Circle-segment geometry, the tides, and maxims on motion

Equivalence of detached circular segments (lunes)

Two portions cut from a circle are labelled c, a, b, f. The note instructs one to make two 'sub-double' portions and remove one 'double' one, or the reverse, so that the areas balance, referring back to the figure at f. It is an exercise in equating curved segments by addition and subtraction.

Circles with inscribed and circumscribed squares

A pair of figures show two circles each with a square inscribed and circumscribed, one carrying the letter f. The accompanying instruction is to divide a portion lengthwise into two equal parts, continuing the study of how circular areas may be split and matched.

Flow and ebb of the tides

In a 'figure of the earth' showing high tide to the north, marked maximum and minimum, the note states that where there is a greater quantity of water there is a greater flow and ebb, and the contrary in narrow waters. Cold gathers and heat separates; the sea reaches its highest flood as the moon crosses the middle of the hemisphere.

The moon governs the sea and its creatures

The tidal motion along d b is said to rise for twelve hours, and shrimps and crabs are described as 'empty' at the waning moon because they can see little light to feed by, while at full moon they feed abundantly. The moon's phase is thus tied both to the sea and to the behaviour of animals.

Maxims on density, weight and descent

A dense block of aphorisms holds that the denser body sustains more, that descent is slower in the deep, that greater width lessens gravity, and that a heavy body grows faster the more it descends. The extremities of a body held at its middle bend easily, and the heavier part of an unequal weight becomes the guide of the motion.

(a) Due cerchi, due quadrati iscritti e circoscritti, colla lettera:

Due porzioni staccate da un cerchio, con:

Porzione divisa per metà fra un cerchio e un settore, con:

In basso, a destra; cerchio su semicerchio, con:

A sinistra, figura con:

Figura simile, con:

Due cerchi e due quadrati iscritti e circoscritti:

Foglio capovolto, in basso a destra. Figura della terra colle lettere:

Figura della terra colle lettere:

A destra, figura della terra coll'alta marea a nord:

A sinistra del precedente.

(b)

(c)

(a) Two circles, two squares inscribed and circumscribed, with the letter:

Two portions detached from a circle, with:

A portion divided in half between a circle and a sector, with:

Below, on the right; a circle upon a semicircle, with:

On the left, a figure with:

A similar figure, with:

Two circles and two squares inscribed and circumscribed:

Sheet turned upside down, lower right. Figure of the earth with the letters:

Figure of the earth with the letters:

On the right, figure of the earth with high tide to the north:

To the left of the preceding.

(b)

(c)