Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/286

 I see that you understand the businesse very well. I believe that you do likewise comprehend, that, in regard the star B is lower than C, the angle which is made by the rayes of the sight, which departing from the two places A and E, meet in C, to wit, this angle ACE, is more narrow, or if we will say more acute than the angle constituted in B, by the rayes AB and EB.

This I likewise understand very well.

And also, the Earth beine very little and almost insensible, in respect of the Firmament (or Starry Sphere;) and consequently the space AE, paced on the Earth, being very small in comparison of the immense length of the lines EG and EF, passing from the Earth unto the Firmament, you thereby collect that the star C might rise and ascend so much and so much above the Earth, that the angle therein made by the rayes which depart from the said stationary points A and E, might become most acute, and as it were absolutely null and insensible.

And this also is most manifest to sense.

Now you know Simplicius that Astronomers and Mathematicians have found infallible rules by way of Geometry and Arithmetick, to be able by help of the quantity of these angles B and C, and of their differences, with the additional knowledg of the distance of the two places A and E, to find to a foot the remotenesse of sublime bodies; provided alwayes that the aforesaid distance, and angles be exactly taken.

So that if the Rules dependent on Geometry and Astronomy be true, all the fallacies and errours that might be met with in attempting to investigate those altitudes of new Stars or Comets, or other things must of necessity depend on the distance AE, and on the angles B and C, not well measured. And thus all those differences which are found in these twelve workings depend, not on the defects of the rules of the Calculations, but on the errours committed in finding out those angles, and those distances, by means of the Instrumental Observations.

True; and of this there is no doubt to be made. Now it is necessary that you observe intensely, how in removing the Star from B to C, whereupon the angle alwayes grows more acute, the ray EBG goeth farther and farther off from the ray ABD in the part beneath the angle, as you may see in the line ECF, whose inferiour part EC is more remote from the part AC, than is the part EB, but it can never happen, that by any whatsoever immense recession, the lines AD and EF should totally sever from each other, they being finally to go and conjoyn in the Star: and onely this may be said, that they would separate, and reduce themselves to parallels, if so be the recession should be infinite, which