Dividing the cube: a tetrahedron is one-sixth of it
Proving the solid c b d g equals 1/6 of the cube a b c d e f g
A geometrical proof, written in Leonardo's mirror-script beside a drawn cube, a triangular prism and several tetrahedra, that the solid c b d g is one-sixth of the whole cube a b c d e f g. The argument builds the cube from tetrahedra sharing common triangular bases (c b g and b f g) and equal-area triangles lying along the diagonal of the square c d f g. The lower drawings are annotated with the words for diagonal (diamitro) and edge (costa), including a greater diagonal and a greater edge.
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The tetrahedron c b d g is one-sixth of the cube
Leonardo asks what part of the cube a b c d e f g the solid c b d g is, and answers that it is 1/6 of the cube's quantity. He argues that the triangle c b g is a base common to two triangles, c b g d and c b g f, lying on this side of the diagonal c g of the square c d f g. He then takes triangle b f g as the common base of two equal triangles, f b g c and f b g n, equal because they stand on the same base with their apices c and n equally distant from the line b f.
Diagonals and edges of the solids (diamitro, costa)
The lower tetrahedra are annotated with the words diamitro (diagonal), diamitro magiore (greater diagonal) and costa (edge). These captions mark which lines of each solid are diagonals and which are edges in the volume decomposition.