PREFACE

the end of a staff is moved, even if it is distant from the other end by many myriads of leagues A league (leuca) was a unit of distance, often roughly three miles.. If the stars are moved and the earth stands still, their motion exceeds the speed of cannonballs by so many parasangs An ancient Persian unit of distance, about 3.5 miles. that there is no one who would not wonder at such rapidity. Indeed, in the space of one second, the stars near the celestial equator travel 1,166 leagues, as stated in the Preface to the Cosmographia: in which time a ball fired from a cannon Original: "tormentum," a piece of artillery or engine for throwing projectiles. covers only one hundred six-foot fathoms Original: "sexpedas," a measure of six feet.; and thus the stars are 1,150 times faster than the cannonball.

I omit the comparison of the speed of that motion by which they complete a single degree in the space of 80 years, which you can find in the aforementioned Preface, so that we may consider the annual or diurnal Daily. motion of the earth. Of these, the diurnal motion covers 300 leagues in an hour, and in one second, almost a league; therefore, that motion is twenty-five times faster than the motion of a cannonball. Since the annual motion of the earth is three times faster than its diurnal motion, it will be seventy-five times faster than the motion of the ball. If anyone among us were moved with such velocity, they would seem to fill such a vast space as if they were a continuous or motionless body, because such swiftness could hardly be perceived by anyone.

Although these velocities seem very slow because of the immense distance, as is clear from the observation of stars and other heavenly bodies, which, if the eyes watching them continuously are believed, will appear motionless. Thus, the highest velocity with respect to us is the same as rest, or the highest slowness; just as it is said by the Psalmist Referring to the biblical Psalm 139:12, "the darkness and the light are both alike to thee." that God's light is as his darkness: not because there is any darkness in him, but because the sharpness of the human mind is dazzled and dulled by excessive light, in much the same way as the vision of our eyes is dazzled and almost extinguished by the motion of a passing cannonball or a flash of lightning.

XXVII. Since heavy bodies traverse immense spaces in a short time, even though they are supposed to pass through all degrees of slowness, I add a few points. Indeed, many things happen which, although they are admirable, are commonly disregarded by those who pay less attention. Such is the accretion Growth or gradual accumulation. of plants and trees, and even of men, which, although it happens by continuous motion, is least perceived because of its excessive slowness. If you were to compensate for this with the acceleration by which heavy bodies descend, eventually the motion would become apparent.

The greatest difficulty seems to consist in this: that a heavy body, descending much more quickly in air than in water, nevertheless passes through all degrees of slowness in air just as it does in water. This difficulty is satisfied in some way by two circles, of which the smaller is considered to have as many points and parts as the larger This refers to a famous paradox in geometry where a small circle and a large circle, when rolled, seem to touch the same number of points on a line..