Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/295

 Now to see my whole proceeding, we may begin from these calculations, which are four, omitted by the Author, perhaps because they make against him, in regard they place the star above the moon by many semidiameters of the Earth. The first of which is this, computed upon the observations of the Landgrave of Hassia, and Tycho; which are, even by the Authors concession, two of the most exact observers: and in this first, I will declare the order that I hold in the working; which shall serve for all the rest, in that they are all made by the same rule, not varying in any thing, save in the quantity of the given summes, that is, in the number of the degrees of the Poles altitude, and of the new Stars elevation above the Horizon, the distance of which from the centre of the Earth, in proportion to the semidiameter of the terrestrial Globe is sought, touching which it nothing imports in this case, to know how many miles that semidiameter conteineth; whereupon the resolving that, and the distance of places where the observations were made, as this Author doth, is but time and labour lost; nor do I know why he hath made the same, and especially why at the last he goeth about to reduce the miles found, into semidiameters of the Terrestrial Globe.

Perhaps he doth this to finde with such small measures, and with their fractions the distance of the Star terminated to three or four inches; for we that do not understand your rules of Arithmetick, are stupified in hearing your conclusions; as for instance, whilst we read; Therefore the new Star or Comet was distant from the Earths centre three hundred seventy and three thousand eight hundred and seven miles; and moreover, two hundred and eleven, four thousand ninety sevenths 373807, and upon these precise punctualities, wherein you take notice of such small matters, we do conceive it to be impossible, that you, who in our calculations keep an account of an inch, can at the close deceive us so much as an hundred miles.

This your reason and excuse would passe for currant, if in a distance of thousands of miles, a yard over or under were of any great moment, and if the suppositions that we take for true, were so certain, as that they could assure us of producing an indubitable truth in the conclusion; but here you see in the twelve workings of the Author, the distances of the Star, which from them one may conclude to have been different from each other, (and therefore wide of the truth) for many hundreds and thousands of miles: now whilst that I am more than certain, that that which I seek must needs differ from the truth by hundreds of miles, to what purppse is it to be so curious in our calculations, for fear of missing the quantity of an inch? But let us proceed, at last, to the working, which I resolve in this manner. Tycho, as may be