"When a mother branch branches in two daughter branches..."

"... the diameters are such that the surface areas of the two daughter branches, when they sum up, is equal to the area of the mother branch."

Leonardo's observation, verified.

"I would contrive catapults, mangonels, trabocchi, and other machines of marvellous efficacy and not in common use."

"And in short, according to the variety of cases, I can contrive various and endless means of offense and defense....  I can carry out sculpture in marble, bronze, or clay, and also I can do in painting whatever may be done, as well as any other, be he who he may."

From the cover letter of Leonardo da Vinci, age 30.