Book IX · Proposition 3

IX.3

If a cube number by multiplying itself make some number, the product will be cube.Heath, 1908

Every step, checked

• the number is genuinegiven
• a cube multiplied by itself makes a cubeby IX.3

What it needs, and what needs it

Needs: nothing earlier.

Depth: 0 steps of argument above the first principles. Parallel postulate: not needed.

What it takes on trust

Nothing. It draws no intersections and reads nothing off the picture.

The proposition as code

@proposition(
    "IX.3",
    THEOREM,
    sample=lambda rng: (rng.randint(2, 10),),
)
def prop_IX_3(a: int) -> Out:
    hypothesis("the number is genuine", a > 1, guard=True)
    cube = a ** 3
    claim("a cube multiplied by itself makes a cube", "IX.3", is_cube(cube * cube))
    return Out(product=cube * cube)