The law of the balance-wheel and its force
Weight times the perpendicular distance to the pole, and the wheel acting at its rim on other poles
This all-text page states the rule of the balance-wheel. A wheel sustained on its pole by attached weights uses each weight together with the distance of its perpendicular from the pole, so a weight whose perpendicular is twice as near needs twice the load to balance. When instead the wheel acts at its rim against things fixed on other poles, its force follows the ratio of the line from the wheel's center to the driving cause versus the line from that center to the thing moved. The passage, numbered 41, sets up the geared-wheel diagram that follows.
On this page
Weight multiplied by perpendicular distance to the pole
The simple wheel, sustained on its pole only by attached weights, employs each weight together with the distance from its perpendicular to the pole. If the upper weight's perpendicular approaches the pole by one braccio and the opposite weight's by two, the first — being twice as near — needs twice the weight of the other to stand in equal power.
A wheel acting at its rim on other poles
When the wheel acts with its extremity upon other things fixed on other poles, one must measure the proportion of the straight line from the wheel's center to the cause of its motion against the line from that center to the thing moved. The proportion of its force equals the proportion of those lines.