Irrational roots, triangle angles and polygons split into triangles
Root 12, Root 27 and Root 324 (=18); the angle sum of a triangle; resolving figures into triangles
A dense sheet of Euclidean geometry. At the top two perpendicular segments carry the labels Root 27 and Root 12, and a rectangle shows that the product of two irrational sides (Root 12 by Root 27) yields the rational square Root 324, that is 18. Below, an isosceles triangle a c b introduces the theorem that a triangle's three angles equal two right angles, followed by a row of a triangle, square, pentagon and hexagon numbered 1 2 3 4 to demonstrate that any rectilinear figure can be resolved into triangles. Faint pencil constructions of squares underlie the inked diagrams.
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A rectangle of two irrational lines makes a rational square
The sides are marked Root 12 and Root 27, irrational lengths, yet the rectangle they enclose is Root 324, that is 18, a rational number. Leonardo notes that the rectangle of two irrational lines makes the rational square.
The three angles of a triangle equal two right angles
An isosceles triangle lettered a c b, its base extended, states the theorem that the three angles of any triangle are equal to two right angles. A stray label By sits toward the folio edge.
Every rectilinear figure resolves into triangles
A triangle, square, pentagon and hexagon are numbered 1 2 3 4, and the square is split into two triangles beneath the note The least. Any rectilinear figure can be resolved into as many triangles as it is distant from the first.