Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/372

 ficies of an oblique Cylinder, which hath for one of its bases the said annual circle, and for the other a like circle imaginarily described by its extremity, or, (if you will) Pole, amongst the fixed stars. And this same cylinder is oblique to the Plane of the Ecliptick, according to the inclination of the Axis that describeth it, which we have said to be 23 degrees and an half, the which continuing perpetually the same (save onely, that in many thousands of years it maketh some very small mutation, which nothing importeth in our present businesse) causeth that the Terrestrial Globe doth never more incline or elevate, but still conserveth the same state without mutation. From whence ensueth, that as to what pertaineth to the mutations to be observed in the fixed stars dependant on the sole annual motion, the same shall happen to any point whatsoever of the Earths surface, as befalleth unto the centre of the Earth it self; and therefore in the present explanations we will make use of the centre, as if it were any whatsoever point of the superficies. And for a more facile understanding of the whole, let us design the same in lineal figures: And first of all let us describe in the Plane of the Ecliptick the circle ANBO [in Fig. 7.] and let us understand the points A and B, to be the extreams towards the North and South; that is, the beginning of [or entrance into] Cancer or Capricorn, and let us prolong the Diameter AB, indeterminately by D and C towards the Starry Sphere. I say now in the first place, that none of the fixed stars placed in the Ecliptick, shall ever vary elevation, by reason of any whatsoever mutation made by the Earth along the said Plane of the Ecliptick, but shall alwayes appear in the same superficies, although the Earth shall approach and recede as great a space as is that of the diameter of the Grand Orb, as may plainly be seen in the said figure. For whether the Earth be in the point A or in B, the star C alwayes appeareth in the same line ABC; although the distance BC, be lesse than AC, by the whole diameter AB. The most therefore that can be discovered in the star C, and in any other placed in the Ecliptick, is the augmented or diminished apparent magnitude, by reason of the approximation or recession of the Earth.

Stay a while I pray you, for I meet with a certain scruple, which much troubleth me, and it is this: That the star C may be seen by the same line ABC, as wel when the Earth is in A, as when it is in B, I understand very well, as also furthermore I apprehend that the same would happen in all the points of the line AB, so long as the Earth should passe from A to B by the said line; but it passing thither, as is to be supposed, by the arch ANB, it is manifest that when it shall be in the