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A50263 A very useful manual, or, The young mans companion containing plain and easy directions for spelling, reading, and uniting English, with easy rules, for their attaining to writing, and arithmetick, and the Englishing of the Latin Bible without a tutor, likewise the plotting and measuring of land, globes, steeples, walls, barrels, timber, stone, boards, glass, &c. ... : and several other considerable and necessary matters, intended for the good of all, and for promoting love to one another : as by the table annexed particularly appears / collected by William Mather. Mather, W. (William), fl. 1695. 1681 (1681) Wing M1286; ESTC R36919 124,932 462

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and for the benefit of those that cannot measure by Arithmetick I have composed a Table which may conveniently be set upon a two foot Rule To measure Brick-Walls or Land by the Rod or Square of 16 ½ Foot to the Pole H. Length Fo. Fo. In. 1 272 0 2 136 0 3 90 8 4 68 0 5 54 5 6 45 4 7 38 10 8 34 0 9 30 3 10 27 2 11 24 8 12 22 8 13 20 11 14 19 5 15 18 2 16 17 0 17 16 0 18 15 1 19 14 3 20 13 7 21 12 11 22 12 4 23 11 10 24 11 4 25 10 2 26 10 5 27 10 1 28 9 9 29 9 4 30 9 1 The use of this Table Example If a Wall be 13 foot high find 13 foot in the first Column and against it is 20 Foot 11 Inches sheweth that 20 Foot and 11 Inches in the length makes a square Rod or Pole The first Column is the height in Feet The second and third are the length in Feet and Inches To reduce Wall-Measure into Standard-Measure which is a Rod of 16 ½ Foot square upon the superficies and 14 Inches or a Brick and a half thick Do thus First measure how many Rods you have upon the side of the Wall as before and take that number and multiply it by the number of the half Bricks that the Wall is in thickness and that product divide always by 3 and the Quotient will shew how many Rods of Standard-Measure is in the Wall If one Yard Pound Bushel Load or Quart cost me so many pence what will any number of Yards Pounds c. cost me Always multiply the number of Yards c. that you would buy by the number of pence that one Yard c. will cost and the product will shew the number of pence that the whole will cost the which divide by 12 to bring it into shillings and the shillings by 20 to see the pounds in the Quotient Proof If 112 pound cost 400 d what will 1 l cost That is 3 d and four seven parts of a penny   20 12 4 l s d q 30 17 3 2 That is 30 pounds 17 shillings 3 pence 2 farthings and the figures above shew that four farthings make a penny 12 pennies make a shilling and 20 shillings is a pound By the same Rule read the figures that follow Averdupoise Weight And 112 l. is a hundred weight   20 4 28 16 Tuns C. Quarters l. Ounces 63 17 2 19 12 Troy Weight   12 20 24 l. Ounces Penny weights Grains 7 6 12 17 Dry Measure   10 8 4 Lasts Quarters Bushels Pecks 7 6 7 2 Liquid Measure   2 18 4 Barrels Kilderkins Gallons Quarts 6 1 12 2 Of Time   13 4 7 24 60 Years Months Weeks Days Hours Min. 6 7 2 3 16 29 Measures in Length   3 8 11 20 3 Leagues miles furlongs scores yards feet 6 2 4 6 17 2 Physical Weights   12 8 3 20 l. Ounces Drams Scruples Grains 9 8 3 1 12 The figures above each Sum are also help● to cast up Sums both in Addition and Substraction For in Addition they shew what you are to dote at or carry to the next row as every 20 Grains must be carried to the place of Scruples as one and the odd set down And in substraction they shew what you are to borrow if need be so that after you have learned to the Rule of Division you may understand all the Questions in this Book How to measure Land or any other thing that lieth flat as the figures following A true Square multiply one side into itself Multiply the length by the breadth Add the length of each end together and half of which multiply by the length Multiply the doted Line into one side Add the two short doted lines together and multiply it by half the longest Multiply half the doted line by any side if a Triangle Multiply half the doted line by the longest side Multiply the doted line by one third of the Compass If any of these be for measuring of Land or any Close may be measured into Triangles and is measured by the Pole of 16 ½ Feet divide the product by 160 and the Quotient shews the number of Acres To know how much Hay a Barn will hold by the Load Multiply the height to the Beam into the breadth in yards and that product by the Length the whole divide by 20 and the Quotient sheweth the Loads of Corn or Hay the Barn will hold to the Beam And for the Roof multiply half the depth into the breadth at Beam and that product by the length and work as before and add it to the other How to find how many square Inches is on the outside of any Globe or other round thing Multiply the thickness or Diameter by the Compass or Circumference and the product sheweth the number of Inches How to find how many solid Inches is in any Globe or Bullet Suppose the thickness or diameter be 21 multiply 21 by 21 and that product by 21 the which multiply by 11 and the product will be 101871 which being divided by 21 gives 4851 the solid Inches in the Globe A Globe of 10 Inches diameter what is the circumference A Globe of 31 3 7 Inches the Circumference what is the diameter If a Globe or Bullet be 5 Inches diameter weigh 16 l. how much shall one weigh that is 4 Inches diameter How to measure Tiling by the square of 10 Foot Multiply the length by the breadth ●n Feet of one side of the Roof and ●hat product divide by 100 and the Quotient shews how many squares of ●0 Foot is in one side the which ●ouble Price of Work Tiling at 3 s. the square Brick work 25 s. the Rod of 16 ½ feet Paving at 2 d. or 3 d. the yard of 9 Feet Rendring 2 d the yard 9 Foot 12 Foot square take 1000 of Tiles 20 Cubical yards to hold a Load of Hay 22 Bushels almost will lie in a square yard 150 or 160 Bricks will lay a yard at one Brick and an half thick in a Wall A Workman will lay 1000 in a day 4600 or 5000 Brick will make a Rod. The value of a single Fraction ½ is the half of any thing ⅔ is two third parts ¼ is one quarter ¾ is three quarters 1 is Numerator 2 is Denominator How to multiply a whole number and a Fraction by a whole number and a Fraction so that if you measure any thing and the length and breadth are Poles or Feet with part of a Pole or Foot Example To multiply 120¼ by 58½ Do thus First multiply the whole numbers together as 120 by 48 and to the Product add one quarter of 48 and the half of 120. Multiply ¼ by ½ is ⅛ Thus 1 time 1 is one 2 times 4 is 8. To Reduce a Fraction into its known parts As ⅚ of a shilling or 12 pence Multiply the Numerator 5 into the
parts of a shilling that is 12 pence and divide that product by the Numerator 6. Example How many square Quarters of a foot is in a solid foot of Timber The square of a ¼ of a Foot is three Inches multiplied in its self Divide 1728 by the Inches in a square Foot by 27 and the Quotient is the Answer Example And in an Inch also is 64 squa● quarterns of an Inch. A Table to reduce Links into Roods and Poles Links R. P. 100000 4 0 90000 3 24 80000 3 8 70000 2 32 60000 2 16 50000 2 0 40000 1 24 30000 1 8 20000 0 32 10000 0 16 9375 0 15 8750 0 14 8125 0 13 7500 0 12 6875 0 11 6250 0 1 5625 0 9 5000 0 8 4375 0 7 3750 0 6 3125 0 5 2500 0 4 1875 0 3 1250 0 2 624 0 1 The use of this Table If you have a number of Links cut off from the Acres in your first Product bring them to the first Column and against them are the Roods and Poles Or take the nearest number and substract Ten hundred thousand or a thousand thousand is a Million To know when it is the middle of the day by the Sun At twelve a clock cut a notch in a Window by the shadow of a stansion or Door post To reduce 5267 Poles into Acres Roods and Poles That is a r p 32 3 27 How to measure any parcel of Land small or great by a Chain and the Rule of Multiplication which may be very useful for the new planter in America the way being in a pocket Book Suppose the length of a piece of Land be 9 Chains and 50 Links the Breadth 6 Chains 25 Links Note that the Chain is called Gunter's Chain being 4 Poles in length and is divided into 100 Links and at every ten Links is a brass Ring price five or six shillings Multiply the Chains and Links as whole numbers and from the product always cut off 5 figures next the Right hand and those to the left hand are Acres   a. r. p.   That is 5 3 30 00000         100000 parts of a Pole Secondly The remaining Figures that is cut off from the 5 Acres must be multiplied by 4 because so many Rood is in an Acre and 5 figures cut off also from that Product and the other are Roods Lastly Multiply the five figures so cut off from the Roods by 40 because there is 40 Pole in a Rood and then cut off five figures from the last product and the Left hand figures are Poles as in the Example appeareth Note that if in your Lengths or Breadths the Links are under 10 add a Cipher to the Left hand How to reduce any number of Chains and Links into feet That is 351 Feet 12 parts 597 Feet 30 parts Always cut off 2 figures from the product towards the Right hand and they are parts of 100 and them on the Left are feet That is 351 12 100 597 30 100 Note that if the number of Links be under 10 place a Cipher to the Left hand as before To know how far it is to a Steeple or Tree that you cannot measure to by reason of water or wood c. Choose two places to stand in to see the same as suppose 20 yards distant for which distance draw a Line on Paper and divide it into 20 parts then lay the edge of a Quadrant at one standing the Quadrant lying flat to point to the other standing and mark how many degrees the sight of the Tree may cut to make an Angle which mark at the end of the Line on the Paper do so at the other standing and bring it to the Paper Lastly draw both the Lines at length till they touch each other and that will shew the distance in yards to be measures by your first Line Note that if the Tree be far distant let your standings be the farther off each other And for want of a Quadrant the square corner of a Board may serve if it be exact square at one corner If you are upon the Land you may take the distance of a Ship at Sea by two standings as before But if you are upon a Ship Mast at Sea or upon a high Tower near the Sea then spie through the sights the Ship observing how many Degrees and Minutes makes the Angle which note upon Paper and let down into the Sea a Line and Plummet the which Line measure into yards and lay it down also on Paper by the Line of equal parts Note that the Angle at the water is a perfect square as one should always be Then draw your Lines to a point as before so that by this Rule the ingenious may find the distance of several Towns and Castles one from another and also their heights and breadths though you cannot come at them by reason of Water or an Enemy c. Note that if the Plummet cut one one quarter of your Quadrant on the right side in taking of sight then twice the distance from your standing to the bottom of the Tree is the height Or if it cut so much of the Left side then half the distance is the height Remember that the sight to the top of the Tree must be as a streight Line to the Ground it may reach 6 7 or 8 foot backward if you stand upright to take the sight How to make black Ink. Take Rain water two Quarts Galls bruised six ounces let them stand one week in the Sun then put in Gum Arabick and Coperas of each four ounces heat it over the fire and stir it with a stick often This Table is called multiplication Table which all have learned by heart that are skill'd in Arithmetick 1 1 2 3 4 5 6 7 8 9   2 4 6 8 10 12 14 16 18     3 9 12 15 18 21 24 27       4 16 20 24 28 32 36         5 25 30 35 40 45           6 36 42 48 54             7 49 56 63               8 64 72                 9 81 How to read this Table Begin at the figure 2 in the second Line and 2 in the first and say 2 times 2 is four 2 times 3 is 6 c. Then begin at 3 in the third Line saying 3 times 3 is 9 and 3 times 4 is 12 3 times 5 is 15 and so to the end Multiply 20 by 5 Thus the Cipher in the 20 set down under the Line then 2 times 5 is 10 set it down so 5 times 20 is 100. Multiply 69 by 87 set it thus Work thus Say 7 times 9 is 63 set down 3 and carry in mind 6 then 7 times 6 is 42 and 6 I bear in mind is 48 set down 8 and bear in mind 4 which 4 set down having no further to carry it Then say 8 times
and 360 of these degrees is round the Earth or Globe as is supposed This North Pole is elevated above our dwelling about 52 degrees 30 Minutes Therefore a man may travel until the South Pole seem to be over his head So being these two Stars are as fixed they are of great help to those that go over the Sea together with the help of a needle placed in the Sea-man's Compass which needle turning upon a point will not be still until it points at one end to the Iron-Mines in the North because of its being touched by a Load-stone that draws always towards the North and the place to which they are travelling to if it bears South or S.S.W. the Compass will shew The height of the Pole in degrees and Minutes are taken by a Quadrant like this Figure following on which Lines may be drawn to find the hour of the day I have only placed the 12 hours ' and by this Table following you may place the rest A Table for the Latitude of 52 Degrees for the Quadrant Hours D. M. D. M.   12 60 0 38 30 11 1 59 43 36 38 10 2 53 45 31 37 9 3 45 42 26 7 8 4 36 41 18 8 7 5 27 17 9 17 0 6 18 11     5 7 9 32     4 8 1 32     Place the hour Lines by the Degrees on the Edge of the Quadrant and to find the hour of the day place a Bead upon the string and on the Edge of the Quadrant is set M for March next A for April betwixt these two or any two Months that the time is when you would know the hour of the day as suppose it is the 15th of March set the Head at the 25th because the Month you must suppose to begin on the 10th of each Month then let the Sun shine through the sights and the Bead will shew the hour of the day In Sun Dials the Stile or straight wire that shaddows every hour Line should point directly to each of these two Stars like as the doted Line which if you can so place upon any flat or upright thing you may with ease draw the hour Lines by the shadow thereof at length by another Sun Dial rightly placed when the Sun shines at any time of the year or by a Clock if it goes right that day as you draw the Lines Or do thus to place a Stile upon and upright Wall that is Southward Just at 12 a Clock set one end of a stick against a Wall and at the other end let a Line and 2 Plummet hang till the shadow of the stick and string hang in a straight Line upon the Wall being held square wise mark both ends of the shadow upon which place your stile that the distant of the lower end from the Wall may be 37 Degrees 3 Minutes and draw the hour Lines as before and when the days are at the longest you may add more hour Lines set the stile square wise from the Wall stile The 37 Degrees 30 Minutes must be taken from the Quadrant for the height of the Stile and ready to fasten upon the Shadow if this stile is placed upon a Board fastened to the South Wall it will serve for a Northern Dial on the other side of the Wall turning the Stile upside down and draw the hour Lines as before And Direct East or West Dials You may place the stile as before by setting a Board Southward by a Wall to find the place by a stick and Plummet and take it away as soon as you have fastened the Stile from the Dial. stile Set the stile upright and exactly North and South at 12 a Clock and draw the hour Lines as before But being that there are so many Books already printed concerning Dialling I shall forbear at this time to write any further thereof that this Book also may not be too big The 32 Winds or Seaman's Compass which are placed round a Circle which they learn by heart in this I have only placed the 4 Winds Now the point or wind any Land bears to may be found in a Table in some Almanacks and the same point may be found in the Compass North. N by E N N E N E by N N E N E by E E N E E by N East S by E S S E S E by S S E S E by S E S E S E by S South S b W S S W S W by S S W S W by W W S W W by S West N by W N N W N W by N N W N W by W W N W W by N North. The Five Senses are 1. Seeing 2. Hearing 3. Smelling 4. Tasting 5. Touching The Compass of some Islands   Miles Compass of England 1532 Scotland 1100 Ireland 948 Isle of Man 91 Isle of Anglesey 58 Isle of Wight 57 Isle of Garnsey 36 Islle of Jersey 28 Acres of several Nations by V. Wing   Acres England 29568000 Scotland 14432000 Ireland 18000000 United States 3599000 Seventeen Provences of the Low Countreys 10791000 France and its 32 Provences 82879000 Eight Kingdoms of Spain 670000535 Italy 44257000 To know when it is Leap-year Divide the present year by 4 what remains shall be for Leap-year o for past 1 2 or 3. Example One remain it 's first after Leap-year To rate Town Taxes Suppose A. hath an Estate worth 35 pounds a year payeth 5 s. 10 d. to a Subsidy or Tax what shall B. pay whose Estate is worth 100 pounds per Annum Answer 16 s. 8 d. If 35 l. pay 70 d. what shall 100. l. That is 16 s. 8 d. Suppose a Tax or rate of 39 l. is laid upon a Town for certain uses whose value of the Town Rent is 900 l. per Annum I demand every mans proportion of what he shall pay according to his Rent If one man in the said Town be worth 100 l. per Annum what shall he pay to the said Rate Reduce the 39 l. into farthings and say If 900 l. give 37440 q. what 100 l. give the Answer To measure Timber of three equal sides being at the end like this Figure following And one side is 16 Inches and the doted Line or perpendicular ten Inches Multiply half the doted Line 5 into the base or one side and that product by 62 if it be the length in Inches and the last product divide by 1728 the Inches in one foot as in round and square Timber measure and the Quotient shews the number of Feet To measure Timber having 5 6 or 7 equal sides Multiply half the Compass by half the thickness and that product by the Length in Inches and work as before To measure a Cone or Spire Steeple Multiply half the Compass at the bottom thereof by half the thickness and that Product by the third part of the length shews the Content in Inches the which divide by 1728 as before To measure part of a Circle First To find the half of the arch Line