Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	carry_v	left_a	right_a	5,159	5	6.7392	4	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A67916	An introduction of the first grounds or rudiments of arithmetick plainly explaining the five common parts of that most useful and necessary art, in whole numbers & fractions, with their use in reduction, and the rule of three direct. Reverse. Double. By way of question and answer; for the ease of the teacher, and benefit of the learner. Composed not only for general good, but also for fitting youth for trade. / By W. Jackson student in arithmetick.	Jackson, William, 1636 or 7-1680.	1660 (1660)	Wing J94; ESTC R210093	23,587	109

thousands then five in the place of hundreds then in regard thee is no tens I supply that place with a 0 and lastly I place 6 in the unite place thus 4506 Q. How value you your places in order to the tenth place A. Thus Unites Tens Hundreds Thousands Tens of Thousands Hundreds of Thousands Millions Tens of Millions Hundreds of Millions Thousands of Millions Q. Can you repeat your places backwards A. Yea thus Thousands of Millions Hundreds of Millions Tens of Millions Millions Hundreds of Thousands Ten of Thousands Thousands Hundreds Tens Unites Addition Q. Now shew what Addition teacheth A. Addition teacheth of several numbers to make one total equal to them all Q. How is that done A. First I set my numbers down one right under another observing still to set the first place or figure toward the right hand of each number under the first place or figure of the uppermost number and so the second under the second and the third under the third c. Q. After you have set down your numbers each in his due place what do you then A. I must begin at the first place toward the right hand and count all the figures in that place together and if they bee less than ten set it down under the first place a line being first drawn under my sum to place my total below Q. What if it come to ten or above A. Then I must consider how many tens it contains and carry so many unites in my mind to the next place and set down the over-plus if there bee any but if it bee even tens then set down a 0 in that place Q. And what do you next A. I must remember to reckon the tens that I bear in mind for unites and add them to the figures in the next place and then do in all points as I did in the former place Q. Why do you count tens in one place but for unites in the next A. because the place answers to the value thereof being ten times the value of the former place Q. What is further to bee considered A. When I have gone thorow all the places if at the last I have any Tens to carry seeing there are no figures to add them withall I set a figure signifying the number of Tens in a place neerer the left hand Q. Give an example hereof A. Then thus Four men owe my Master mony A. oweth 4560 l. B. oweth 5607 l. C. oweth 6078 l. D oweth 385 l. I would know how much these four debts amount to in all Q. And how will you do that A. First I set the several sums right under each other thus 4560 5607 6078 0385 16630 Then I begin with those figures next the right hand and say 5 and 8 is 13 and 7 makes 20 now in regard it is just 2 times Ten I set a cipher underneath the line in that place and bear in minde 2 to reckon with the figures in the next place and say 2 that I bear in my mind and 8 is 10 and 7 is 17 and 6 makes 23 then I set down the odd 3 in the second place below the line and for the 2 Tens I carry 2 in minde to the next place then I say 2 that I carry and 3 is 5 and 6 is 11 and 5 is 16 the odd 6 I set below the line and carry one in lieu of the ten to the next place and say 1 I carry and 6 is 7 and 5 is 12 and 4 is 16 so I set the 6 below the line and in regard there is not another place to reckon the one I bear in minde withall I set that 1 a place neerer the left hand and so the total is 16630 l. the sum of those four debts Q. What if you have numbers of several kinds or denominations to add together A. I must set down each number under the denomination of the same kinde as pounds under pounds shillings under shillings and pence under pence c. and the like is to bee observed of weight measure or any other kinde Q. And how must they bee added together A. I must begin with the smallest denomination which is next the right hand and count all those figures together and consider how many of the next denomination is contained in them and carry so many unites to the next place and set down the over-plus if there bee any right under beneath the line and it there bee no over-plus I set a cipher in the place And the like I observe in every several denomination Q. Shew two or three examples of several denominations A. First then for pounds shillings and pence take this l. s. d. 365 6 8 456 7 6 567 8 4 1389 2 6 Then beginning with the smallest denomination toward the right hand which is pence I say 4 and 6 is 10 and 8 is 18 which is 1 shilling and 6 pence the 6 pence I set down in its place below the line under its own denomination and carry the one shilling in my minde to the next place which is the place of shillings and say 1 I carry and 8 is 9 and 7 is 16 and 6 is 22 that is one pound and two shillings the 2 odd shillings I set in its place under its own denomination below the line and carry one pound in minde to reckon with the pounds then I come to the first place of pounds and say 1 I carry and 7 is 8 and 6 is 14 and 5 is 19 so I set down 9 and carry 1 then I say one I carry and 6 is 7 and 5 is 12 and 6 makes 18 the 8 I set down and carry one and then I say one I carry and 5 is 6 and 4 is 10 and 3 is 13 the odd 3 I set right under and the one ten I set one place further towards the left hand so the total is 1389 l. 2 s. 6. d. Q. What is your next example A. Take this of haberdupoize weight wherein note that 16 ounces make a pound 28 pound make a quartern 4 quarterns make a hundred weight and 20 hundred make a tun weight Example tun C. q l. o â„¥ 123 9 3 16 10 234 8 2 12 8 345 7 1 08 6 703 5 3 09 8 Where as before I begin with the least denomination next the right hand and say 6 and 8 is 14 and 10 is 24 which is one pound and eight ounces the 8 ounces I set down below and I carry one in minde to the pounds then I say one I carry and 8 is 9 and 12 is 21 and 16 is 37 that is one quartern and 9 pound the 9 I set down and carry one and say one that I carry and one is two and two makes 4 and 3 is 7 that is one hundred and three quarterns the three quarterns I set down and carry one and say further one I carry and 7 is 8 and 8 is 16 and 9 makes 25 that is one tun and five hundred the five

AN Introduction of the First Grounds or Rudiments OF Arithmetick Plainly explaining the five Common parts of that most useful and Necessary Art In whole Numbers Fractions With their use in Reduction and The Rule of three Direct Reverse Double By way of Question and Answer for the ease of the Teacher and benefit of the Learner Composed not only for general good but also for fitting Youth for Trade By W. Iackson Student in Arithmetick LONDON Printed by R. I. for F Smith neer Temple-Bar 166● Courteous Reader I Have on purpose omitted Progression as also many other Rules following partly because that these being well learned not only by rote but also by reason the young learner for whose sake I wrote this will be inabled hereby in a good measure to understand what hee findes in other books concerning such And if this prove but as useful as I wish it may and hope it will by the Teachers care and Scholars diligence I may be incouraged to add somewhat to it hereafter that may bee of further use or else these weak indeavours may provoke some others of better parts to bring them to the publick Treasurie of Art In the mean time accept of this mite from him that is one that would count it an honour to bee but one of the meanest of those that might present any thing on the behalf of this most Noble and most Necessary Art of Arithmetick that might further the growth of such as are entring upon the practice of the same which I presume if this small Tract may bee as a small Table wherein to see the first Rudiments in briefly and plainly which being by the Masters discretion appointed the young Scholar to get by heart may prove an ease to both to the Master in that if hee please to spend some set time in examining his Scholars as they use to catechize little ones hee by that means may teach the Rules to twenty in teaching one and not only print the Rules in the memory of such as are past such Rules who perhaps may bee apt to forget but also teach the Rudiments to other even before they come to the practice of them whereby hee may save the pains of often telling them and may only fit them with examples suitable to the Rule sometimes descanting a little upon the Rules as they lye in order as he findes occasion and by this course being observed he will with the blessing of God finde by the childrens growth in knowledge that the pains bestowed will not be in vain but not to be tedious I leave each to use his own discretion how to use this or any other help only I have thoughts that a thing of this nature will bee profitable and have its use So wishing this most Noble Art and all those that love it to flourish in our Land I bid thee farewel W. J. AN Introduction of the First Grounds and Rudiments of Arithmetick NUMERATION Quest WHat is Arithmetick Answ. It is the Art of numbring Q. What is the subject of this Art A. The subject of it is Number Q. Whereof doth Number consist A. It consisteth of unites Q. What is an unite A. It is the original or beginning of number and is of it self indivisible so that it still remaineth one Q. Is not one a Number then A. No for Number is a collection of unites Q. How are Numbers said to bee divided into kinds A. They are divided into many sorts but vulgarly into whole numbers and broken numbers called fractions Q. Are fractions numbers A. Not properly for number consisteth of a multitude of unites but every fraction is lesser than its unite Q. How many several parts are accounted in common Arithmetick A. These five Numeration Addition Substraction Multiplication and Division Q. What then is extraction of roots A. Although it bee another part of Arithmetick yet it is not so common Q. What teacheth Numeration A. It teacheth how to set down any number in figures and also to express or read any such number so set down Q. How many figures are there A. Nine significant figures and a cipher which cipher signifieth nothing of it self only it serveth to supply a place and thereby increaseth the value of the other figures Q. Which be the significant figure A. 1 2 3 4 5 6 7 8 9. Q. What do these signifie A. They signifie only each their own simple value being alone Q. What if they be joyned with other figures or ciphers is their signification altered A. Yea their value is thereby much increased according to the place they stand in removed from the place of unites Q. Do Ciphers then only supply places that are void and so increase the value of the other figures A. No they do also in decimal fractions diminish the value of those figures that stand toward the right hand of them according to the place they stand in removed from the unite place Q. Which is the place of unites A. In whole numbers it is the first place towards the right hand and any figure standing in that place signifieth only its own simple value Q. Why make you a distinction here of whole numbers doth it differ infraction A. Yea for in decimal fractions the unite place standeth to the left hand of the fraction Q. Why say you its own simple value A. Because a figure by being put in the second third or fourth place c. may signifie ten times an hundred times or a thousand times its own value c. Q. What is the reason of that A. Because every place exceeds the place next before it ten times in value so that the figure that signifies but four in the first place signifies ten times 4 in the second and an hundred times four in the third place and a thousand times four in the fourth place c. and in that proportion increaseth infinitely according as its place is further removed from the unite place Q. Is the proportion of diminishing decimal fractions like this of augmenting whole numbers A. Yea for as these are augmented in a decupled proportion so those are diminished or made less in a decupled proportion by being removed from the unite place Q. What must you do when you have a number to set down where some have not a significant figure to stand in it A. I must supply that place with a cipher 0 for no place must bee void Q. How will you set down one thousand six hundred and sixty A. First I consider the fourth place is the place of thousands and there I set down 1 then 6 in the third place which betokeneth so many hundreds then 6 in the second place signifying six tens or sixty and because there is no figure to set in the place of unites I supply it with a 0 cipher to make the number consist of its due number of places thus 1660 Q. How set you down four thousand five hundred and six A. First I set 4 in the place of

the multiplier toward the right hand and multiply it by the first figure of the multiplicand and set the product right under it beneath the line if it exceed not nine Q. If it exceed nine what then A. Then I must keep in minde how many tens is in it and carry so many unites to the next place and set down the odd figure that is more than even tens underneath but if it bee even tens then set down a cipher underneath Q. And what is then to be done A. Then I multiply the said first figure of the multiplier by the second figure of the multiplicand and to the product add the unites reserved in my mind then do in all respects as I did before and so I continue my work till I have multiplied the first figure of the multiplier by all the figures of the multiplicand in order Q. And what do you next A. Then I multiply the second figure of the multiplier by all the figures of the multiplicand in like sort as I did the first only I must observe to set my first place in this second work one place nearer the left hand that it may fall right under the figure I multiply by Q. What is the reason of that A. Because every unite in the second place signifies 10 in the third place 100 c. Q. Is this order then to be kept in a sum of many figures or places A. Yea the same order is to bee observed in any sum be the places never so many I must still set my first figure right under the figure I multiply by and then the rest in order toward the left hand Q. Having so set down all your figures what remains further to bee done A. Only to add the several numbers together in order beginning still at the first place next the right hand Q. Give one Example A. Let this bee it then 2345 234 9380 7035 4690 548730 Where first I say 4 times 5 is 20 where I set a cipher below the line and carry 2 then I say 4 times 4 is 16 and 2 that I carried is 18 the 8 I set down below and carry 1 then 4 times 3 is 12 and 1 that I carried is 13 then I set down 3 and carry one 4 times 2 or 2 times 4 for it is all one makes 8 and one that I carried is 9 which I set down in its place and cancel the first figure of my multiplier with a dash through it to signifie that it hath done its office then I begin with the next figure saying 3 times 5 is 15 the five I set down right under the 3 I multiply by and carry one in minde then I say 3 times 4 is 12 and one that I carried is 13 the 3 I set down in the second place and carry one and say 3 times 3 is 9 and one I carried is 10 where I set down a 0 and carry one then I say 3 times 2 is 6 and one I carry is 7 which I set down and cancel my second figure of the multiplier and begin with the third saying 2 times 5 is 10 then I set down a cipher in that place right under my multiplier 2 and carry one in mind to the next place then I say 2 times 4 is 8 and one I carried is 9 which I set down in the next place in order then I say 2 times 3 is 6 which I set in its due place and lastly I say 2 times 2 is 4 which I write down also so have I multiplied all my figures of the multiplier by all the figures of the multiplicand there remains to add up all into one sum which to do I begin at the right hand and work as in Addition and so the product is 548730 as in the example Here is another Example for Imitation 963852 3741 963852 3855408 6746964 2891556 3605770332 Q. What proof is for Multiplication A. The truest proof is by Division but it is ordinarily proved thus they make a cross X And then cast away so many nines as can bee found in the multiplicand and set the remainder on the upper side of the cross and do the like with the multiplier set the remainder under the cross then multiply the 2 remaidners 1 by another and cast out the nines out of the product of them setting the rest at one side of the cross and last of all cast out the nines out of the product of the Multiplication and mark the rest if it be like that which is placed on the side of the cross it appears to bee right or else it is not well done A Table for Multiplication to bee got by heart 2 times 2 is 4 2 3 6 3 4 8 2 5 10 2 6 12 2 7 14 2 8 16 2 9 18 3 times 3 is 9 3 4 12 3 5 15 3 6 18 3 7 21 3 8 24 3 9 27 4 times 4 is 16 4 5 20 4 6 24 4 times 7 is 28 4 8 32 4 9 36 5 times 5 is 25 5 6 30 5 7 35 5 8 40 5 9 45 6 times 6 is 36 6 7 42 6 8 48 6 9 54 7 times 7 is 49 7 8 56 7 9 63 8 times 8 is 64 8 9 72 9 times 9 is 81 Division Q. Now shew mee what Division teacheth A. Division teacheth to finde how many times one number is contained in another number Q. How many numbers are to bee noted in any Division A. Three namely the dividend or number to bee divided secondly the divisor or number dividing thirdly the quotient which sheweth how often the divisor is contained in the dividend Q. In what manner is Division performed A. First I set down my dividend and under it I place my divisor in such sort that the figures next the left hand stand right under one another and so each following place in order except the divisor bee a greater number than so many figures of the dividend as stand over it for then the divisor must bee removed a place nearer the right hand Q. And what do you then A. Then I draw a crooked line to the right hand of my figures to place my quotient beyond and I consider how often I can take the divisor out of the number over it and set the number of times in the quotient and multiplying the said quotient figure by the divisor I substract the product from the figures above the divisor setting the remainder over head cancelling the other figures that were over the divisor and also the divisor Q. And how proceed your further A. Then I remove my divisor one place nearer the right hand and consider as before how often I may take it out of the figures over head and work in all points as before Q. If there bee many removings of the divisor is that order still to bee observed A. Yea where the divisor can bee substracted once or oftner out of the dividend Q. But what if you cannot take the divisor out of the