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 Subtraction. Cap. 3. (Book 3)

WHat doth Subtraction teach?

It teacheth to take a lesser number out of a greater and to sée what remay∣neth.

What is to be obserued in this kind?

First, you must set downe your grea∣ter number aboue, and then the lesser number right vnder the same. As for ex∣ample, I haue lent to one 564. l. and hée hath paide me thereof 57. l. Here to knowe what remaineth, I first set downe the number lent, and vnder that the number paid, and then drawe a line as you sée in this manner.

• Lent. 564. l.
• Paide. 57. l.

Here beginning on the right hand, I first say, take 7. out of 4. that cannot bée: wherfore I take one Article of the next figure or place of the lent number, which Article being added to 4. maketh 14. then I say take 7. out of 14. and there remaineth 7. which I set downe vnder the 4. then I adde that one Article which I borrowed, to the se∣cond figure of the paide number which is 5. saying that 5. and 1. in minde maketh 6. then take 6. out of 6. and there remaineth no∣thing, wherefore I set downe a Cypher, vnder the 5. of the paide number, then I procéede to the third figure of the lent number,

which is 5. and because I finde nothing written vnder it, nor haue nothing in minde to take out of it, I say, take nothing out of 5. and their remaineth still 5. so as the remainder is 507. l as you sée in this example following.

• Lent. 564. l.
• Paid. 57. l.
• Remaine. 507

How shall I knowe whether this bee right or not?

By adding the remainder and the num∣ber paide together, the Somme whereof (if you haue done well) wilbe all one with the number lent, as in the former example, I first adde 7. and 7. together and that maketh 14. wherefore accor∣ding to the precepts of Addition before taught, I set downe 4. kée∣ping the Article in minde, then I say, one in mind and 5. maketh 6. which I also set downe, then I say nothing and 5. is 5. which I set downe in the third place, which in all maketh 564. a number equall to the number lent, as you sée here following.

• Lent, 564. l.
• Paid. 57:
• Remaine. 507.
• Proofe. 564.

You may perceiue by this, that if any fi∣gure of the paid number be greater then the figure ouer him, out of the which it is to bée Subtracted, you must alwaies borrow one Article of his next fellow, to be added againe to him in his proper place. But you haue to note, that hauing to deale with numbers of diuerse Denominatiōs, thē in borrowing any number, you must alwaies haue respect to the Denomination or name of the thing, from whence you borrow, as in borrowing from shillings you bor∣row 12. and not 10. from pounds you borrow not one Article but 2. Articles which doe make 20. s̄ but when the whole number is altogether of one selfe Denomination, then you must alwaies bor∣row one Article which is 10. to make vp your nūber y^t wanteth. As you shall more plainely perceiue by this example containing num∣bers of diuerse Denominations, as of pounds, shillinges and pence, halfe pence, and farthings. Suppose therefore that you haue lent to one 467. l 13. s̄. 4. d. ob. q. and hee hath paide you againe thereof, 89. l. 16. s̄. 9. d. ob. q. Here hauing set downe the Somme lent in seuerall Collums, according to their diuerse names, and then the Somme paide, right vnder the same, drawe a line as you sée in this example following.

	l	s̄	d	ob	{que}
Lent.	467	13	4	1	1
Paide.	89	16	9	1	0
Remaine.	377	16	7	0	1

Here beginning with the first Collum on the right hand, I say take nothing out of one, and one stil remaineth, which I set down, then procéeding to the next, I say take one out of one and no∣thing remaineth, wherefore I set downe a Cypher, then procée∣ding to the next Collum, I say take 9. out of 4. that cannot bée, wherefore I borrow a shilling of the next Collum that is 12. d. which being added to 4. maketh 16. pence, then I say take 9. out of 16. and there remaineth 7. which I set downe, then procéeding to the next, I adde the one shilling which I borrowed, to the 16. which maketh 17. s̄. then I say take 17. s̄. out of 13. s̄. that cannot be. wherefore I borrow one pound which is 2. Articles of the next rancke, y^t is 20. s̄. which being added to the 13. s̄. maketh 33. s̄. then I say take 17. out of 33. s̄. and there remaineth 16. s̄. which I set downe, then I adde the one pound which I borrowed, to 9. and that maketh 10. then I say take 10. out of 7. that cannot be, wher∣fore I borrow one Article out of the next 6. which being added to the 7. maketh 17. then I say take 10. out of 17. and there remay∣neth 7. which I set downe, then the one, which I borrowed, I adde to the 8. of the next rancke, and that maketh 9. Againe I say take 9. out of 6. that cannot be: wherfore I borrow one Article of the next 4. which being added to 6. maketh 16. then I say take 9. out of 16 and there remaineth 7. which I set downe, then I take the one which I borrowed out of the 4. & there remaineth 3. so as the re∣mainder is as you sée in y^e former example. 377. l. 16. s̄. 7. d. 0. q.

How shall I trie whether this be true or not?

By adding the remainder and the Somme paid together: as in the former example, and of that Addition, will rise if you haue done truely a Somme like in euery condition to the Somme lent: In making which proofe or triall you cannot lightly erre, if you remember to reduce pence to shillings, and shillings to poundes, and therefore in the Collum of pence, no particular Somme can be aboue 11. d, nor in the Collum of shillings no particular somme can be aboue 19, s̄ for if it be 20, s̄, then it is a pound and must bée brought to the Collum of poundes,