Dividing a line in three; walking, oxen and river control
A compass construction with notes on human gait, oxen bending trees, and keeping rivers in their banks
A closely written sheet of mirror script headed by a small triangle diagram that illustrates a geometric construction for dividing a line into three equal parts with a fixed compass opening. The notes then range across several subjects: the crosswise motion of a man's limbs in walking, compared to the trot of a four-footed animal; the habit of oxen that climb slender poplars to bend them down and feed on their foliage; and two paragraphs on rivers, urging that a large river needs an appointed official to maintain its banks and observing that the straighter a river runs the better it keeps within them.
On this page
Dividing a line into three equal parts
To split the line a c into three equal parts with a compass opened no wider than a d, one draws an auxiliary line a b at random and marks off the compass opening three times along it. Parallel lines are then drawn from those points to the line a e, always setting off at right angles, so as to carry the equal divisions across.
On the walking of man
The gait of man follows the universal walking of four-footed animals, whose feet move crosswise like a horse's trot. So too a man moves his four limbs crosswise: when he thrusts the right foot forward to walk, he thrusts the left arm forward with it, and it continues so.
Oxen feeding on tall plants
To reach the foliage of slender, tall plants such as small poplars, oxen climb up and straddle the base of the plant with their forelegs, pushing continually forward. Unable to resist the unfitting weight, the plant gives way and is brought down to the ground.
On the governing and maintaining of rivers
Every large river that is to keep within its banks needs an official with authority to command the neighbouring peoples and always to repair wherever it breaks through. It is added that the river which runs straightest will best keep within its banks.