Opposite Angles Where Two Lines Cross
Isosceles triangles, a divided rhombus, and the rule of intersecting lines
Continuing the geometry of triangles, the folio couples isosceles triangles with a rhombus split by its diagonals, its inner triangles labelled a, c and b. Leonardo heads the propositions 'Sixteenth' and 'Fifteenth' and cites 'opposite interiors' and 'by the fourth'. A closing note states the vertical-angle rule: wherever two lines intersect, the opposite angles are equal, so a and b are equal.
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The sixteenth: opposite interior angles
An isosceles triangle has one side extended upward, with 'opposite interiors' noted above and below the base. The figure opens the sixteenth proposition, comparing the interior angles set opposite one another by the extension.
Rhombus divided by its diagonals, angles a c b
A rhombus is cut by its diagonals, one side extended upward and the parallel side cancelled, with the inner triangles marked a, c and b. The caption 'By the fourth' cites an earlier result to establish the marked angles as equal.
Opposite angles of crossing lines are equal
The concluding note gives the vertical-angle rule: whenever two lines intersect, the opposite angles are equal. Applying it to angles a, b and c, Leonardo concludes that a and b are equal.