Book IX · Proposition 4

IX.4

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

Every step, checked

• the numbers are genuinegiven
• cube multiplied by cube makes a cubeby IX.4

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.4",
    THEOREM,
    sample=lambda rng: (rng.randint(2, 8), rng.randint(2, 8)),
)
def prop_IX_4(a: int, b: int) -> Out:
    hypothesis("the numbers are genuine", a > 1 and b > 1, guard=True)
    claim("cube multiplied by cube makes a cube", "IX.4", is_cube(a ** 3 * b ** 3))
    return Out(product=a ** 3 * b ** 3)