Chamberlain's Arithmetick being a plain and easie explanation of the most useful and necessary art of arithmetick in whole numbers and fractions, that the meanest capacity may obtain the knowledge thereof in a very short time : whereunto are added many rules and tables of interest, rebate, purchases, gaging of cask, and extraction of the square and cube roots / composed by Robert Chamberlain, accomptant and practitioner in the mathematicks.

Example.

It is required to extract the square Root of 22429696, set a mark or prick with your Pen, under the first figure towards your right hand, and so under every second figure as you see, so will your given num∣ber

be divided into four parts or points, whereby you must note that the Root will admit of four figures, for the square Root of the given number doth always admit of as many figures as the given number doth admit Points. Then proceed to the Ex∣traction thus, beginning at the left hand the first Point being 22, by the former Table of Squares, I find 16 to be the great∣est Square number contained therein, whose Square Root is 4, therefore I set down 4 in the Quotient, and the Square thereof 16 I set underneath 22, and I subtract one from the other and there remains 6, which I set underneath; to this remainer 6 I draw down the next Point 42, which doth make the number 642; next I double the Quo∣tient 4 which is 8, which I set down one figure short of the right hand as you see; then do I seek how many times 8 will go in 64, which is 7 times, set down 7 under that vacant figure towards your right hand 2, and likewise set down 7 in the Quotient, and multiply 87 by 7, whose Product 609 set under the line, and subtract it from the number made of the last remainer, and the Point last brought down 642, and the re∣mainer of this subtraction will be 33, to

which remainer draw down the next point 96, and it makes the number 3396; next double the Quotient 47, it makes 94, which set under the number 3396, that it may stand one figure short towards the right hand, as you see in the following Example; then ask how many times 94 is contained in the number or figures standing over them 339? answer is three times, there∣fore I set down 3 to the right hand of 94, also I set down 3 in the Quotient, then do I multiply 943 by 3 the last figure in the Quotient, and the Product of the multi∣plication 2829 I set underneath the line, and subtract it from the number made of the last remainer, and the point last brought down which is 3396, and of this subtra∣ction there doth remain 567; lastly to this remainer I draw down the next point 96, and it makes the number 56796, now double the Quotient 473, which makes 946, and set it under the number 56796, that it stand one figure short towards your right hand as you see, and ask how many times 946 is contained in the figures stand∣ing over him 5679? answer is 6 times, set∣ting down 6 to the right hand of 946, and also in the Quotient, and multiply 9466 by

6 the last figure set in the Quotient, and the Product of such multiplication I set down under the line being 56796, which I subtract from the number composed of the last remainer, and last point brought down which is 56796, and there will remain 0, and having no more points to draw down, I therefore conclude I have finished my Ex∣traction, wherefore the square Root of the given number 22429696 is 4736, as was required, as by the following Example doth appear.

〈 math 〉〈 math 〉

The Proof of the Extraction of the Square Root, is done by multiplying the Root found in it self, and the Product is the number given whose Square Root is required.