Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...

To the Courteous READER.

Courteous Reader,

AS there is no part of Mathematicall learning more excellent, so is there none more difficult then this of Astronomy, it hath for some thou∣sands of yeares been much studied, and not without great expence of treasure, brought to that perfection, in which we now enjoy it; nor can we ex∣pect, that those mistakes, to which this noble Science is yet too often lyable, should ever be redressed, without the ex∣pence of more, and hard it is to perswade the men of this earthly-minded age, to look higher then the earth they tread upon, and wallow in; they will not look so high as Heaven themselves, nor give encouragement unto those that would; but that our Students should neglect the benefit of that knowledg they might enjoy; that they should be in love with those difficulties they might avoid, in a study that is too intricate and difficult at the best, can never be sufficiently admired.

It is therefore our chief and principal aime to shew how

much of trouble may be avoyded in computing the moti∣ons of the heavenly bodies; if only the form of our Tables were changed from Sexagenary into Decimall, the excellen∣cy of Decimal Arithmeticke will in part appeare, if wee but consider the manner of working, in our Sexagenary Canons of naturall Sines and Tangents, in which (to avoid the vast trouble, if not almost the impossibity of working with a Canon that should consist of vulgar Fractions) the Sine and Tangent of every minute is nothing else but the Decimall of a Unite; and this that famous Mathematician of our age Mr. Henry Brigges did well perceive, when (having perfe∣cted that noble invention of Logarithms, first found out by the Right Honourable, John, Lord Neiper, Baron of Merchi∣ston in Scotland) he tooke the paines to make a new Canon of Sines and Tangents, dividing the degrees into Decimals, as well as the parts of the Radius answering unto those de∣grees; and according to which Canon, Mr. Henry Gille∣brand did since prepare a Treatise of Astronomy for the Presse, but his death prevented the publication: To these I may adde Mr. William Oughtred, who is the present wonder of our age, for his extraordinary knowledge in this kind of learning, who in his Clavis Mathematica, doth not only wish that this Decimall form were observed in all Astronomical Ca∣nons, but hath also lately professed, that he ever found so much trouble in the Sexagenary way, that he took the pains to turn the Equations in the Rudolphin Tables into Decimals before he used them; besides the trouble of Reduction this advantage our Decimal Tables have above the Sexagenary, that in finding the part proportional, the half of your work is done before you begin, there being a necessity both of Multiplication and Division, in Sexagenary numbers, but here of Multiplication onely, or onely of Division.

And now that this wonderful ease in calculation, com∣mended

to us by these famous men, might not still lie buried in oblivion, & that our Artists might be no longer enforced to use those labyrinthical Tables in the Sexagenary form, we have adventured to publish these, which never should have seene the light, if there had been any hope of those which Mr. Gillebrand did long since compose, or that Mr. Moore could have found encouragement to have published his; or that any other could have been perswaded to this Decimal form.

The ease then that is in the form of our Tables, is in truth the reason for which we have undergone this labour, and yet the method of Calculation, which Dr. Ward professor of Astronomy in Oxford hath lately published (in his Book en∣tituled Inquisitio in Bullialdi Astronomiae Philolaicae fundamenta) and which we have used in the composure of our Tables, is so brief, so easie, and so exact, as that a better is not to be expected. I am not ignorant, that some (which have a de∣sire to make others and themselves work) are not therewith satisfied, they will rather take the pains of seven or eight o∣perations, and yet the aequation at last found, is not so legiti∣mate as that w^ch here we find at one; of which there needs no other proof then the Geometry of our Method, our very Enemies being Judges; yet all that we shall promise is the places of the Planets prope rerum, at a cheaper rate; if we do fail of their true Phenomenon, it shall be with less trouble and expence of time. Our Middle-motions, Aphelions, Excen∣tricities, and Dimensions of the several Orbs mentioned in the ensuing Treatise, we have borrowed from Bullialdus, the me∣thod by which they are computed is the same in all, and therefore as to the Excentricities & Aphelions, we thought it sufficient to instance in the Sun or Earth: and for the pro∣portions between the Earths Orb, and the Orbs of the other Planets with their angles of Inclination, we have given an

Example in Saturn only, and refer you to Bullialdus for the rest. And although this method of his be not Geometrically true, yet knowing no better; we have contented our selves with his, untill there be a better found; and to make his Middle-motions to us more useful, we have reduced their E∣poches to the Meridian of London, the most famous City of this our Island of Great Britain: For which reason, and for the easiness of the calculation which our own Country-man hath invented, and we here used, the Treatise it selfe doth carry the style of Astronomia Britannica.

And whether this method of finding the first inequality will agree with observation, cannot be known; until a Geo∣metrical way of finding the Excentricities & Aphelions of the Planets in an Ellipsis be also propounded to us; and if at last, when all things in this Elliptical Astronomy shall geometrical∣ly be demonstrated, the places of the Planets thus found shall not agree with observation, it will be hard to say in what particular the fault doth lie, and therefore we must not then impute it to the first inequality, much lesse now, when the Geometry of that is demonstrated, & other parts are defective, but a new Hypothesis must be thought of; and until this shall be effected, as there are no Tables extant, by which the places of the Planets can be computed with so much ease, so none can be expected, by which their places may be computed with more probability of truth, then by these which wee must now submit to thy censure, and do commend to thy perusal.

IOHN NEWTON.