Squares on a triangle's sides and an 'irrational' height
A half-circle triangle of base 12 and side 8; squares of 64, 144 and 80 on a right triangle
The leaf explores square numbers arising from triangles. A scalene triangle inscribed in a half-circle, with apex at a, has base 12 and one side 8, and a further measure marked 'irrational'. A right triangle carries a square on each of its three sides, linked in pairs by curved pen-strokes, and the values 64, 144 and 80 (with an 8) are entered nearby as the squares of the sides. Three squares also stand in a column, and the numerals were written in the ordinary, non-mirrored sense. Much of the page is faint, with show-through from adjacent leaves.
On this page
Squares built on the three sides of a right triangle
A right triangle set point-down has a square raised on each side, with curved strokes joining two pairs of squares. The construction is the Pythagorean figure relating the square on the hypotenuse to those on the legs.
Side-squares 64, 144 and 80
Nearby the values 64, 144 and 80 are written, with an 8, as the squares of the sides — 64 being 8 squared. The numbers were written the ordinary way round rather than mirrored.
Half-circle triangle with an 'irrational' measure
A scalene triangle inscribed in a half-circle touches the arc at a; its base is 12 and one side 8, while a further measure is labelled 'irrational'. The note flags a length not expressible as a whole number.