Making two unequal triangles equal in area
Completing the rule: aligning the axes of triangles a b c and e d f
A wide triangle at the left and a narrower one share a pair of lines that converge to a point toward the right of the sheet. The note completes a rule begun on the previous page for making two triangles of unknown proportion, and different in shape, equal in area. Leonardo places the axis and base of triangle a b c on the converging lines, extends the axis in a straight line, and cuts off along it a length equal to the axis of the second triangle e d f. Joining the two axes end to end and drawing the base line f g then fixes the bases of the higher and the lower triangle.
On this page
Setting the two axes on one straight line
On the two lines b c that meet at a, Leonardo sets the axis and base of triangle a b c so each touches the converging lines, then continues that axis straight on. Along it he cuts a length equal to the axis of the second triangle e d f, joining the two axes at their ends so they form a single straight line.
Fixing the bases f g of the two triangles
From the far end of the second axis a line is drawn to the same meeting point a as the others, and beneath the base e f of the first triangle the line f g is drawn. That line becomes the base of the higher triangle, and the other becomes the base of the lower triangle, making the two equal in area.