Why does Archimedes principle f float = g row I understand the derivation process of the formula. Don't tell the story of the crown

Why does Archimedes principle f float = g row I understand the derivation process of the formula. Don't tell the story of the crown

Can be verified from the experiment, first you can use the weighing method to measure the buoyancy of submerged objects in the water, and then weigh out the gravity of the discharged water, and then compare the secondary values