spheres, being transferred into that other circle M N O P, which is part of the sphere that the eye describes to itself about that earth.

From whence we may plainly discern, that though the earth be never so far distant from the centre of the world, yet the parts and degrees of that imaginary sphere about it, will always be proportional to the parts and degrees of

the earth.

2. Another demonstration like unto this former, frequently urged to the same purpose, is this. If the earth be out of the centre of the world, then must it be situated in one of these three positions: either in the equator, but out of the axis; or 2dly, in the axis, but out of the equator; or 3dly, besides both of them. But it is not placed according to any of these situations, therefore must it needs be in the centre *.

1. It is not in the equator, and beside the axis: for then, 1st, there will be no equinox at all in some places, when the days and nights shall be of an equal length; 2dly, the afternoons and forenoons will not be of the same length; because, then our meridian line must divide the hemisphere into unequal parts.

2. It is not in the axis, but out of the equator; for then, first, the equinox would not happen when the sun was in the middle line betwixt the two solstices, but in some other parallel, which might be nearer to one of them, according as the earth did approach to one tropic more than another. Secondly, there would not be such a proportion between the increase and decrease of days and nights, as now there is.

3. It is not besides both of them: for then, all these inconveniencies, and sundry others must with the same necessity of consequence be inferred. From whence it will follow, that the earth must be situated there where the axis and equator meet, which is in the centre of the world. To this we grant, that the earth must needs be placed

* Vid. Carp. Geog. 1. 1. c. 5.

both in the axis and equator; and so consequently, in the centre of that sphere which we imagine about it. But yet this will not prove, that it is in the midst of the universe: for let our adversaries suppose it to be as far distant from that, as they conceive the sun to be; yet may it still be situated in the very concourse of these two lines; because the axis of the world is nothing else, but that imaginary line which passes through the poles of our earth, to the poles of the world. And so likewise the equator is nothing else but a great circle in the midst of the earth, betwixt both the poles, which by imagination is continued even to the fixed stars. Thus also, we may affirm the earth to be in the plane of the zodiac, if by its annual motion it did describe that imaginary circle: and in the plane of the equator, if by its diurnal motion about its own axis, it did make several parallels, the midst of which should be the equator. From whence it appears, that these two former arguments proceed from one and the same mistake; whilst our adversaries suppose the circumference and centre of the sphere, to be the same with that of the world.

Another demonstration of the same kind, is taken from the eclipses of the sun and moon; which would not always happen when these two luminaries are diametrically opposed, but sometimes when they are less distant than a semicircle, if it were so that the earth were not in the centre.

I answer: this argument, if well considered, will be found most directly to infer this conclusion; that in all eclipses, the earth is in such a strait line (betwixt the two luminaries) whose extremities do point unto opposite parts of the zodiac. Now, though our adversaries should suppose (as Copernicus does) the earth to be situated in that which they would have to be the sun's orb; yet would there not be any eclipse, but when the sun and moon were diametrically opposite, and our carth betwixt them; as may clearly be manifested by this figure, where you see the two luminaries in opposite signs: and according as any part of

our earth is situated by its diurnal revolution, so will every eclipse be either visible, or not visible unto it.

سالة

The last and chief argument, is taken from the appearance of the stars; which in every horizon, at each hour of the night, and at all times of the year, seem of an equal bigness*. Now this could not be, if our earth were sometimes nearer unto them by 2000000 German miles, which is granted to be the diameter of that orb wherein the earth is supposed to move.

I answer: this consequence will not hold, if we affirm the earth's orb not to be big enough for the making of any sensible difference in the appearance of the fixed stars.

Yea, but (you will say) it is beyond conceit, and without all reason, to think the fixed stars of so vast a distance from us, that our approaching nearer unto them by 2000000 German miles, cannot make any difference in the secming quantity of their bodies †.

I reply: there is no certain way to find out the exact distance of the starry firmament; but we are fain to con

*Arist. de cœlo, lib. 2. c. 14.

+ Copern. 1. 1. cap. 5, 6.

clude of it by conjectures, according as several reasons and observations seem most likely unto the fancies of divers men. Now that this opinion of Copernicus does not make it too big, may be discerned from these following considerations.

The words great and little, are relative terms, and do import a comparison to something else: so that where the firmament, (as it is according to Copernicus) is said to be too big, it is likely that this word is to be understood in reference to some other thing of the same kind, the least of which is the moon's orb. But now if its being so much bigger than this, may be a sufficient reason why it should be thought too great, then it seems that every thing which exceeds another of the same kind in such a proportion, may be concluded to be of too big a quantity; and so consequently, we may affirm that there is no such thing in the world. And hence it will follow, that whales and elephants are mere chimæras, and poetical fictions, because they do so much exceed so many other living creatures. If all this eighth sphere, (saith Galilæus) as great as it is, were a light body, and placed so far from us that it appeared but as one of the lesser stars, we should then esteem it but little; and therefore we have no reason now to thrust it out from being amongst the works of nature, by reason of its too great immensity. It is a frequent speech of our adversaries, Tycho, Fromondus, and others, in excuse of that incredible swiftness which they imagine in their primum mobile, that it was requisite the motion of the heavens should have a kind of infinity in it, the better to manifest the infiniteness of the creator, And why may not we as well affirm this concerning the bigness of the heavens? Difficilius est accidens præter modulum subjecti intendere, quam subjectum sine accidente augere (saith Keplar.) His meaning is, that it is less absurd to imagine the eighth sphere of so vast a bigness, as long as it is without motion, or at least has but a very slow one; than to attribute unto it such an incredible celerity, as is altogether disproportionable to its bigness.

2. It is the acknowledgment of Clavius*, and might easily be demonstrated, that if the centre were fastened upon the pole of the world, the orb wherein he supposes the sun to move would not be able to reach so far in the eighth sphere (being considered according to Ptolemy's hypothesis) as to touch the pole star; which notwithstanding (saith he) is so near the pole itself, that we can scarce discern it to move: nay, that circle which the pole-star makes about the pole, is above four times bigger than the orb of the sun. So that according to the opinion of our adversaries, though our earth were at that distance from the centre, as they suppose the sun to be, yet would not this eccentricity make it nearer to any one part of the firmament, than the pole-star is to the pole; which according to his confession, is scarce sensible. And therefore according to their opinion, it would cause very little difference in the appearance of those stars, the biggest of which does not seem to be of above five seconds in its diameter.

3. It is considerable, that the spheres of Saturn, Jupiter, Mars, are, according to the general opinion, of very great extension; and yet each of them is appointed only to carry about its particular planet, which are but very little in comparison of the fixed stars. Now if for the situation of these fixed stars, there should be allotted a proportionable part of the world, it is certain that their orb must be far bigger than it is commonly supposed, and very near to this opinion of Copernicus,

4. We usually judge the bigness of the higher orbs by their different motions: as because Saturn finishes his course in thirty years, and Jupiter in twelve, therefore we attribute unto those orbs such a different proportion in their bigness. Now if by this rule we would find out the quantity of the eighth sphere, we shall discern it to be far nearer unto that bigness which Copernicus supposeth it to have, than that which Ptolemy, Tycho, and others ordinarily ascribe unto

*Comment. in Sphær. cap. 1.