The old monk though quite busy with other work still takes his turn walking into town to buy groceries not available within the monastery for the sick and infirm. The path is long but walking gives time to reflect. A donkey cart passes him, the drover calling out a friendly greeting in response to his silent wave. Sunlight reflecting off a wheel catches the monk's eye and he pictures the wheel's rotation in relation to the road, drawing a cycloid in his mind as the cart bounces away.
Just the shape Brother Carpenter requires to smooth the action of the mill, he thinks. The gear teeth should merge not unlike the rim of a wheel touches the surface of the road each rotation, a circle marking out the shape of the sprockets.
Entering the town market the monk selects brown onions carefully inspecting for rot, then green leeks and two heads of garlic with intact firm bulbs. Finally he enters the butcher shop whose owner greets him fondly. The monks had provided clear panes from their glass works for the butcher to display his wares in return for soups bones and the odd meat cut to serve in the infirmary.
Happy to be of service to such a learned man the butcher directs the monk's attention to the beef displayed on two shelves behind glass. Gesturing grandly the butcher asks,"Will that be Choice cut, Brother Mersenne, or Prime?".