Let ♂ be _Mars_, D the point on the Earth’s superficies, where _Mars_ is vertical when he is in opposition to the Sun, which may be found exactly enough by calculation, at which time let an observer, at the point Z (whose situation from D must be known) take the altitude of _Mars_, whose complement will be the angle ♂ ZR; then in the triangle ♂ ZC will be given the angle Z ♂ C, the angle C (whose measure is the arch DZ) and consequently the angle Z ♂ C the Parallax, and also the side Z C the semidiameter of the Earth; by which we may find C ♂ the distance of _Mars_ from the Earth. The extreme nicety required in this observation, makes it very difficult to determine the exact distances of the Planets from the Sun; but the celebrated Dr. _Halley_ has, in the Philosophical Transactions, shewed us a more certain method for finding the distances of the Planets; which is by observing the Transit of _Venus_ over the Sun. [Sidenote: How the Magnitudes of the Planets are determined.] [Sidenote: _Fig. 8._] The eye judgeth of the magnitudes of far distant objects, according to the quantities of the angles under which they are seen (which are called their apparent magnitudes;) and these angles appear greater or less in a certain proportion to their distances. Wherefore the distances of the Planets from the Earth, and their apparent diameters being given, their true diameters (and from thence their magnitudes) may be found. How the distances of the Planets may be found has been already shewn; their apparent diameters are found by a telescope, having a machine fix’d to it for measuring of angles, called a Micrometer. Let BD, or the angle BAD be the apparent diameter of any Planet, and AB, or AD, (which by reason of the great distance of the Planets in respect of their magnitudes) may be considered as being the distance of the said Planet from the observer. Now in the triangle ABD, having the sides AB, AD, given, and the angle, A, we have also the other angles B and D, (because the Side AB, AD, are equal) whence the side BD the diameter of the Planet may be easily found by Trigonometry. [Sidenote: Why the Moon appears bigger than any of the Planets.] From hence it appears, that the same body at different distances, will seem to have very different magnitudes. Thus the diameter BD will appear from the point E, to be twice as large as from the point A. It also follows, that a small body, when at no great distance from us, may appear to be equal, or even to exceed another at a great distance, tho’ immensely bigger. Thus _b d_ appears under the same angle, and consequently of the same bigness from the point A, that the line B D doth, tho’ one vastly exceeds the other. And this is the reason, why the Moon, which is much less than any of the Planets, appears to us vastly bigger than either of them, and even to equal the Sun himself, which is many thousand times greater in magnitude.