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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 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
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
A B C divide the Line A C into four equal parts and set three of the parts from Z to K and draw the doted Line K Z which suppose to be 18 and the whole 36. Secondly Multiply the half of the arch Line 18 by 14 the doted Line A to X the Center as if it had been half a Circle and it gives 252 Inches How to find a true square Draw a Line at Pleasure and divide it in the middle and set one Foot of the Compasses at one end and make a mark and cross it at the other end and from the cross draw a Line to the middle of the first Line Example To lay down upon paper an Angle containing any number of Degrees and Minutes by the Line of Chords Line of Chords The Line of equal parts for platting of Ground The Line of equal parts is of great use in taking the plat of a Close in Paper The Line of Chords is of use for to take the height of a stile in making o● Sun-Dials c somewhat there of in this Book Example Draw a Line at pleasure as A B from the point A let it be required to make an Angle of 40 Degrees 20 Minutes First Extend the Compasses upon the Line of Chords from the beginning thereof to 60 Degrees always and with that extent set one foot upon the point A and with the other describe the doted Line D C then with the Compasses take 40 Degrees 20 Minutes which is the quantity of the desired Angle Example To take the plot of a Close by the Line of equal parts Measure the length of one hedge in Chains and Links or Poles and the tenth part of a Pole and for every pole take one part from the Line and the tenth part and draw the length on Paper do so with the next hedge and to know how to set these two hedges in their right place make an Angle like the Figure following do so with the other part of the Close Measure this to find the Angle Two places only differing in Latitutde to find their distance First If the two places do differ only in Latitude and lye both of them on one side of the Equinoctial in which the Sun is in when the days and nights are equal you must substract the lesser Latitude from the greater and the remainder is the distance required Or Secondly But if the two places propounded lie the one on the Northside the Equinoctial and the other on the Southside then you are to add the two Latitudes together and the Sum will give their distance in Degrees and Minutes the which reduce into Miles allowing 60 Minutes for 60 Miles The Latitude of places is known by a Table in some Almanacks Of Reduction l. multiplied by 20 are s. s. multiplied by 12 are d. d. multiplied by 4 are q. Of Division q. divided by 4 are d. d. divided by 12 are s. s. divided by 20 are l. Example In 896 l. how many shillings pence and farthings Proof In 860160 farthings how many pence shillings and pounds Pounds multiplied by 3 are Nobles and the Nobles divided by 2 are Marks Pounds multiplied by 4 are Crowns Pound weights divided by 112 are Hundreds Ounces divided by 16 are pounds Inches divided by 12 are Feet Minutes divided by 60 are hours So minding the parts you may reduce all sorts of measures or weights backward and forward c. Of Division To divide 576 pounds amongst 4 men set it in this manner BEgin thus saying how many times 4 can I have in 5. one time but if I could not have taken 5 or the figure in that place out of the figure above then it should be set a place further as under the 7 then set one in the Quotient or crooked line and say 1 time 4 is 4 take 4 from 5 and there rests 1 set one over the 5 and cancel the 4 and the 5 and the work stands thus Now the divisor 4 must be removed a place further that is under the 7 then say how many times 4 can I have in 17 the figures above 4. I can have 4 times then set 4 in the Quotient and say 4 times 4 is 16 take 16 from 17 and there rests 1 set the one over the 17 and cancel the 17 and the work stands thus Lastly there is one place more to set your Divisor 4 that is under 6 saying how many times 4 can I have in 16 just 4 times set 4 in the Quotient and say 4 times 4 is 16 take 16 from 16 and there remains nothing and the work is done and stands thus By this Rule you may divide any number by one Figure but to divide by 2 3 or 4 Figures is harder I will give you one example by which the ingenious may by the practice of the Pen find out the rest Example Divide 288 l. amongst 16 men set it down thus Saying how many times 1 in two once If I say twice then I cannot take twice 6 out of 8 then set one in the Quotient and say 1 time 1 is 1 take 1 from 2 and there rests 1 set 1 over the 2 and cancel the 2 then one time 6 is 6 take 6 from 8 and there remains 2 set 2 over the 8 and cancel the 8 and 1 and 6 and the work will stand thus Then remove the divisor 16 and say how many times 1 in 12 I say 8 times but if I had said 9 times I could not have taken 9 times 6 out of 38 therefore set 8 in the Quotient saying 8 times 1 is 8 take 8 from 12 and there rests 4 set 4 over the 12 and cancel the 12. Lastly say 8 times 6 is 48 take 48 from 48 and there remains none or 8 from 8 and 4 from 4 and the work is done and stands thus Note that whereas you were to take 48 out of the Figures above suppose you had been to have taken 48 out of 56 above you might borrow 10 to put to the 6 as in Substraction paying it as one in the next figure or figures to the Left hand as thus from 56 take 48 rests 08 To prove a Division Sum. Multiply the Quotient by the Divisor and the Product is the same with the dividend if it be right adding thereto the remainder if any be Example To divide any number by 10 100 1000 c. Cut off so many Figures from the Right hand of your dividend as there are Ciphers in your Divisor and the figures remaining towards the Left hand in your dividend is your Quotient Example How to measure a Wood by the help of a Quadrant and measuring only round the same FIrst set up marks at each corner of the Wood that three Marks may be seen at once then at one of these corners place a Stool and lay the Quadrant flat thereon and take sight to two of the marks on each side and mark upon Paper the Degrees of the Angle and measure to the said
9 is 72 set down 2 under 8 and carry 7 and work as the other Line Lastly add up the two Lines saying 3 set it down then 2 and 8 is 10 set down a Cipher and carry 1 then 1 that I carried and 5 is 6 and 4 is 10 set down a Cipher and carry 1 saying 1 and 5 is 6. 23 times 100 is 2300 A Pattern to mark Linnen by One pound 2 ounces 12 penny weight Troy is equal to 16 ounces or one pound Averdupois Or 1 l. Averdupois is equal to 14 ⅗ ounces Troy One ounce Troy is 5 shillings Silver 8 grains Troy is one shilling in Gold If the Date of the year when an antient Book was printed or a man born in the year of our Lord 1616 what is his age this year 1681. Do this by Substraction from 1681 take 1616 rests 0065 Say take 6 from 1 that I cannot do but must borrow 10 to put to the 1 makes 11 then again 6 from 11 and there remains 5 now one that I borrowed and 1 is two so two from 8 and there rests 6 then 6 from 6 and 1 from 1. A Table shewing the Length of the longest artificial day in any place of the World having the height of the Pole   Day Poles height H. M. 0 12 0 6 12 20 12 12 42 16 12 58 20 13 12 24 13 30 27 13 42 30 13 56 32 14 06 34 14 16 35 14 22 36 14 28 37 14 34 38 14 38 39 14 44 40 14 52 41 14 58 42 15 04 P.h. H. M. 43 15 12 44 15 18 45 15 26 46 15 34 47 15 42 48 15 52 49 16 0 50 16 10 51 26 20 52 16 30 53 16 42 54 16 54 55 17 8 56 17 22 57 17 36 58 17 52 59 18 10 60 18 30 P.h. Days H. M. 61   18 54 62   19 20 63   19 50 64   20 24 65   21 10 66   22 18 ½ 66   24 0 67   20 0 68 42 1 16 69 52 16 25 70 64 13 46 71 74 0 0 72 82 6 36 73 89 4 58 74 96 17 0 75 104 1 4 76 110 7 27 77 116 14 22 78 122 17 6 79 127 9 55 80 134 4 58 81 139 31 36 82 145 6 40 83 152 2 6 P.h. D. H. M. 84 156 3 3 85 161 5 23 86 166 11 23 87 171 21 47 88 176 5 29 89 181 21 58 90 181 6 39 The use of this Table Suppose the height of the Pole at London be 52 Degrees how many hours is the longest day Look for 52 in the first Column and against it is 16 hours 30 minutes the length of the longest day Of the four Quarters of the Earth In Europe is Old England c. In Asia is Jerusalem c. In Africa is Egypt c. In America is New England c. Some remarkable times since Adam Year of the World   1 Adam created the 6th day 130 Seth born 395 Methuselah lived 969 years 930 Adam's age 930 years 1656 Noah's Flood 1948 Abraham born 2108 Isaac born 2287 Joseph in Egypt 2046 Sodom and Gomorrah destroyed 2047 Circumcision instituted 2843 London built 2369 Job's time 2433 Moses and Aaron in Egypt 2552 Israelites murmur for Water 2591 Joshuah died 2919 David born   Solomon 7 years and an half in 3012 building the Temple 3029 Rehoboam Solomon's Son 3278 Hezekiah's good Reign 3405 The Captivity 3932 Virgin Mary born Year of Christ   1 Christ born 30 Christ baptised 33 His Resurrection 60 Paul carried to Rome 68 Jerusalem destroyed 92 First of the ten persecutions 304 The last of the ten 665 Printing first in England 1128 Mens hair like Womens 1605 Powder Treason 1607 Bible translated 1665 A great Plague at London 1666 87 Parishes in London burnt 1678 Popish Plot. 1681 A great Dearth A Register of the sufferings and Martyrdom of the Prophets and Apostles according to the Testimony of Scripture and other Historical Records Isaiah was sawn asunder with a wooden Saw Jeremiah was often persecuted and imprisoned yea he was thrown into a deep Dungeon where it is said he stood in the mire to the head and at length was stoned to death in Egypt Ezekiel was slain in Babilon by the Duke of the People Daniel was thrown among the hungry Lions yet the Lord preserved him The three Children were thrown into the fiery Furnace but the Fire did them no harm Micah was thrown down and his neck broken Amos was smitten with a Club on the Temples of the head and so brained Zachariah was stoned to death John the Baptist was beheaded of Herod the Tetrarch Stephen was stoned to death James was beheaded by Herod Agrippa Peter was crucified at Rome with his head downwards under Nero. Paul was likewise beheaded at Rome under Nero. Andrew was crucified by Aege●● King of Edessa James Alphaeus was thrown down from on high and brained with a Club. Thomas was slain at Calamina a City of Judea he was run through with a Dart or Spear Philip was crucified at Hierapolis in Asia Bartholomew was slain in Judea it is said his Skin was pulled over his ears and after all beheaded Matthew was run through with a Sword in Aethiopia Simon was crucified Jude was slain John was scourged and often persecuted it is said that Domition the Emperor caused him to be thrown into a Tun of scalding Oil yet took no harm Matthias was knockt on the head with an Ax and afterwards beheaded Mark the Evangelist had a Rope tied about his neck by which he was drawn through the Streets of Alexandria until his flesh was rent in pieces and in the end he was burned to ashes Barnabas had a Rope tied about his neck by which he was pulled to the Stake and burned He that is born after the Flesh persecuteth him that is born after the Spirit as it is at this day and so it will be until he Christ Jesus reign in the hearts of people through their obedience to his Grace in which Grace the Righteous know his Reign and the Government is upon his Shoulders in their hearts for he is worthy for ever and ever An exact way to measure round Timber by one that can multiply Co. F. Parts 10 0 055 11 0 066 12 0 077 13 0 093 14 0 108 15 0 124 16 0 141 17 0 159 18 0 179 19 0 200 20 0 221 21 0 243 22 0 267 23 0 292 24 0 318 25 0 343 26 0 374 27 0 403 28 0 433 29 0 465 30 0 497 31 0 531 32 0 566 33 0 602 34 0 639 35 0 677 36 0 176 37 0 756 38 0 798 39 0 840 40 0 884 41 0 929 42 0 974 43 1 021 44 1 070 45 1 119 46 1 169 47 1 220 48 1 273 49 1 327 50 1 381 51 1 437 52 1 496 53 1 552 54 1 612 55 1 671 56 1 732 57 1 795 58 1 860 59 1 923 60 1 988