The English academy, or, A brief introduction to the seven liberal arts grammar, arithmetick, geometrie, musick, astronomie, rhetorick & logic : to which is added the necessary arts and mysteries of navigation, dyaling, surveying, mensuration, gauging & fortification, practically laid down in all their material points and particulars, highly approved to be known by the ingenious, and as such are desirous to profit, or render themselves accomplished : chiefly intended for the instruction of young scholars, who are acquainted with no other than their native language, but may also be very useful to other persons that have made some progress in the studies of the said arts / by John Newton.

As for Example.

Let the Year begin in the Vernal Aequi∣nox, or Spring, in the Emperours time, that fell out to be the 24th of March, but now this year it fell out the 10th of March, 13 days backward and somewhat more; and so if it be let alone, will go back to the first of March, and first of February, till Easter come to be on Christmas day, and so infi∣nitely.

To reform this difference in the accompt, some of the latter Roman Bishops earnestly endeavoured, and the thing was brought to that perfection it now standeth, (so much as it is,) by Gregory the Thirteenth, in the year 1582. his Mathematicians, (whereof Lylius was the chief) advised him thus: That considering there had been in agitation in the Council of Nice, somewhat concerned in this matter upon the motion of the Que∣stion about the Celebration of Easter; and that the Fathers of that Assembly, after due deliberation with the Astronomers of that time, had fixed the Vernal Aequinox; at the 21th of March, and considering also, that since that time a difference of 10 whole days had been past over in the Calender, that is, that the Vernal Equinox or Spring, which began upon the 21th of March, had prevented so much as to begin in Gregories

days, at the 10th of the same, 10 days dif∣ference, or thereabout; they advised, that 10 days should be cut off from the Calender, which was done, and the 10 days taken out of October, in the Year 1582, as being the Month of that Year in which the Pope was born, so that when they came to the 5th of the Month, they reckoned the 15th, and so the Aequinox was come up to its place again, and happened upon the 21th of March, as at the Council of Nice. But that Lylius should bring back the beginning of the year to the time of the Nicene Council, and no farther is to be mar∣velled at; he should have brought it back to the Emperours own time, where the mi∣stake was first entred; and instead of 10, cut off 13 days; however this is the reason why these two Calenders differ the space of 10 days one from another.

And thus I have given you an accompt of the year as it now stands with us in England, and with the rest of the Christian World, in respect of the Sun; some other particulars there are with us and them, that do depend upon the motion of the moon, for the better understanding of them, I will give you a brief accompt of her Revolution.

The Solar year consisting, as hath been said, of 11 days more than the Lunar year; those 11 days called the Epact, are there∣fore added to the Lunar Year, to made it e∣qual

with the Solar, by the addition of which access, in every three years there is gotten a number more than 30, but because the Moon between change and change doth never pass 30 days, the Epact cannot exceed that num∣ber, and the time in which the Moon is sup∣posed to make her several Motions and so return to the place where she first began, is a circle or Revolution of 19 years, first found out by Meton, and Athenian, who lived about 439 years before Christ, this Cycle is therefore called Cyclus Decenno ••ennalis, and from the Autor A••nus Metonicus from whose Atheni∣ans, the Aegyptians may seem to have receiv'd it, as the Romans from them, in letters of Gold, from whence (if not from the more precious use of it) it attained to be called, as yet still it is, the Numerus Aureus, or Golden Number: It is made Christian, by the Fathers of the Ni∣cene Council, as being altogether necessary to the finding out of the Neomenea Paschalis, up∣on which the Feast of Easter and all the rest of the moveable Feasts depend: It self is found by adding a Unite to the year of our Lord, and dividing the whole by 19, the Remainder shall be the Cycle of the Moon, or if nothing remain, the Cycle is out, that is, 19.

And the Epact is found by Multiplying the golden Number by 11, and dividing the Pro∣duct by 30, what remains is the Epact; but to save this trouble of Calculation, you have it set down to your hand in the table before the Ca∣lender

the use whereof as of the Golden Number is to find the Change of the Moon, for the Ancient Philosophers supposing the Moon to make a perfect Revolution in 19 years, did Calculate the several Changings of the Moon that happened in each Month for that time, and placed the golden number for each year, right against the day of the Month on which the Moon changed, that so having found the golden number, they might thereby presently know on what day of the month the Moon did change, in any Month of the year for ever, as also the time, when the Feast of Easter was to be observed, according to the Canon made at a General Council held at Nice, in the year of our Lord, 322, in which it is commanded that Easter should be Celebra∣ted upon the next Sunday following the first Full Moon after the Vernal Aequinox, which then was upon the 21th day of March, and accor∣ding to this rule is this Feast observed with us at this day, and not according to the true Mo∣tion of the Moon, or precise time of the Ver∣nal Aequinox, which now is about the 10th of March; This use of the Golden Number is well expressed in these Distichs.

In March after the first C, Look the Prime where e're it be; The third Sunday after Easter day shall be, And if the Prime on the Sunday be, Then reckon that for one of the three.

To find the New Moons by the Epact, do thus, To the Epact for the year given add the number of the months from March including both Months, and the days of that Month past, the Sum of these three Numbers shall give you the age of the Moon, if they exceed not 30, if more than 30, cast away 30, and the Remainder shall be the Age as before.