Squares on a right triangle and parallelograms between parallels
Consideration 35; equal parallelograms proved by the thirty-fourth, fourth and twenty-ninth
A geometry page whose upper figures set two and three squares upon the sides of a right triangle, with diagonals drawn in one square. A number, 35, is encircled to mark the consideration. The lower half studies parallelograms lying between two parallels, cut by diagonals, with equal angles dotted and the leftover triangles isolated after the parallels are removed; the equalities are justified with the thirty-fourth, the fourth, and the fourth together with the twenty-ninth propositions. Faint pencil constructions underlie the inked diagrams.
On this page
Squares raised on the sides of a right triangle
The upper figures build two and three squares on the sides of a right triangle, with diagonals ruled inside one of the squares. The arrangement studies the areas standing on the legs and hypotenuse.
Equal parallelograms between parallels
Parallelograms lying between two parallels are cut by diagonals, with equal angles marked by dots and the residual triangles isolated once the parallels are removed. The relations are proved with the thirty-fourth, with the fourth, and with the fourth and the twenty-ninth.