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.

How to take the square roote of Astronomicall Fractions. Cap. 29.

THe greatest difficultie hereof consisteth in finding out the true denomination of the roote, for if the Fraction be seconds, then the roote therof are my∣nutes, and if the Fraction be fourths, then the roote are seconds, for the Fraction must alwaies haue such denomination as may be halfed, as se∣conds, fourths, and such like, the one halfe whereof giueth alwaies

name to the roote, for if the question bee of thirds, you must first reduce them to fourths before you can take the roote, and you must doe the like with any other Fraction, whose denomination is od and not euen. As for example, if you would take the roote of 43‴· here by multiplying these 43‴· by 60. you shall reduce them into 1580''''· the roote whereof is 50″· Moreouer the Fractions where. with you haue to deale, are either simple or compound, if they bée simple and lesse then minutes, and therewith haue euen denomi∣nations and not odde, then you néede to make no further reducti∣on, but to worke as if you had to deale with whole numbers. As in seeking the square roote of 1600″· you find it to be iust 40′· but if the number be compound, that is to say, consisting ot Integrums and Fractions, or of many Fractions hauing diuers denomina∣tions, then you must first reduce them all to the smallest Fraction that hath an euen denomination before that you can take the roote: As for example, you would know the roote of 4. degrées, 25′· here you must by the Sexagenarie Multiplycation and Addition of the next Fraction, reduce the degrées to minutes, and the minutes to seconds, as you were taught before in Diuision, and then to worke as you were wont to doe in taking the square roote of whole numbers, and in so doing, you shall finde the summe of seconds to be 15900″· the square roote whereof is 126′· which if you diuide by 60. it will make 2. degrées, 6′· Another example, as to take the roote of 13. degrées, 42′· and 45″· here by reduction as before, you shall bring the degrées and minutes to 49365″·. the square roote whereof is 222′· which being diuided by 60. maketh 3. degrées, 42′· And thus I end with the Astronomicall Fractions, which kinde of Fractions, though they be very learnedly and orderly taught by Reinoldus in the beginning of his Prutenicall tables, yet in mine opinion not in so plaine order, and so fit for euery mans vnderstanding, as I haue here set them downe according to the doctrine of Gemma Frisius, which being once learned, you shall the soner attaine to the other. And without the knowledge of these Fractions, you can neuer truely calculate any thing out of the Astronomicall tables, and therefore such Fractions are most ne∣cessarie to be learned.