Mean Proportional Found by Parallels in a Triangle
The line 6 between the segments 4 and 9
A triangle is lettered f, d, b, a with the measures 9, 6 and 4 and marked 'parallels', beside a separate segment c of length 6. The values continue the notebook's worked example in which 6 is the mean proportional between 4 and 9. Here parallels drawn within the triangle are used to obtain that middle term. The pencil drawing is faint, and a curved arc is also traced over the figure.
On this page
Parallels within the triangle
The triangle carries the points f 9 d 6 and 6 b 4 a with the word 'parallels', showing that parallel lines are drawn across it. Such parallels cut the sides proportionally and yield the required middle length.
The segment of length 6
A separate segment is marked c - 6. Together with the segments 4 and 9 of the triangle, this 6 is the mean proportional between them, the recurring numerical example of these pages, since 6 times 6 equals 4 times 9.