Refuting Unequal Sides in Nested Isosceles Triangles
Two isosceles triangles inscribed one within another; points a, b, c, d, f, r
Two isosceles triangles are drawn one inside the other, their apexes labelled c and b above a shared lower vertex a. Leonardo refutes two claims in turn: that side a b is smaller than a c, and that angle b is larger than angle c. A second pair, with a side of the inner triangle carried up to meet the outer at d (and points f and r), supports a proof 'with d f r, removing the sides', echoed by two smaller repetitions of the figure.
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Nested isosceles triangles a, b, c
A smaller isosceles triangle is inscribed within a larger, upper vertices c and b over a shared lower vertex a. The note refutes that a b is smaller than a c, and then refutes the second claim, that angle b is larger than c.
Proof with d, f, r, removing the sides
In a second pair one side of the smaller triangle (apex c) is extended upward to meet the larger at point d, with further points f and r on the outer triangle. The proof proceeds 'with d f r, removing the sides'.
Smaller repetitions of the figure
Two further, smaller sketches restate the triangle combination shown alongside. They serve as reduced trials of the same nested arrangement.