at a point. Numbered references ('seventh', 'second of the fifth', 'by the fifth') tie the figures to a sequence of Euclidean propositions Leonardo was working through. Nested triangles at the lower right explore whether the two sides of a triangle are equal.
On this page
Triangle b a e and lines meeting at a point
A triangle is built on the segment joining points b and a, its apex at e. The note 'seventh' ties the figure to a numbered proposition, and the accompanying remark concerns lines that terminate together at a single point.
Rhombus and the claim that 'the part is greater than the whole'
A rhombus is shown twice, divided once across and once along by a diagonal, captioned 'Proof'. The paired remark states, as the conclusion of the demonstration, that 'the part is greater than the whole.'
Triangles inscribed within triangles
Several views show a smaller triangle set inside a larger one, their upper vertices joined by a vertical line and their sides extended to meet. Captions 'First' and 'Second of the fifth' mark the steps of the construction.
Whether the two sides of a triangle are equal
In the lower-left figure a triangle a n m sits within a larger triangle, with a vertical line joining the two apices a and n and a lower vertex labelled m. The note asks 'whether the two sides of a triangle are equal, by the fifth', invoking an earlier proposition.