gall pts grains of wh 1 2 2 63 8 7680 1 2 4 252 2016 15482880  1 2 126 1008 7741440   1 63 504 3870720    1 8 61440     1 7680 Thus you see that according to the standard of England a pint doth contain 7680 grains of Natural wheat but whosoever shall try the wheat growing in Norfolk shall find a Concave inch that is a hollow or hole made just the bigness of an inch to contain 280 kernels of wheat and if you admit of 28 ⅞ solid Inches in a pint which according to the Judgment of Artists is the content of a pint wine-measure the least of all measures then a pint of such measure will contain 8085 grains of wheat which is very different from the standard but these things Quere 7. The least Denominative part of dry measure is also a pint and this is likewise taken from Troy weight The Table of whose division followeth The Table of Dry Measure 1 pint make 1 pint 2 pints 1 quart 2 quarts 1 pottle 2 pottles 1 gallon 2 gallons 1 peck 4 pecks 1 bushel 4 bushels 1 Comb 2 Combs 1 quarter 4 quarters 1 Chalder 5 quarters 1 Wey 2 Wey's 1 Last And therefore last wey qts com bush peck gall pints 1 2 5 2 4 4 2 8 1 2 10 20 80 320 640 5120  1 5 10 40 160 320 2560   1 2 8 32 64 512    1 4 16 32 256     1 4 8 64      1 2 16       1 8 8. The least Denominative part of Long Measure is a Barley-corn well dryed and taken out of the middle of the ear whose Table of parts followeth The Table of Long Measure 3 barley cornes make an Inch 12 Inches 1 foot 3 feet 1 yard 3 feet 9 inches or a yard and quart 1 Ell English 6 feet 1 fadom 5 yards and an half 1 pole or perch 40 poles or perches 1 furlong 8 furlongs 1 English mile And Therefore mile furl poles yards feet Inches barl corns 1 8 40 5 ½ 3 12 3 1 8 320 1760 5280 63360 190080  1 40 220 660 7920 23760   1 5 ½ 16 ½ 198 594    1 3 36 108     1 12 36      1 3 And note that the yard as also the ell is usually divided into 4 quarters and each quarter into 4 Nailes Note also that a Geometrical pace is 5 feet and there are 1056 such paces in an English mile 9. The parts of the Superficial measures of land are such as are mentioned in the following Tables viz. The Table of Land Measure 40 Square Poles or Perches make 1 Rood or quarter of an Acre 4 Roods 1 Acre By the foregoing Table of long Measure you are Informed what a pole or which is all one perch is and by this that 40 square perches are 1 Rood Now a square perch is a Superficies very aptly resembled by a square Trencher every side thereof being a Perch or 5 Yards and a half in length 40 of them is a Rood and 4 Roods an Acre So that a Superficies that is 40 perches long and 4 broad is an Acre of land the Acre containing in all 160 square Perches 10. The least Denominative part of Time is a Minute the greatest Integer being a Year from whence is produced this following Table The Table of Time 1 Minute make 1 Minute 60 Minutes 1 Hour 24 Houres 1 Day natural 7 Dayes 1 Week 4 Weeks 1 Moneth 13 moneths 1 day 6 hours 1 Year But the year is usually divided into 12 unequal Calendar Moneths whose names and the number of Days that they Contain follow viz.  days Ianuary 31 February 28 March 31 April 30 May 31 Iune 30 Iuly 31 August 31 September 30 October 31 November 30 December 31 So that the year containeth 365 days and 6 hours but the 6 hours is not reckoned but onely every 4 year and then there is a day added to the latter end of February and then it containeth 29 days and that year is called Leap-year and containeth 366 days And here Note that as the Hour is divided into 60 Minutes so each Minute is subdivided into 60 Seconds and each Second into 60 Thirds and each Third into 60 Fourths c. The Tropical year by the exactest observations of the most accurate Astronomers is found to be 365 Days 5 Hours 49 Minutes 4. Seconds and 21 Thirds CHAP. III. Of the Species or Kinds of Arithmetick 1. ARithmetick is either Natural Artificial Analiticall Algebraical Lineal or Instrumental 2. Natural Arithmetick is that which is performed by the Numbers themselves and this is either Positive or Negative Positive which is wrought by certain infallible numbers propounded and this is either single or Comparative Single which considereth the nature of numbers simply by themselves and Comparative which is wrought by numbers as they have Relation one to another And the Negative part relates to the Rule of False 3. Artificial by some called Logarithmetical Arithmetick is that which is performed by Artificial or borrowed numbers invented for that purpose and are called Logarithmes 4. Analiticall Arithmetick is that which shews from a thing unknown to find truly that which is sought always keeping the Species without Change 5. Algebraical Arithmetick is an obscure and hidden art of Accompting by numbers in resolving of hard Questions 6. Lineal Arithmetick is that which is performed by lines fitted to proportions as also Geometrical projections 7. Instrumental Arithmetick is that which is Performed by Instruments fitted with Circular and Right lines of proportions by the motion of an Index or otherwise 8. The parts of single Arithmetick are Numeration and the Extraction of Roots 9. Numeration is that which by certain known numbers propounded we discover another Number unknown 10. Numeration hath four Species viz. Addition Subtraction Multiplication and Division CHAP. IV. Of Addition of whole Numbers 1. ADdition is the Reduction of two or more numbers of like kind together into one Sum or Total Or it is that by which divers numbers are added together to the end that the Sum or Total value of them all may be discovered The first number in every addition is called the Addable number the other the number or numbers added and the number invented by the Addition is called the Aggregate or Sum containing the value of the Addition The Collation of the numbers is the right placing of the numbers given respectively to each denomination And the Operation is the Artificial adding of the numbers given together in order to the finding out of the Aggregate or Sum. 2. In Addition place the numbers given respectively the one above the other in such sort that the like degree place or denomination may stand in the same Series viz. Units under Units Tens under Tens Hundreds under Hundreds c. Pounds under
of three also by 〈◊〉 things of 〈…〉 are reduced to another 〈…〉 any Number of Integers by the price of the Integer the Product will discover the price of the Quantity or Number of Intâ—gers given In a Râ—ctangular Solid if you multiply the bredâ—h of the base by the depth and that Product by the length this last Product will discover the Solidity or content of the same Solid Some Questions proper to this Rule may be these following Quest. 1. What is the content of a square piece of ground whose length is 28 perches and breadth 13 perches Answer 364 square perches for multiplying 28 the length by 13 the breadth the Product is so much Quest. 2. There is a square battail whose Flank is 47 men and the files 19 deep what Number of men doth that battail contain Facit 893 for multiplying 47 by 19 the Product is 893. Quest. 3. If any one thing cost 4 shillings what shall 9 such things cost Answer 36 shillings for multiplying 4 by 9 the Product is 36. Quest. 4. If a piece of Money or Merchandize be worth or cost 7 shillings what shall 19 such pieces of Money or Merchandize cost Facit 133 shillings which is equal to 6 l. 13 s. Quest. 5. If a Souldier or Servant get or spend 14 s. per moneth what is the Wages or Charges of 49 Souldiers or Servants for the same time multiply 49 by 14 the Product is 686 s. for the Answer Quest. 6. If in a day there are 24 hours how many hours are there in a year accounting 365 dayes to constitute the year Facit 8760 hours to which if you add the 6 hours over and above 365 dayes as there is in a year then it will be 8766 hours now if you multiply this 8766 by 60 the Number of Minutes in an hour it will produce 525960 for the Number of Minuts in a Year CHAP. VII Of Division of whole Numbers 1. DIVISION is the Separation or Parting of any Number or Quantity given into any parts assigned Or to find how often one Number is Contained in another Or from any two Numbers given to find a third that shall consist of so many Units as the one of those two given Numbers is Comprehended or contained in the other 2. Division hath three Parts or Numbers Remarkable viz. First the Dividend Secondly the Divisor and Thirdly the Quotient The Dividend is the Number given to be Parted or Divided The Divisor is the Number given by which the Dividend is divided Or it is the Number which sheweth how many parts the Dividend is to be divided into And the Quotient is the Number Produced by the Division of the two given Numbers the one by the other So 12 being given to be divided by 3 or into three equal parts the Quotient will be 4 for 3 is conâ—ained in 12 four times where 12 is the Dividend and 3 is the Divisor and 4 is the Quotient 3. In Division set down your Dividend and draw a Crooked line at each end of it and before the line at the left hand place the Divisor and behind that on the right hand place the figures of the Quotient as in the margent where it is required to divide 12 by 3 First I set down 12 the Dividend and on each side of it do I draw a crooked line and before that on the left hand do I place 3 the Divisor then do I seek how often 3 is contained in 12 and because I find it 4 times I put 4 behind the Crooked line on the Right hand of the Dividend denoting the Quotient 4. But if the Divisor being a single Figure the Dividend consisteth of two or more places then having placed them for the work as is before directed put a point under the first Figure on the left hand of the Dividend provided it be bigger then or equal to the Divisor but if it be lesser then the Divisor then put a point under the second Figure from the left hand of the Dividend which Figures as far as the point goeth from the left hand are to be Reckoned by themselves as if they had no dependance upon the other part of the Dividend and for distinction sake may be called the Dividual then ask how often the Divisor is contained in the Dividual placing the answer in the Quotient then multiply the Divisor by the Figure that you placed in the Quotient and set the product thereof under the Dividual then draw a line under that product and Subtract the said Product from the Dividual placing the Remainder under the said line then put a point under the next figure in the Dividend on the Right hand of that which you put the point before and draw it down placing it on the Right hand of the Remainder which you found by Subtraction which Remainder with the said Figure annexed before it shall be a new dividual then seek again how often the divisor is contained in this new dividual and put the Answer in the Quotient on the Right hand of the Figure there before then multiply the divisor by the last Figure that you put in the Quotient and subscribe the Product under the dividual and make Subtraction and to the Remainder draw down the next Figure from the grand dividend having first put a point under it and put it on the right hand of the Remainder for a new dividual as before c. Observing this general Rule in all kind of Division first to seek how often the divisor is contained in the dividual then having put the answer in the quotient multiply the Divisor thereby and Subtract the Product from the dividual An Example or two will make the Rule plain Let it be Required to divide 2184 by 6 I dispose of the Numbers given as is before directed and as you see in the margent in order to the work then because 6 the divisor is more then 2 the first Figure of the dividend I put a point under 1 the second Figure which make the 21 for the Dividual then do I ask how often 6 the divisor is contained in 21 and because I cannot have it more then 3 times I put 3 in the Quotient and thereby do I multiply the divisor 6 and the product is 18 which I set in order under the dividual and Subtract it therefrom and the Remainder 3 I place in order under the line as you see in the Margent Then do I make a point under the next Figure of the dividend being 8 and draw it down placing it before the Remainder 3 So have I 38 for a new dividual then do I seek how often 6 is contained in 38 and because I cannot have more than 6 times I put 6 in the quotient and thereby do I multiply the divisor 6 and the product 36 I put under the dividual 38 and Subtract it therefrom and the remainder 2 I put under the line as you see in the Margent Then do I put a point under the
and divide them by 14 the Gallons in a Rundlet and the Quotient 216 is your Answer See the work following Reduction of Long Measure Quest. 22. I demand how many Furlongs Poles Inches and Barley Corns will Reach from London to York it being accounted 151 Miles Quest. 23. The Circumference of the Earth as all other Circles are is divided into 360 Degrees and each degree into 60 Minutes which upon the Superficies of the Earth are equal to 60 miles now I demand how many miles Furlongs perches yards feet and Barley-corns will Reach round the Globe of the Earth Facit 4105728000 Barley Corns And so many will reach Round the World the whole being 21600 Miles so that if any Person were to go Round and go 15 Miles every Day he would go the whole Circumference in 1440 Days which is 3 Years 11 Months and 15 Days Reduction of Time Quest. 24. In 28 years 24 weeks 4 days 16 hours 30 minutes how many Minutes Note that in Resolving the last question after the method expressed there is lost in every year 30 Hours for the year consisteth of 365 Days and 6 Hours but by multiplying the years by 52 weeks which is but 364 days you loose 1 day and 6 hours every year wherefore to find an exact Answer bring the odd weeks dayes and hours into hours and then multiply the years by the Number of hours in a year viz. 8766 and to the Product add the hours contained in the odd time and you have the exact time in hours which bring into Minutes as before See the last Question thus Resolved So you see that according to the method first used to Resolve this Question the hours contained in the given time are 248752 but according to the last best or true method they are 249592 which exceeds the former by 840 hours But for most occasions it will be sufficient to multiply the given years by 365 and to the product add the dayes in the odd time if there be any and then there will be only a loss of 6 hours in every year which may be supplyed by taking a fourth part of the given years and adding it to the contained days and you have your desire Quest. 25. In 438657540 Minutes how many years Facit 834 years 4 dayes 19 hours Quest. 26. I desire to know how many hours and minuits it is since the birth of our Saviour Jesus Christ to this present year being accounted 1677 years This Question is of the same Nature with the 24th foregoing and after the same manner is Resolved viz. Multiply the given Number of years by 8766 the Product is 14700582 hours and that by 60 and the product is 882034920 minutes See the work Note that as Multiplication and Division do Interchangeably prove each other so Reduction Descending and Ascending prove each other by Inverting the Question as the 13 and 14 and likewise the 16 and 17 Questions foregoing by Inversion do Interchangeably prove each other the like may be performed for the proof of any Question in Reduction whatsoever Thus far have we discoursed concerning single Arithmetick whose Nature and parts are defined in the second eighth ninth and tenth definitions of the third Chapter of this book for although Reduction is not reckoned or defined among the parts of single Arithmetick yet considered Abstractly it is the proper effect of multiplication and division and as for the extraction of Roots which ought to be handled in the next place as parts of single Arithmetick we shall omit untill the Learner is made acquainted with the Doctrine of Decimals and Immediately enter upon Comparative Arithmetick CHAP. IX Of Comparative Arithmetick viz. The Relation of Numbers one to another 1. COmparative Arithmetick is that which is wrought by Numbers as they are considered to have Relation one to another and this consists either in quantity or in quallity 2. Relation of Numbers in Quantity is the Reference or Respect that the Numbers themselves have one to another where the Terms or Numbers propounded are always two the first called the Antecedent and the other the Consequent 3. The Relation of Numbers in quantity consists in the differences or in the Rate or Reason 〈◊〉 is found betwixt the Termes propounded the difference of two Numbers being the Remainder found by Substraction but the Rate or Reason betwixt two Numbers is the Quotient of the Antecedent divided by the Consequent So 21 and 7 being given the difference betwixt them will be found to be 14 but the rate or reason that is betwixt 21 and 7 will be found to be Triple Reason for 21 divided by 7 quotes 3 the reason or rate 4. The Relation of Numbers in Quality otherwise called Proportion is the Reference or Respect that the Reason of Numbers have one unto another therefore the Terms given ought to be more than two Now this Proportion or Reason between Numbers relating one to another is either Arithmetical or Geometrical 5. Arithmetical proportion by some called Progression is when divers Numbers differ one from another by equal Reason that is have equal differences So this Rank of Numbers 3 5 7 9 11 13 15 17 differ by equal Reason viz. by 2 as you may prove 6. In a Rank of Numbers that differ by Arithmetical proportion the Sum of the first and last term being multiplyed by half the number of terms the Product is the total Sum of all the Terms Or if you multiply the Number of the terms by the half Sum of the first and last terms the Product thereof will be the total sum of all the Terms So in the former Progression given 3 and 17 is 20 which Multiplyed by 4 viz. half the Number of terms the Product gives 80 the Sum of all the terms or multiply 8 the Number of terms by 10 half the sum of the first and last terms the Product gives 80 as before So also 21 18 15 12 9 6 3 being given the Sum of all the terms will be found to be 84 for here the Number of terms is 7 and the Sum of the first and last viz. 21 and 3 is 24 half whereof viz. 12 multiplyed by 7 produceth 84 the sum of the terms sought 7. Three numbers that differ by Arithmetical proportion the double of the mean or middle number is equal to the sum of the Extreams So 9 12 and 15 being given the double of the mean 12 viz. 24 is equal to the sum of the Extreams 9 and 15. 8. Four numbers that differ by Arithmetical proportion either continued or interrupted the sum of the two means is equal to the sum of the two Extreams So 9 12 18 21 being given the sum of 12 and 18 will be equal to the sum of 9 and 21 viz. 30 also 6 8 14 16 being given the Sum of 8 and 14 is equal to the sum of 6 and 16 viz. 22. c. 9. Geometrical Proportion by some called Geometrical Progression is when divers numbers
following Quest. 1. If 22 things cost 66 shillings what will 1 such like thing cost facit 3 shillings for if you divide 66 by 22 the Quotient is 3 for the Answer so if 36 yards or ells of any thing be bought or sold for 108 l. how much shall 1 yard or ell be bought or sold for facit 3 l. for if you divide 108 l. by 36 yards the Quotient will be 3 l. the price of the Integer Quest. 2. If the expence charges or wages of 7 years amounts to 868 l. what is the expence charges or wages of one year facit 124 l. for if you divide 868 the wages of 7 years by 7 the number of years the Quotient will be 124 l. for the Answer see the work Quest. 3. If the content of a superficial foot be 144 Inches and the breadth of a board be 9 Inches how many Inches of that board in length will make such a foot facit 16 Inches for by dividing 144 the number of square Inches in a square foot by 9 the Inches in the breadth of the board the Quotient is 16 for the number of Inches in length of that board to make a superficial foot Quest. 3. If the content of an Acre of Ground be 160 square Perches and the length of a furlong propounded be 80 Perches how many Perches will there go in bredth to make an Acre facit 2 Perches for if you divide 160 the number of Perches in an Acre by 80 the length of the furlong in Perches the Quotient is 2 Perches and so many in breadth of that furlong will make an Acre Quest. 5. If there be 893 men to be made up into a battail the front consists of 47 men what Number must there be in the File Facit 19 deep in the File For if you divide 893 the Number of men by 47 the number in front the Quotient will be 19 the file in depth the work followeth Quest. 6. There is a Table whose Superficial Content is 72 feet and the breadth of it at the end is 3 feet now I demand what is the Length of this Table Facit 24 feet long for if you divide 72 the content of the Table in feet by 3 the bredth of it the Quotient is 24 feet for the length thereof which was Required See the operation as followeth The proof of Multiplication and Division Multiplication and Division Interchangably prove each other for if you would prove a summe in Division whether the operation be Right or no Multiply the Quotient by the Divisor and if any thing Remain after the Division was ended add it to the Product which Product if your summe was Rightly divided will be equal to the Dividend And Contrariwise if you would prove a summe in Multiplication divide the Product by the Multipliar and if the work was Rightly performed the Quotient will be equal to the Multiplicand See the Example where the work is done and undone Let 7654 be given to be Multiplyed by 3242 the product will be 24814268 as by the work appeareth And then if you Divide the said Product 24814268 by 3242 the Multipliar the Quotient will be 7654 equal to the given Multiplicand In like manner to prove a Summe or Number in Division If 24814268 were Divided by 3242 the Quotient would be found to be 7654 then for proof if you Multiply 7654 the Quotient by 3242 the Divisor the Product will amount to 24814268 equal to the Dividend Or you may prove the last or any other Example in Multiplication thus viz. Divide the Product by the Multiplicand and the Quotient will be equal to the Multipliar see the work From whence ariseth this Corollary that any operation in Division may be proved by Division for if after your Division is ended you divide the Dividend by the Quotient the new Quotient thence ariseing will be equal to the Divisor of the first operation for Tryal whereof let the last Example be again Repeated For proof whereof divide again 24814268 by the Quotient 7654 and the Quotient thence will be equal to the first Divisor 3242 see the work But in proving Division by Division the Learner is to observe this following Caution that if after his Division is ended there be any Remainder before you go about to prove your work Subtract that Remainder out of your Dividend and then work as before as in the following Example where it is Required to divide 43876 by 765 the Quotient here is 57 and the Remainder is 271 See the work following Now to prove this work Subtract the Remainder 271 out of the Dividend 43876 and there Remaineth 43605 for a new Dividend to be divided by the former Quotient 57 and the Quotient thence arising is 765 equal to the given Divisor which proveth the operation to be Right Thus have we gone through the four Species of Arithmetick viz. Addition Subtraction Multiplication and Division upon which all the following Rules and all other operations whatsoever that are possible to be wrought by numbers have their Immediate dependance and by them are Resolved Therefore before the Learner make a further step in this Art let him be well acquainted with what hath been delivered in the foregoing Chapters CHAP. VIII Of Reduction 1. REDUCTION is that which brings together 2 or more numbers of different denominations into one denomination or it serveth to change or alter Numbers Money Weight Measure or Time from one Denomination to another and likewise to abridge fractions to their lowest Termes All which it doth so precisely that the first Proportion Remaineth without the least jot of Error or Wrong Committed So that it belongeth as well to Fractions as Integers of which in its proper place Reduction is generally performed either by Multiplication or Division from whence we may gather that 2 Reduction is either Descending or Ascending 3. Reduction Descending is when it is Required to Reduce a Sum or Number of a greater Denomination into a lesser which Number when it is so reduced shall be equal in value to the Number first given in the greater Denomination as if it were Required to know how many shillings pence or farthings are equall in value to a hundred pounds or how many ounces are contained in 45 hundred weight or how many dayes hours or minutes there are in 240 Years c. And this kind of Reduction is generally performed by Multiplication 4. Reduction Ascending is when it is Required to Reduce or bring a Sum or Number of a smaller Denomination into a Greater which shall be equivalent to the given number As suppose it were Required to find out how many Pence Shillings or Pounds are equal in value to 43785 Farthings or how many Hundreds are equal to or in 3748 l. pounds c. and this kind of Reduction is alwayes performed by Division 5. When any Sum or Number is given to be Reduced into another Denomination you are to consider whether it ought to be Resolved by the
Divisor then it is a Direct Rule As In the following Questions Quest. 1. If 8 Labourers can do a certain piece of work in 12 dayes in how many dayes will 16 Labourers do the same Answer in 6 dayes Having placed the numbers according to the 6 Rule of the 10th Chapter I consider that if 8 men can finish the work in 12 dayes 16 men will do it in lesser or fewer dayes then 12 therefore the biggest Extream must be the Divisor which is 16 and therefore it is the Rule of 3 Inverse wherefore I multiply the first and second numbers together viz. 8 by 12 and their product is 96 which divided by 16 Quotes 6 days for the Answer and in so many days will 16 Labourers perform a piece of work when 8 can do it in 12 days Quest. 2. If when the measure viz. a peck of wheat cost 2 shillings the peny Loaf weighed according to the Standard Statute or Law of England 8 ounces I demand how much it will weigh when the peck is worth 1 s. 6 d. according to the same Rate or Proportion Answer 10 oz. 13 p.w. 8 grs. Having placed and reduced the given Numbers according to the 6 and 9 rules of the 10th Chapter I consider that at 1 s. 6 d. per Peck the peny Loaf will weigh more then at 2 s. per Peck for as the price decreaseth the weight Increaseth and as the price Increaseth so the weight diminisheth wherefore because the term Requireth more then the second the lesser Extream must be the Divisor viz. 1 s. 6 d. or 18 peâ—â—e and having finished the work I find the Answer to be 10 oz. 13 p.w. 8 gr and so much will the peny Loaf weigh when the peck of wheat is worth 1 s. 6 d. according to the given Rate of 8 ounces when the peck is worth 2 shillings the work is plain in the following operation Quest. 3. How many pieces of money or Merchandize at 20 s. per piece are to be given or Received for 240 pieces the value or price of every piece being 12 shillings Answer 144. For if 12 s. Require 240 pieces then 20 shillings will Require less therefore the biggest Extream must be the Divisor which is the 3 number c. See the work Quest. 4. How many yards of 3 quarters broad are Required to double or be equal in measure to 30 yards that are 5 quarters broad Answer 50 yards For say If 5 quarter wide Require 30 yards long what length will three quarters broad require here I consider that 3 quarters broad will Require more yards then 30 for the narrower the cloth is the more in length will go to make equal measure with a broader piece Quest. 5. At the Request of a friend I lent him 200 l. for 12 moneths promising to do me the like Curtesie at my necessity but when I came to Request it of him he could let me have but 150 l. now I desire to know how long I may keep this money to make plenary Satisfaction for my former kindness to my Friend Answer 16 Moneths I say If 200 l. Require 12 Moneths what will 150 l. Require 150 l. will Require more time then 12 Moneths therefore the lesser extream viz. 150 must be the Divisor Multiply and Divide and you will find the 4th inverted Proportional to be 16 and so many Moneths I ought to keep the 150 l. for satisfaction Quest. 6. If for 24 s. I have 1200 l. weight carried 36 M. how many M. shall 800 l. be carried for the same mony Answer 24 M. Quest. 7. If for 24 s. I have 1200 l. carried 36 Miles how many pound weight shall I have carried 24 miles for the same money Answer 800 l. weight Quest 8. If 100 workmen in 12 dayes finish a piece of work or service how many workmen are sufficient to do the same in 3 dayes Answer 400 workmen Quest. 9. A Colonel is besieged in a Town in which are 1000 Souldiers with provision of Victuals only for 3 Moneths the Question is how many of his Souldâ—ers must he dismâ—ss that his Victuals may last the Remaining Souldiers 6 Moneths Answer 500 he must keep and dismiss as many Quest. 10. If wine worth 20 l. is sufficient for the ordinary of 100 men when the Tun is sold for 30 l. how many men will the same 20 pounds worth suffice when the Tun is worth 24 l. Answer 125 men Quest. 11. How much plush is sufficient to line a Cloak which hath in it 4 yards of 7 quarters wide when the Plush is but 3 quarters wide Answer 9 â…“ yds of Plush Quest. 12. How many yards of Canvas that is Ell wide will be sufficient to line 20 yards of Say that is 3 quarters wide Answer 12 yards Quest. 13. How many yards of matting that is 2 foot wide will cover a floor that is 24 foot long and 20 foot broad Answer 240 foot Quest. 14. A Regiment of Souldiers consisting of 1000 are to have new Coats and each coat to contain 2 yds 2 qrs of Cloth that is 5 qrs wide and they are to be lined with Shalloon that is 3 quarters wide I demand how many yards of Shalloon will line them Answer 16666 â…” yards Quest. 15. A Messenger makes a Journey in 24 dayes when the day is 12 hours long I desire to know in how many dayes he will go the same when the day is 16 hours long Answer in 18 dayes Quest. 16. Borrowed of my friend 64 l. for 8 Moneths And he hath occasion another time for to borrow of me for 12 Months I desire to know how much I must lend to make good his former kindness to me Answer 42 l. 13 s. 4 d. 4. The General Effect of the Rule of 3 Inverse is contained in the Definition of the same that is to find a fourth term in a Reciprocal Proportion inverted to the Proportion given The second Effect is by two prises or values of two several pieces of money or Merchandize known to find how many pieces of the one price is to be given for so many of the other And consequently to Reduce or Exchange one sort of Money or Merchandize into another Or contrariwise to find the price unknown of any piece given to Exchange in Reciprocal Proportion The third Effect is by two dâ—ffering prizes of a measure of wheat bought or sold and the weight of the Loaf of bread made answerable to one of the prises of the measure given to find out the weight of the same Loaf answerable to the other price of the said measure given Or contrariwise by the two several weights of the same prized Loaf and the price of the measure of wheat answerable to one of those weights given to find out the other price of the measure answerable to the other weight of the same Loaf The Fourth Effect is by two lengths and one breadth of two Rectangular planes known to find out another breadth unknown Or by two