M. Blundevile his exercises containing sixe treatises, the titles wherof are set down in the next printed page: which treatises are verie necessarie to be read and learned of all yoong gentlemen that haue not bene exercised in such disciplines, and yet are desirous to haue knowledge as well in cosmographie, astronomie, and geographie, as also in the arte of navigation ... To the furtherance of which arte of navigation, the said M. Blundevile speciallie wrote the said treatises and of meere good will doth dedicate the same to all the young gentlemen of this realme.

Of the Diuision of Fractions Astronomicall.

VVHat is to be obserued therein?

First you must consider whether your Diuisor be com∣pound, or simple, I cal that compound which containeth Fracti∣ons of diuers denominations, and that simple which consisteth of Integrums, or is one whole number of one selfe denomination, wherein there is no dificultie, for then you haue no more to do but to diuide euery particular number contained in the diuidend by y^e same Diuisor and to place the product of euery one vnder such de∣nomination, as the little table of denominations sheweth, & there∣fore it shall not bee amisse to set the foresaid little table ouer your diuidend euen as you did in Multiplycation: Also the Sexagenary progression is alwaies to be vsed, as well in Diuision as in Multi∣plycation. Moreouer if your Diuisor be not exactly contained in y^e diuidend, then hauing multiplyed the diuidend by 60. you must adde to the product therof the next Fraction following: As for ex∣ample, knowing by Alphonsus tables that the daily motion of the Moone is 13. degrées, 10′· 35″· 1‴· 15''''· you would know how much the goeth in the space of an hower, here because that one day con∣taineth

24. howers, the number must be 24. your Diuisor which is simple and not compound, first then set downe in the front of your worke the rowe of denominations onely, and not the natural numbers, because they are not to be vsed in this way of Diuision, that done, right vnder the rowe of denominations place your di∣uidend, and right vnder y^• your Diuisor, as you sée in this example.

Degree••	′	″	‴	''''	v	The denominations.
13	10	35	1	15		The diuidend.
24						The diuisor.
	32	56	27	33	7	The seuerall summ of euery quotient.

In which example because the Diuisor 24. is not contained in 13. therfore I mul∣tiply 13. by 60. which maketh 780. where∣vnto by adding the next Fraction on the right hand which is 10′· the whole summe is 790′· which being diuided by 24. the quoti∣ent is 32′· which because they are minutes, I place them vnder the denomination of minutes, and the remainder is 22′· which being multiplyed by 60. maketh 1320″· wherunto I adde the next figure which is 35. and so the whole summe is 1355″· which being diuided by 24. the quotient is 56″· which I place vnder the denomination of seconds, and the remainder of this Diuision is 11″· which being multiplyed by 60. maketh 660‴· whereto I adde the next Fraction which is 1‴· so that now the whole summe is 661‴· which being di∣uided by 24. the quotient is 27‴· which I set downe vnder the de∣nomination of thirds, and the remainder is 13‴· which being mul∣tiplyed by 60. maketh 780''''· whereunto I adde the next Fraction which is 15''''· which maketh in all 795''''· which being diuided by 24. the quotient is 33''''· which I place vnder the denominatiō of fourths. and the remainder is 3''''· which being multiplyed by 60. maketh 180^v· whereunto hauing no Fraction to adde, I diuide the same by 24. and so I find in the quotient 7^v· which I set vnder the denomi∣nation of fifts, so as I find the howerly motion of the Moone to bée 32′· 56″· 27‴· 33''''· 7^v· and somewhat more, for I leaue to deale any fur∣ther with the smaller Fractions that would stil grow by multiply∣ing the remainders by 60. thinking this sufficient to shew you in what order you haue to worke, to diuide your diuidend by a simple Diuisor, into as many small parts as you will: but if your Diui∣sor be compound, then the Diuision is to be done either by reducti∣on into the smallest Fractions, or without reductiō: which last way

is very hard and tedious, and therefore I will onely shew you how to make your diuision whereof the Diuisor is compound by reduc∣tion, and that by this one example here following. Suppose then that the Moone according to her owne course which is from West to East, is distant from some fixed Starre 36. degrées. 30′· 24″· 50‴· and 15''''· and that you would know in what time she will runne that distaunce, according to her daily moouing which as hath béene said before is 13. degrées, 10′· 35″· 1‴· and 15''''· here to make this di∣uision by reduction, you must doe thus. First reduce all the num∣bers of your diuidend into the smallest Fractions thereof by the Sexagenarie Multiplycation and Addition of the next Fraction vnto the product of that Multiplycation: that done, reduce all the numbers of your Diuisor by like Multiplycation and Addition, into the smallest Fractions, so as the diuidend & the Diuisor may be both of one selfe denomination, and diuide the one by the other, euen as they were Integrums, as in this example you must first multiply 36. degrées, by 60. and it will make 2160′· whereto by adding 30′· you make the whole summe of minutes to be 2190′· which being multiplyed againe by 60. doe make 131400″· whereto if you adde the 24″· the summe of secondes will bee 131424″· and so procéeding still with the Sexagenarie Multiplycation and Addi∣tion of the next Fraction as you did before, you shall find the diui∣dend to be 473129415''''· Then in like order reduce your Diuisor in∣to the smallest Fraction, and you shall find the totall summe ther∣of to be 170766075''''· this reduction being made, diuide the diui∣dend by the diuisor, so shal you find in the quotient 2. Integrums, that is to say 2. daies, and the remainder to be 132597365''''· which remainder if you multiply by 60. and diuide the product by the self same Diuisor, you shal haue in the quotient minutes, then mul∣tiply againe that remainder by 60. and diuide the product thereof by the same Diuisor, and you shall haue in the quotient seconds, and so by obseruing still that order you shall bring it into as smal Fractions as you will, thus shall you finde that the Moone accor∣ding to her daily motion, will runne the foresaide space of distance that was betwixt her and the fixed Starre in 2. daies, 46′· and 14″·