Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	hour_n	minute_n	pole_n	5,045	5	12.8170	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A88112	Arithmetick: vulgar, decimal, instrumental, algebraical. In four parts: conteining I Vulgar arithmetick, both in whole numbers and fractions, in a most plain and easie method. II Decimal arithmetick, with the ground and reason thereof, illustrated by divers examples. III Instrumental arithmetick, exactly performing all questions of what nature soever in a decimal way, by scales, with much more ease and facility then can be effected, either by vulgar or decimal arithmetick, the work of reduction being wholly avoided. Nothing in this kind having been hitherto published by any. IV Algebraical arithmetick, conteining an abridgement of the precepts of that art, and the use thereof, illustrated by examples and questions of divers kinds. Whereunto is added the construction and use of several tables of interest and annuities, weights and measures, both of our own and other countries. / By William Leybourn.	Leybourn, William, 1626-1716.; Billy, Jacques de, 1602-1679.	1660 (1660)	Wing L1893; Thomason E1755_1; ESTC R209688	136,634	402

of Avoirdupois little Weight There is another kind of weight most commonly used in England called Avoirdupois little weight by which is weighed all sorts of wares or merchandise Garbable as Suger Pepper Cloves Mace c. This weight is commonly divided into these denominations Pounds Ounces and Drams of which 16 Drams make 1 Ounce thus charact cu. 16 Ounces make 1 Pound thus charact li. for a dram we write dr In the addition of Avoirdupois weight you must observe the very same method and order as in Money and Troy weight having due respect to the quantity of the denomination as in the addition of drams to make a prick at every 16 setting down the remainder and for every prick carrying a unite to the next place The preceding rules being so copious in this particular I shall forbear to make any verball illustration but only give you some examples ready wrought together with the most usual parts into which the Weights and Measures now used in England are divided into which to the ingenious will be of most validity Examples of Addition of Avoirdupois little weight li. ou dr 12 11. 09 76 05 12. 32 10. 00 91 07. 13. 32 13 07 246 00 09 li. ou dr 06 13. 07. 05 09. 12 06 03 09. 10 00 00 05 07 09 34 02 05 4 Addition of Avoirdupois great weight There is a weight commonly used in England by which is weighed all commodities that are sold by the hundred as Corents Wool Flesh Butter Cheese and the like the which hundred weight containeth 112 pounds and the hundred weight is divided into quarters pounds and ounces so that 16 Ounces makes 1 Pound thus chaeactred li. 28 Pounds makes 1 quarter of a C. thus chaeactred qr 4 quarters makes 1 Hundred weig thus chaeactred C. for an Ounce we write oz. Examples of Addition of Avoirdupois great Weight C. qr li. ou 37 03. 21 12. 09 01 06 03 33 02 20. 00 10 00 00 00 12 03. 07 03 103 02 27 02 C. qr li. ou 05 01. 00 07 03 02 18 06. 00 01 06 08 11 03. 04 00 06 01 10 05 17 01 11 10 I might further proceed to shew you Examples of addition of common English measures viz. of long measures Liquid measures and dry measures as also of Time Motion c. but the preceding Examples being of sufficient extent I shall forbear to trouble either my selfe or the Reader with that which I conceive superfluous Only before I leave Addition I will give you a brief view of the most usual measures in England which take as followeth And 1 Of Liquid Measures Liquid measures are those in which all sorts of Liquid substances are measred of which according to the Statute of 12 Hen. 7. chap. 5. a Pinte is the least from which the greater Liquid measures are deduced according as is expressed in the Table following 2 Pintes make 1 Quart 2 Quarts make 1 Pottle 2 Pottles make 1 Gallon 8 Gallons make 1 Firkin of Ale Sope or 9 Gallons make 1 Firkin of Beer Herings 10 ½ Gallons make 1 Firkin of Salmon or Eels 2 Firkins make 1 Kilderkin 2 Kilderkins make 1 Barrel 42 Gallons make 1 Tierce of Wine 63 Gallons make 1 Hogshed 2 Hogsheads make 1 Pipe or But 2 Pipes or Buts make 1 Tun of Wine 2 Of Dry Measures Dry Measures are these in which all kind of dry substances are measured as Corn Salt Cole Sand c. of which a pinte is the least 2 Pintes make 1 quart 2 quarts make 1 Pottle 2 Pottles make 1 Gallon 2 Gallons make 1 Peck 4 Pecks make 1 Bushel Land measure 5 Pecks make 1 Bushel Water measure 8 Bushels make 1 quarter 4 quarters make 1 Chaldron 5 quarters make 1 Wey 3 Of Long Measures Long Measure is that by which is measured Cloth Land Board Glasse Pavement Tapestry c● of which measures according to the Statute of 33 Ed. 1. and 25 El. a Barley corn is the least So that 3 Barley Corns make 1 Inch 12 Inches make 1 Foot 3 Foot make 1 Yard 3 Foot 9 inches make 1 Ell 6 Foot make 1 Fadome 5 ½ Yards or 16 ½ Foot make 1 Pole or Perch 40 Perches make 1 Furlong 8 Furlongs make 1 English mile 4 Of Time Time consisteth of Years Moneths Weeks Dayes Houres and Minutes So that 60 Minutes make 1 Hour 24 Hours make 1 Day natural 7 Dayes make 1 Week 4 Weeks make 1 Moneth of 28 dayes 13 Moneths one day 6 houres make 1 Year 5 Of Apothecaries Weights The weights used by Apothecaries are Grains Scruples Drams and Ounces of which 20 Grains make 1 Scruple thus charact ℥ 3 Scruples make 1 Dram thus charact ʒ 8 Drams make 1 Ounce thus charact ℈ 12 Ounces make 1 Pound thus charact li. By help of these Tables and the rules and cautions before expressed any man may make addition of any of the abovesaid measures one with another and therefore I shall forbear to illustrate them by Examples but leave them to every mans own practice and thus I conclude Addition The Proof of Addition Having placed your numbers in order and added them together and set the Total under the line cut off the upper number by drawing a line with your pen betwixt that and the others then adde all the numbers together except the uppermost and set the Total of them under the Total before found then adde this last Total and the first number which you cut off with your pen together and if the sum of those two numbers be equal with your Total sum first found then is your work right otherwise not Example In the first example of whole numbers the sums to be added were 7833 5609 376 and 8547 these numbers placed in due order and added together the total or grosse sum of them is 22364 now to prove whether this Total be true or not I cut off the uppermost number to wit 7832 with a dash of the pen and I adde the other three numbers together namely 5609 376 and 8547 and the Total of them is 14732 which number being added to 7832 the number cut off the sum of them is 22364 exactly agreeing with the Total first found cleerly evidenceth that the addition was truly performed but if they had disagreed then the work had been erroneous The like course must be taken for the proof of those sums which have different denominations as in Money and Weight as by the examples following will appear Other Examples proved 1 Example of Money li. s. d. q. 37 16 9 3 21 9 8. 1 13 12 9 2 1 Total 72 19 3 2 2 Total 35 2 5 3 Proof 72 19 3 2 li. ou pw gr 32 9 12 16 17 11 6 9 34 8 15 10 8 10 4 7 94 3 18 18 61 6 6 2 94 3 18 18 There are are other wayes to prove Addition by casting away of all the nines in numbers of one denomination and of all the twelves twenties and nines in

Examples for Practice Compendiums in Multiplication 1 If the Multiplier consist of cyphers in the last place or places you may omit the multiplcation of them and place the former figures of the Multiplier under the Multiplicand thus if it were required to multiply 3257 by 2600. place the numbers as you see in the margent then multiplying 3257 by 26 the Product will be 84682 to which if you add two cyphers because there were two cyphers in the Multiplier it will be 8468200 which is the true product of the multiplication 2 If it be required to multiply any number by 10 100 1000 10000 c You have no more to do but to add so many cyphers to the multiplicand as there are cyphers in the multiplier thus if you were to multiply 365 by 10 the product will be 3650 or by 100 it would be 36500 or by 1000 it would be 365000 or by 10000 it would be 3650000 c. 3 If any number given were to be multiplied by 5 you may abreviate your worke thus adde a cypher to the Multiplicand take halfe that number and it shall be the product required thus if it were required to multiply 8627 by 5 adde a cypher to the multiplicand then it is 86270 the halfe whereof is 43135 which is the product required The Proof of Multiplication The most certain proof of Multiplication is by Division but because Division is not yet known I will here shew a neer way by which Multiplication may be proved Which is thus THE RVLE First take a Crosse as in the Margine then any sums being multiplied you may prove the truth of your work in this manner 1 Cast away all the nines which you can find in the multiplicand what remaineth set on the right side of the Crosse 2 Cast away also the nines in the Multiplyer and what remains set on the left side of the Crosse 3 Multiply the figure on the right side of the Crosse by that on the left side of the Crosse and out of that product cast away the nines setting the figure remaining over the Crosse then 4 Cast away all the nines in the product and if the figure remaining be the same with that which standeth over the Crosse then is your multiplication truly performed otherwise not 1 Cast away all the nines in the Multiplicand saying 4 and 3 is 7 and 2 is 9 which being rejected there remains 4 which I set on the right side of the crosse then 2 Cast away all the nines in the Multiplier saying 2 and 3 is 5 which being lesse then 9 I set on the left side of the crosse then 3 Multiply 4 by 5 saying 4 times 5 is 20 from which cast all the nines and there remain 2 place 2 over the crosse and 4 Cast away all the nines in the Product saying 2 and 5 is 7 and 4 is 11 cast away 9 and there remains 2 which exactly agrees with the figure over the crosse and demonstrates that the multiplication is truly performed To multiply by any of the nine Digits without charging the memory To multiply any number by 2 Either double the number in your mind or adde it by setting it down twice so 57325 produceth 115750. To multiply any number by 3 To the number given adde the double thereof the sum is the product so 57325 produceth 171975. To multiply any number by 4 Double the duplication in your mind so 57325 produceth 229290. To multiply any number by 5 Conceive a cypher added to the given number and in your mind half thereof is the product thus a cypher added to 57325 maketh it 573250 the halfe whereof is 286625. To multiply any number by 6 Take half adding a cypher and adde to the half the figure standing next before thus 573250 produceth 343950. To multiply any number by 7 Take half and adde it to the double of the former figure supposing a cypher added as before so 57325 thus ordered produceth 401275. To multiply any number by 8 Double each former figure and subtract it from the following so 57325 produceth 458600. To multiply any number by 9 Suppose the number multiplyed by 1 then subtract each former figure from the following beginning with that next before the cypher the remainer is the product so 57325 produceth 515925. Questions performed by Multiplication only Question 1. If a piece of land be 236 perches long and 182 perches broad how many square perches are contained therein multiply 236 the length by 182 the breadth the product is 42952 and so many square perches are contained in such a square piece of land Question 2. In a year there are 365 dayes natural and in every day 24 houres how many houres be there in a year Multiply 365 the number of dayes by 24 the number of houres the product is 8760 and so many houres be there in a year Question 3. From London to Coventry it is accounted 76 miles how many yards therefore is it from London to Coventry Multiply 1760 which are the number of yards contained in one mile by 79 the product is 133760 and so many yards are between London and Coventry Division DIvision is the just contrary to Multiplication for that turnes small denominations to greater as Multiplication turns greater to smaller Or in whole Numbers of which only we yet speak Division is the asking how many times one Sum is contained in another and the number which answereth to that question is called the Quotient And the number containing which is to be divided is called the Dividend And the number contained or by which the Dividend is to be divided is called the Divisor And as often as the Dividend contains the Divisor so often doth the quotient containe Unity The wayes of performing Division are divers I will begin with that which is most used and taught which is as followeth THE RVLE Place the Divisor under the Dividend so that the figures next to the left hand stand directly one under the other if the rest of the Divisor be not greater or if all the Divisor be greater then that above it then the said Divisor must be devolved one place further toward the right hand having so placed them try how many times the lower figures are contained in the upper figures and write that figure which answereth that question within a crooked line in the margine of the work which is called the Quotient and by it multiply the first figure of the Divisor and take the product out of the figures directly over it beginning the Subtraction toward the left hand then cancel that figure of the Divisor and also that of the Dividend which hath been already used with a light dash of a pen and write the remaine when the product of the first figure multiplied by the quotient is subtracted as before just over the figure used and cancelled the● proceed to doe the like with the second third and fourth figure of the Divisor if there be so many till having cancelled it

2 is 4 place 4 under 5 so is the product of this multiplication 4690 which you must subtract from 5975 saying 0 from 5 and there remains 5 place 5 over 5 and cancel 0 and 5 then 9 out of 17 there remains 8 place 8 over 7 and cancel 9 and 7 then 1 carryed and 6 is 7 from 9 there remains 2 place 2 over 9 and cancel 6 and 9 lastly 4 from 5 rests 1 place 1 over 5 and cancel 4 and 5 so have you finished your second figure and your work will stand thus and your remainder will be 128. Thirdly make a prick under the next figure of your dividend namely under 8 and aske how many times 2345 can I have in 12858 or how many times 2 can I have in 12 say 5 times place 5 in the quotient by which multiply the divisor saying 5 times 5 is 25 place 5 under 8 and carry 2 then 5 times 4 is 20 and 2 is 22 place 2 under 0 and carry 2 then 5 times 3 is 15 and 2 is 17 place 7 under 9 and carry 1 then 5 times 2 is 10 and 1 is 11 place 11 under 4 and 6 so is the product of this multiplication 11725 to be subtracted from 12858 saying 5 from 8 rests 3 place 3 over 8 and cancel 5 and 8 then 2 from 5 rests 3 place 3 over 5 and cancel 2 and 5 then 7 from 8 rests 1 place 1 over 8 and cancel 7 and 8 then 1 from 2 rests 1 place 1 over 2 and cancel 1 and 2 lastly 1 from 1 rests nothing so is your work ended which you shall find to stand as in the margent the remainder being 1133. The Proof of this Division This kind of division is also proved by Addition for if you draw a line under the work and adde all the figures between the two lines together in order as they there stand taking in the remainder if any be the Total of this addition will be equal to the Dividend if the work be true Other Examples for Practice proved Questions performed by Division only Question 1. If a square piece of Land contained 42952 square perches and one of the sides thereof be 236 perches long how long must the other side be Divide 42952 by 236 the quotient will be 182 and so many perches long must the other side be Question 2. In a yeaar there are 8760 houres and in every natural day there are 24 houres I demand how many dayes be there in a year Divide 8760 by 24 the Quotient will be 365 and so many dayes be there in a year Question 3. The distance from London to Coventry is 133760 yards and in one mile there is contained 1760 yards now I would know how many miles it is from London to Coventry Divide 133760 by 1760 the quotient will be 76 and so many miles is it from London to Coventry These Questions performed by Division only are the converse of those that were performed by Multiplication which I the rather make choice of that the reader might see how Multiplication and Division prove each other There are one or two more kinds of Division something like these last but I shall forbear exemplifying them for much variety helps to make a Book rather great then fit ¶ Here is to be noted that in the following Rules where there is continual use of Division I sometimes use one kind of Division and sometimes another for variety sake but the practicioner may use which he is best skill'd in for they all produce the same effect Reduction IS twofold first that which turns greater denominations into smaller as pounds into shillings or pence this is done by Multiplication as followeth Example 1. Let it be asked how many pence are contained in 729 li. 11 s. 7 d First a shilling is contained in a pound 20 times therefore multiply 729 by 20 or which is the same but shorter by 2 and put o to the product as in the margine this shews that in 729 l. there are 14580 shillings To which adde 11 s. it makes 14591 shillings Again because one peny is conteined in one shilling 12 times multiply 14591 by 12 it produceth 175092 to which adde the 7 pence so the summe will be 175099 and so many pence are contained in 729 li. 11 s. 7 d. Example 2. Let it be asked how many pintes are contained in 4 Tun 3 Hogsheads and 27 Gallons First 1 Tun is equal to 4 Hogsheads therefore 4 Tun is equal to 16 Hogsheads to which adde the 3 Hogsheads so there is 19 intire Hogsheads Againe because one Hogshead containes 63 Gallons multiply 19 by 63 it produceth 1197 Gallons to which add 27 it gives 1224 Gallōs Lastly because every Gallon contains 8 pintes multiply 1224 by 8 it produceth 9792 and so many pintes are contained in 4 Tuns 3 Hogsheads and 27 Callons After the same sort might drie Measures be reduced as quarters to bushels pecks or gallons and likewise all weights and outlandish Coins of which the proportion of the greater to the lesser is before known or given Secondly it is often requisite to turn smaller denominations to greater this is done by Division as followeth Example 1. Let it be asked how many pounds are contained in 80976 shillings Divide 80976 by 20 the quotient is 4048 li. and 16 s. remaining which is the true answer Example 2. Let it be asked how many pounds are in 109754 d Because a pound contains a shilling 20 times-and a shilling containes a peny 12 times there fore if 109754 be divided first by 12 the quotient 9146 shillings and 2 pence over then if 9146 be divided by 20 the quotient is 457 pounds and six shillings remaining so that 109754 pence is equal to 457 li. 6 s. 2 d. Or if 109754 had been at first divided by 12 times 20 that is by 240 which is the number of pence contained in a pound the quotient had been 457 pounds and 74 pence remaining which is all one with the former for 74 pence is equal to 6 shillings 2 pence More instances shall not need herein because the thing of it self is very clear Progression IS also of two sorts the first is of certain numbers in Arithmetical Proportion from 1 that is such as differ equally as 1 2 3 4 5 6 where the common difference is 1 as is easily seen or 1 3 5 7 9 11 where the common difference is 2 or any other as 1 8 15 22 29 36 where the common difference is 7 this is called Arithmetical Progression 2 Secondly of certaine numbers in Geometrical proportion from 1 that is such as increase by a common Multiplication as 1 2 4 8 16 32 where the common multiplier is 2 that is the first by 2 produceth the second and the second multiplied by 2 produceth the third and so on Or as 1 3 9 27 81 243 where the common Multiplier is 3 this is called Geometrical Progression Both the common difference in the