Joining Equal Angles; Parallelograms on Triangles
Combining figures by equal angles and the application of areas
This faint pencil page carries the note 'bring together the angles c which are equal' beside several small geometric figures. They include two triangles joined at a vertex, squares set against triangles, and parallelograms, the last described as exceeding a given parallelogram by a similar one, the Euclidean application of areas. Numbers such as 272 and 283 are set beside the parallelograms, apparently as areas or measures. Additional faint construction lines are present on the sheet.
On this page
Bringing together equal angles
A marginal note directs one to join the angles c which are equal, so that figures are matched where their equal angles coincide. This pairing of equal angles underlies the transformation of one rectilinear figure into another of equal area.
Parallelogram exceeding by a similar parallelogram
The final construction is labelled a parallelogram exceeding a given parallelogram by one similar to it, marked h - a c b - f g. This is the application of areas 'in excess' from Euclid's Book VI.
Triangle with divided base
At the foot of the page a right-angled triangle is drawn with its base marked off into segments and a diagonal rising across it. Points along the base carry the letters used in the accompanying figure notes.