Triangle Divided by its Altitude; Squares on Two Sides
The 13-14-15 triangle, its base split into 5 and 9, with the squares 225, 196, 169
A faint pencil page working through a triangle divided by the perpendicular dropped to its base. The values 225, 196 and 169 are the squares of the sides 15, 14 and 13, while the base is split into segments 5 and 9 by the foot of the altitude. A companion figure carries the squares built on two of the sides, and a straight line below is divided into 8 and 4.
On this page
Triangle split by the altitude to its base
A triangle is cut by the perpendicular let fall onto its base. The annotations give the squares 225, 196 and 169 (of the sides 15, 14 and 13) and the base segments 5 and 9 into which the altitude divides it.
Squares constructed on two sides
A similar triangle is drawn with the squares raised on two of its sides, relating each side to the area of its own square. It sits beside the divided triangle as a paired figure.
A line divided into 8 and 4
A straight line lower on the page is divided into two parts, 8 and 4. It gives a simple proportional division to accompany the triangle work above.