How Wind Forms, and Why a Cloud's Shadow Outruns It
Wind from excess or scarcity of moisture, with a geometric proof of cloud-shadow speed
Under 'Wind', the first note explains wind as arising from excess or scarcity: southern regions disperse and then condense drawn-up moisture, driving it back toward a vacuum in the cold region where it re-forms into clouds. The second note, headed 'On the speed of clouds', proves geometrically that a cloud's shadow moves faster over the earth than the cloud does through the air: with the sun as e, cloud as a, and shadow as c, the shadow's rays converge toward the sun's centre, so by 'the fourth' proposition the sections nearer the point of convergence are smaller, and the shadow makes the greater journey. A triangle diagram of sun, cloud, and shadow labelled e, a, b, c, d sits in the upper right.
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Wind generated by excess or scarcity of moisture
Wind is created by excess or by scarcity: the southern regions disperse the moisture they have drawn up, then condense it, and—unable to hold such increase—drive it back toward the vacuum formed in the cold region, where it gathers again into clouds, or into the northern parts where other clouds form.
A cloud's shadow outruns the cloud
The course of a cloud is in itself slower than its shadow moving over the earth. With sun e, cloud a, and shadow c, as the cloud goes from a to b the shadow goes from c to d; the shadow therefore travels the greater distance in equal time.
Converging rays to the sun's centre (the 'fourth' proposition)
Because the shadow-lines running from earth to cloud converge toward the centre of the sun, the note invokes 'the fourth' proposition: sections equidistant from the angle of two converging lines are smaller the nearer they lie to the point of convergence. Since the cloud is nearer the sun than its shadow, the shadow must make the greater journey.