6 37. 2. 0 3. 3. 0 1. 20 7 43. 3. 0 4. 1. 20 1. 30 8 50. 0. 0 5. 0. 0 2. 0 9 56. 1. 0 5. 2. 20 2. 10 Poles into Acres observe this Table The Denominations of the several Numbers are known by the Marks under which they are set as all under Ac. are Acres under Ro. are Roods under Po. are so many Pole and so the first Column under M. answereth to Thousands that under C. to Hundreds that under X. to Tens and the odde Pole if any be are set down under Pole As e. g. 1442 Pole To know how many Acres by this Table first for the One thousand in the Table under M. is 6 Acres one Rood set that down as you see in the preceding Page then four Hundred under C. and against 4 is 2 Acres 2 Roods set that down then in the Table under X. and against 4 is one Rood set that down then the odde Poles set down alwayes under the Poles as 2 under Poles then summe them up and you shall find it is 9 Acres 2 Pole as before This Table being so plain there needs no more Examples A Table of superficial long Measure from an Inch to a Mile according to the Standard of England Inch.       12 A foot      36 3 A yard     45 3 ¾ 1 ¼ Ell.    198 16 ½ 5 ½ 4 ⅖ Pole   7920 660 220 176 40 Furlong  63360 5280 1760 1408 320 8 Mile A Table of square Measure Acres 4 160 4840 43560  Rood 40 1210 10890   Pole 30 ¼ 272 ¼    Yards 9     Feet An Example of the Table of long Measure Suppose you were to find out how many Inches were in a Pole long look under Inches and against Pole there is 198 and so many Inches are in a Pole long and 16 ½ Foot 5 ½ Yards And in the Table of Square Measure to know how many square Yards is in a Pole look against Pole and above Yards there is 30 ¼ the square yards in a Pole There be several other sorts of superficial Measures as Pavings Plaisterings Wainscotings and Painting which are to be measured by the Yard square and may be measured by some of the Rules before shewed your readiest way is by the Yard divided into ten parts so will you odde Measure come into Decimal Fractions which are as easily cast up as whole Numbers Or if you measure by the Foot Rule have it divided into 10 parts and when you have found the Content in feet divide it by 9 the Quotient will shew you how many yards and if any remain they be feet Some sorts of Work are measured by the square of 10 foot the side so that such a Square is 100 foot for ten times Ten is a Hundred By this Measure is your Carpenters Work measured as Floors Partitions Roofs of Houses So also is Tiling and Slatting measured this is very ready to measure and to cast up for if you multiply the Breadth by the Length so many hundreds as you find so many Squares are there and what remains are parts of a Square Board and Glass c. are measured by the foot which may be divided into ten parts which will be much easier to count up But if you would be more fully satisfied in the Rules of Surveying see the work of Mr. Leyborn Mr. Wing Mr. Rathborn c. Having the Length of a Field to know what Breadth will make one Acre of Ground by the Four-pole Chain and Line of Numbers Ex. The Length is 12 Chains 50 Links to find the Breadth to make that Length just one Acre do thus Extend your Compasses from 12.50 the Length to 10 that Extent will reach from one to 80 which is the Breadth in Links to make one Acre for if you multiply 12.50 by 80 it yields 100000 from which if you take off five Cyphers there remains one which is one Acre c. CHAP. XLI Of Measuring Holes and Borders that be under a Pole broad by which you may the better lett or take them to doe by the Pole-square c. with several Tables of Measures HOles for to set Trees in are seldome made under one foot Diameter or above eight foot Diameter the Depth may be reduced to a foot deep The Rules to measure any Circle by are the same which is thus To take the Semi-circumference and the Semi-diameter and multiply these Halfs the one by the other sheweth the superficial Content or Area of that Circle This you may work either by the Pen or Line of Numbers As by the line of Numbers thus The Diameter being four foot extend the Compasses from 1. to 4. the Diameter keep your Compasses fixed and alwayes on the Number 7854 set one point and turn twice to the Right hand but if they fall off at the End at the second turn then must you set them on the first part of the Line when you have turned them once c. Having taken the distance of 1 to 4. and set one poynt on the standing Number 7854 the other poynt goes to 31 and neer ½ thence if you turn another turn it will go off from the Line therefore you must find the poynt 31 and near ½ on the first part of the Line and set one poynt there the other will reach to 12 and about 58 100 which tells you that in a Circle of 4 foot Diameter there are 12 superficial square feet and a half and better Now to work it according to the Rule above by the Line if you multiply the Semi-diameter by the Semi-circumference it giveth the Content the same way I shall do it with my Pen Example First having the Diameter I must find the Circumference Extend the Compasses from 7 to 22. the same will reach from 4 to 12. 58 the Circumference then ½ of 12. 58 is 6 29 100 the Semi circumference which multiply by 2 the Semi diameter Extend the Compasses from 1 to 2 the same Extent will reach from 6. 29 to 12. 58 as before that is twelve foot and a half and 8 100 You here may see how easily and readily the Golden Rule and Multiplication may be performed by the Line of Numbers which I use the oftener that you might take the more notice of the Easiness of it to work any of the Rules of Arithmetick by Being once perfect in this you will soon understand the Sector with its excellent uses in the Mathematicks performed by Lines and Compasses but according to the last Rule see the same Question wrote with the Pen that you may see the Agreement that is between Geometry and Arithmetick Example 144 Which 741 Barly-corns is above half a foot as was shewed before but in finding the Circumference I adde a Cypher to 4 which makes it 40 from that I take 6 times 7 which is 42 and should be
pole as in the first Example then always such a Figure ends in ¾ of a pole as that doth But if a Figure be two pole and ¾ one way and two pole and ¼ the other as the last was it ends always in such a Decimal as this 1875 that is half a quarter and half half a quarter that is ⅛ and 1 16 parts of a pole square This way may you cast up the Content of a Ground very speedily and Exact if the middle Length and middle Breadth fall out in ¼ ½ or ¾ of a Pole and this way you may summe up a Field before you do it decimally And then one will be good proof to the other which with little Practice will make you so perfect that in small Fields you will readily tell the Content without Pen or Rule only by Memory These Rules may also be done by two turns of your Compasses on the Line of Numbers and there is no way so ready if once you come but to understand that most usefull Line well For as the distance of one of the Numbers to be multiplyed is from one at the End of your Line the same distance is the product from the other Number Example of the Second Figure As One is to Two and a half the same Extent of your Compasses will reach from 2 and a half to 6 ¼ the Product A Table of Board-Measure by having the breadth of the Board in Inches against which is shewed the Quantity of one foot thereof in Length The use of this Table Bredth of the board in Inches The quantity of one foot in Length  f.pts. 1 0.083 2 0.167 3 0.250 4 0.333 5 0.417 6 0.500 7 0.583 8 0.667 9 0.750 10 0.833 11 0.917 12 1.000 13 1.083 14 1.167 15 1.250 16 1.333 17 1.417 18 1.500 19 1.583 20 1.667 21 1.750 22 1.833 23 1.917 24 2.000 25 2.083 26 2.167 27 2.250 28 2.333 29 2.417 30 2.500 31 2.583 32 2.667 33 2.750 34 2.833 35 2.917 36 3.000 Having taken the Breadth of the Board in Inches see what Number answereth it in this Table and what Number you find against the Breadth in Inches multiply by the Length of the Board or Glass and cut off the three last Figures to the Right hand thereby you shall have the Number in feet and the parts cut off are parts of a foot Example A Board ten Inches broad and ten foot long against 10 you see is 0.833 which multiplyed by 10 gives 8330 then taking off 3 Figures there remains 8 that is 8 foot and 33 100 But if you would measure this Board by the Line of Numbers then set one point of your Compasses on 12 extend the other to the breadth in Inches the same Extent will reach from the length in feet to the Content For as 12 the side of a superficial foot square is to the breadth in inches which here is 10 so is the length in feet which in this Example is 10 to the Content in feet and parts which is 8 foot 33 100 Note this for a general Rule that if the Breadth be less than 12 Inches then must you turn the Compasses to the left hand on your Rule and if more than 12 then turn your Compasses from the Length in feet to the Right hand Learn but to read your Line well and this Rule then may you measure any Board or Pain of Glass as easily as to tell ten c. CHAP. XLII Of measuring Timber and other solid Bodies with several Tables usefull thereunto c. IN Board Glass Land c. we onely took notice of the Length and Breadth which was sufficient to find the superficial Content but to measure solid Bodies we must take notice of the Length Breadth and Depth Most of solid Figures are measured by finding first the superficial Content of the Base or one End and multiplying that by the Length if both Ends alike but if tapering then by ⅓ of the Length and as superficial Measure hath 144 square Inches in one foot and 72 square Inches in half a foot and 36 square Inches in a Quarter So In solid Measure 1728 square Inches make one foot And 8.64 square Inches make half a foot And 432 square Inches make a quarter of a foot For every Inch square is like a Die and so is a foot of solid Measure supposed to be for what it wants either in Breadth or in Thickness it must have in Length so that in what form soever your solid Body is that you measure there must be 1728 solid Inches to make a foot for 12 the side of a foot multiplyed by 12 gives 144 for one side and 144 multiplyed by 12 another side gives 1728 the Cube-square Inches in a Cube-square foot Now to find the solid Content of any piece of Timber or Stone that hath the sides equal first find the superficial Content of the End in Inches and parts and multiply that by the Length in Inches the Product is the Content in solid Inches Then divide that summe by 1728 the Inches in a foot the Quotient sheweth you the Content in solid feet and what remain are Inches If you would work this by the Line of Numbers the Rule is thus Extend the Compasses from one to the Breadth in Inches The same Extent will reach from the Depth to the Content of the End Then extend the Compasses from one to this Content of the End Keep your Compasses fixed and that Extent will reach from the Length to the Content in solid Inches But if your solid Figure hath both Ends alike and in form of a Regular Polgone that is a piece of Timber hewed into 5 6 7 or 8 equal sides c. which is called by some A prisme then take the Semi-circumference and multiply that by the Radius or Semi-diameter that product by the Length giveth the Content But if your solid Figure be a Cylinder that is a round piece of Timber or Stone having both Ends equal Diameter as a Roller c. here take the Semi-circumference multiply it by the Semi-diameter and the Area of that by the Length giveth the solid Content Now many of the Bodies of our Timber-trees will be near this form of a Cylinder but Custom hath got such footing though very false that men will not measure their Timber the true way but will still keep their Error which is to gird the middle of the Tree about with a Line and take the fourth part thereof for the true square and so measure it as a four-square piece of Timber but how false that is may appear by the ensuing Tables Whoever is pleased to trye will find that there may be four Slabs taken off to bring that to a Square and that squared piece then will be near equal to the Measure they first measured the piece of Timber by so that when they have brought their piece square by hewing or sawing they then have the Measure that it was measured for when it
is broken Bricks and Stones and Lime is very good for the Roots of Trees in a stiffe cold Ground the Reason is told you Chalk broken small into pieces is a very good Compost for stiffe cold grounds There is much difference in Chalk but that which is soft fat Chalk is good for such Ground as aforesaid and for ground that is not very stiffe Let your Reason instruct you further Lime is a very rare Compost for cold Grounds and stiffe Clayes for its heat causeth a fume and its tenderness makes way for the Roots to fetch home their Nourishment and its heat is great at first therefore lay not on too much on no ground and let that be slacked If your dry ground be it your Tree delight to grow in and you are forced to set them on wet then adde some of this Lime among your Earth Clay especially that sort which is a light Brick-Earth is very good for such Land that is a light shovey Gravel or hath too much sand in it Such grounds as these they do not retain the spirit of Plants for when Nature hath by the two Lovers Star-Fire and VVater generated their Babe such ground as this doth drink down too fast and again doth drye too hastily so that the water cannot have time to leave nor to prepare its slime which is the Mercury that makes that fume which feeds all Plants and their seeds But this Clay must not be digged too deep for then it wanteth of that which feedeth Plants c. I have taken the green Slime that is common in standing waters I do not mean the Frogs Spawn which is cast many times into this and have dryed it and beat it into fine dust and then have mixed it with good fresh Earth and have found very good success in raising several sorts of Flower-seeds and others Though I have Notes of them yet it is out of my Road to speak of them now being I am Writing of the stately Forrest-trees However I may its possible write somewhat of them if the Lord permits and according as I find these few Lines Accepted of by some of the Royal Oaks of this our Age. For I do suppose that there is not one thing in Gardening yet well known For as a Learned Author hath it he that knows a thing well must know what it was is and shall be Therefore all humane Knowledge is but a shadow of superficial Learning reflecting upon mans Imagination but not the least thing comprehended substantially But to the business in hand take Clay or Loom and lay it on your Ground not too thick the beginning of Winter and there let it be till the Frost hath made it fall into Mould then in some dry open time harrow it all over and if it be Ground you plow then plow it in a drye time but if it be Ground you trench for Forrest or Fruit-trees observe to order it so for by thus doing the Clay will mix with the Sand or Gravel much the better The better that any man cheweth his Meat it is certainly the easier to digest and the dryer you put it into your ground provided it hath but time to water it self well before your trees be set 't is the better for then it draws the Mercury and stores it up till the Roots have occasion for it for 't is quickly exhaled out of sand but the Clay holds his store till a time of Necessity and then contributes to the Roots that is in drye weather and the smaller you make it to mix with your ground the likelier the small Roots as well as the great are to meet with it Note further that the smaller your Plants be the finer must your Earth be made by skreening fifting beating turning c. I know by good success this to be true for the Right Honourable my Lord and the more to be honoured because a great Planter and as great a Lover thereof gave me order to make three Walks of Line-trees from the New Garden to the New Bowling-green and withall to make them descend towards the House as neer as we could which to doe I was forced to cut through one Hill thirty Rod most of the Hill two foot-deep into a sharp Gravel and the greatest part of all the length of the Walks was the same they being Trees that I raised of Seeds most of them and the rest of Layers at Hadham-Hail they being with my Lord ever since their Minority and he many times their Barber engaged him to have the more particular Kindness for them therefore he ordered me to doe what I thought good in preparing the ground for them which I did as followeth First I levelled the Hill and when I had brought the Ground neer to the Level concluded on I staked out my ground where every Tree should stand and then ordered my holes to be made for my Trees each hole three foot-deep and four foot-wide being the ground was so bad This I did neer a Year before I set my Trees and having the convenience of Brick-Earth near I got near a Load to every hole and mixed this with the Earth digged out of the Holes turning it over twice and in dry weather throwing out the greatest Stones but the Turf I did throw into each Hole the grass-side downward as soon as they were made but the Hill of Gravel I trenched that with Loom Cow-dung and the Litter under the Cow-racks two Spade deep and five foot on each side every row of Trees Thus having prepared my ground and the season of the year come about the beginning of November 1672. I had the Trees taken up with good help as carefully as I could and carried to Cashiobury the place of their now Abode and then having good store of help and good Mould prepared of the smallest and finest I set the Trees with the upper part of the Roots of each Tree level with the top of the Ground making a round hill half a foot high about every tree and the Compass of the Hole Having prun'd the heads of each Tree and cut off the bruised Roots and the Ends of such roots as were broken I sorted the Trees and observed this Method in placing them namely I set the highest next the Bowling-green and so shorter and shorter till the lowest were next to the Garden which I did for these Reasons Next the Green was the worst Ground and the Trees more in danger of being spoyled by reason of a Market-path that goeth cross that end of the VValks to Watford Thus having set my Trees streight in their Rows and trod the Earth close to their Roots and made my Hills I then laid round every Tree upon those Hills wet Litter taken off from the Dung-hill a good Barrow-full to every Tree and covered that with a little Mould leaving them to take their rest for a time but early in the Spring I found them to begin their Progress and that Summer they had such Heads
such up you spoyl their spearing by breaking it off or by letting in the drye Aire and so kill it therefore keep your Beds clean from weeds and about the middle or latter end of August they will be come up About the midst of September sift a little richer Mould all over the Bed but not so much as to cover them thus doe the next Summer and take off the side â— boughs though young and when they have stood two years on that Bed then plant them on beds in your Nursery keeping them with digging and pruning up yearly till you have got them to the stature you think convenient to plant abroad In setting this or any sort of Tree forget not to top the ends of the tap-root or other long ones and also not to leave a bruised End uncut off You may set them in streight lines in your Nursery about a yard one Row from another and about a foot and a half one Tree from another in the Rowes mind the Natural depth it first did grow at and set it so when you remove it have a care of setting any Tree too deep and also keep not this Tree nor a Walnut long out of the ground for their spongy Roots will in a little time grow Mouldy and be spoyled Therefore if you cannot set them let them be covered with Earth and then you shall find this Tree as patient in removing and as certain to grow as any Tree I know The ground they like best is a light Brick-earth or Loom as I said before that they dislike most is a rocky ground or a stiffe clay but if one have a mixture of Brick-earth c. and the other of small Gravel Drift-sand Sand c. then there they will do pretty well They naturally increase very much of themselves and the more where they meet with natural ground if you fell a thriving Tree and fence in the place you then may have a store to furnish your Woods and Hedge-rows with the worst and the straightest to nurse up in your Nurseries for to make VValks Avenues Glades c. with for there is no tree more proper for the certainty of its growing especially if you make good large and deep holes and where the ground is not natural there help it by some that is and then you may hope for a stately high growing Tree if you take care in pruning it up as is before shewed of the Oak You need not much fear its growing top-heavy for it having such a thick bark the sap is subject to lodge in it and break out many side-boughs and the Roots apt to break out with suckers the more when pruned therefore prune it up high and often but let the season be February for then its fine dark green-coloured Leaf and long hanging on it is the more ornamental and fit for walks As for the way to increase it from the Roots of another Tree I doe referre you to the seventh Chapter which will shew you fully how to perform the same observing but them Rules you may raise many fine young Trees from the Roots of another much better than naturally they will be produced from the Roots I advise you where you find your ground Natural in your Hedge-rowes there to plant some of this most usefull wood for it will run in the Banks and thicken your Hedges with wood and is very courteous to other sorts of wood growing by it Do not let ignorant Tradition possess you that it will grow of the Chips or of Truncheons set like Sallowes though the Author of the Commons Complaint saith it will for I assure you it neither doth nor will In Lopping of this be carefull to cut your boughs close and smooth off minding to keep them perpendicular to the Horizon the better to shoot off the wet It will grow well of Laying as is before noted and also directed in the Chapt. of Laying in which if you take but a little labour more than ordinary from one Tree you may have in a few years many in your Hedge-rowes or elsewhere therefore deferre not but put this in practice especially the great Kind My Lord Bacon adviseth to bud it to make the Leaves the larger but that is needless Part of these Rules I wrote some years agoe at the request and for the use of the truely ingenious Planter and Lover thereof Sir Henry Capell and I shall give you the same Conclusion now that I did then to him which take as followeth Since Gard'ning was the first and best Vocation And Adam whose all are by Procreation Was the first Gard'ner of the World and ye Are the green shoots of Him th' Original Tree Encourage then this innocent old Trade Ye Noble Souls that were from Adam made So shall the Gard'ners labour better bring To his Countrey Profit Pleasure to his King CHAP. XII Of Raising and Ordering the Ash AND as for Raising the Ash I shall give you the same Rules as I did to the aforesaid Honourable Person the same time before the Discourse of Forrest-trees was written Let your Keyes be thorow ripe which will be about the middle or end of October or November When you have gathered them lay them thin to dry but gather them off from a young straight thriving Tree My Reason to gather them off a young thriving tree is because there will the Keyes or seeds in the Keyes be the larger and solider therefore by consequence they are the abler to shoot the stronger and to maintain themselves the better and longer Though I know by experience that the seeds of some old Plants will come up sooner so the seed be perfect than the seed of young Plants and also that old seed so it will but grow will come up sooner than new Seed My aforesaid Reasons do in part demonstrate this Or thus Nature finding her self weak doth like a provident Mother seek the sooner to provide for her weak Children for Nature is one in divers things and yet various in one thing Now if you gather them off from a straight tree 't is the likelier they will run more up and grow straighter than those which be gathered off a Pollard or crooked tree for it is well known and might be proved by many Instances that Nature doth delight in Imitation and the Defects of Nature may be helped by Art for the great Alterations which many times we find visible in many Vegetables of the same species they all proceed either from the Earth the Water or the Heavenly Influences but the last is the greatest Author of Alteration both in Sensibles Vegetables and Animals However Like still produceth its Like and since there is such plenty of Forrest-trees that bear seed you may as well gather all sorts of Keyes and Seeds off or under such Trees as not As for the time of sowing them let it be any time between the latter end of October and the last of January for they will lie till Spring
a great Bearer and a Tree that doth not last very long my Ground being also a shallow Ground I think of 22 foot asunder to plant these Trees at or as neer that as the Ground will permit Then Secondly I go round my Ground and observing my Fence well and finding no great Trees in it I then resolve to set my Trees at six foot from my Fence but note if there be great Trees in your Hedge that fences your Ground then this is too nigh then I set off six foot at one Corner of my Orchard and six foot at the other Corner of the same side which is the East side then I set off six foot at one Corner of the West side it matters not which only that End which is the Levellest is the best for Measuring Having set these three stakes I strain a Line from one stake to the other on the East side then I lay a square to this Line removing it along the Line till I find the other End of the Square point exactly against the Stake on the west side then laying a Line right square to that Line till you come at the Stake on the VVest side I then measure by this Line as many 22 foots as I can noting how many times 22 foot I find and what you find is over or more than 11 foot then make your distance the less to make that up the equal distance for one Tree more but if it be less than half the distance your Trees are to stand asunder then adde that which is under the 11 foot to the number of Trees that be to stand asunder Observe but this and then you need not fear that your Trees will stand too far off on one side and too near on the other it being the same Charge to plant in good Order as at Random as too many doe nay many times less Charge and how much more pleasing Order is I leave them to judge to whom the great God of Order hath given a great delight to imitate him in his glorious works But as for this my piece of Ground which I pitch on only for Example viz. One Acre and a Square I must find the square Root of 160 Rod or as near it as my Chain will give and then substract but the 12 foot out for the distance of the Trees from the Fence and divide the Remainder by 22 the Quotient tells you how many Trees will stand in a Row the over-measure substracted from or added to as your Reason teacheth you Note this that it is most commonly the best way for your Rows to goe the longest way of your Ground for though your Trees stand 22 foot asunder yet your Rowes in their straight Lines will not stand so far Now to find the square Root there are very many Rules but none that are to my Apprehension so exact and easie as by Logarithmes find but the Logarithme of your Number then take half that Log. the Number answering is the square Root Exam. The Log. of 160 is 2. 204 11998. The half of this Log. is 1. 10205999. The nearest Number answering this Logarithme is 12 Rod 65 100 that is 12 Rod 65 Links of a one Pole-Chain divided into 100 parts The Proof may appear by these three Examples following By this it doth plainly appear that 12.65 is the nearest Number that can be found by your Decimal Chain it is but 225 10000 more and by Logarithmes but 2 of a Link put into 100 parts therefore exact as need be for this purpose unless it were for Calculation in Astronomy or the like And you see that 12.64 multiplyed in it self amounts to 159 Rod and 7696 10000 so that I take 12 Rod and 65 of 100 to be Length or Breadth it being a Square they both be as one Now being the Question is propounded in Feet we must turn this 12 Rod and 65 100 into feet also but note you may work the same by the Links of your Chain better than by foot Measure but some 't is possible have not a Chain therefore observe both wayes and first by Foot measure 12 Rod multiplyed by 16 Foot and a half shew the Feet in 12 Rod. Then for the 65 Links of one Rod put into 100 parts or if it be your four Pole-Chain as is most usual now put into 100 Links then are these 65 Links but 16 Links and a 1 49 by that Chain then by the Rule of Three say if 25 the Links in one Rod be equal to 16 foot and a half the feet in one Rod how many feet are equal to 16 Links and a Quarter The Question ranks it self thus in Decimal Fractions As 25 is to 16. 50 so is 16. 25 to 10 foot 725 1000 of a foot Do you desire to know what this Fraction 725 1000 is in Inches or Barley-Corns which be the lowest vulgar terms in surveying to satisfie you and also my self and likewise to instruct those that desire to learn this Excellent Rule the Rule of Three which rightly for its excellent Use is called the Golden Rule Observe this if one foot or 12 Inches be put into 1000 parts as here it is and must be being 't is the Integer or whole summe of 725 the Rule orders it self thus as 1000 is to 12 Inches so is 725 to 8 Inches 700 1000. Now to know what this 700 1000 is in Barley-Corns do as before say thus If 1000 be equal to 3 Barley-Corns what is 700 equal unto I say as here you see it proved that 700 is equal to two Barley-corns and one tenth part of one for 100 is one tenth of 1000. By this it doth plainly appear that if 12 Rod 65 100 be turned into feet it maketh 208 foot 8 Inches 2 Barley-corns and one tenth of a Barley-corn So that you see the square Root of an Acre is near 208 foot 8 Inches two Barley-corns neglecting 1 10 because 65 100 is somewhat too much Now from this 208 foot 8 Inches I take the 12 foot for the Trees to stand off from the Fence there remains 196 foot 8 inches then I divide this by 22 the distance the Trees are to stand asunder So I find there may stand ten Trees for here you see there may be open places and 20 foot 8 inches for one more so there wants but one foot 4 Inches or 16 Inches to make 10 Trees in a Row for there is alwayes a Tree more than the open Note that in planting of Walks this is of good use that as I said before to make one Tree more this 16 inches I divide by 9 being there are 9 opens between the ten Trees the Quotient is near 2 inches which substract from 22 foot and there remains then 21 foot 10 Inches and so much must every Tree stand asunder the proof is as followeth Here you see that'tis 196 foot and 6 Inches it wants but 2. In. Then to know what distance your Rows may stand asunder the Rule is If
pleasant Prospect as too many doe by making the Walks too narrow If you make any Walk that leads to any pleasant Front of a House or other Object if it be but half a mile long let it be at least forty foot wide but if longer more as 50 or 60 foot wide or the breadth the length of your Front But if you be for walks of shade then make three Walks the middle one 40 the two out-side walks each 20 foot or 50 and 25 the out-side walks or divide your Front into two parts and let the middle be as broad as both the side-walks so that if you make three walks together let the middle one be as much as both the other so will the Trees range much the better whether you set them square or triangular but however keep to one of them though I think the square to be the best because then four Trees in the four Rows end all together fit to end in either Semicircle segment of a Circle Oval Triangle or Circle for all walks of any Length especially in Parks should end in some one of these Figures or lead into some other walk but where they doe fall into another walk there should be a Circle to receive them or else they seem much defective I shall now endeavour to shew you how to make a walk through a wood and then I will give you an Example of some of the Figures that Walks ought to end in Suppose you were to clear a Walk or Line through a Wood for to run the Mid-line true about three yards wide having the Centre given doe as before run your Mid-line as far as you can into the wood and at one yard distance on each side the Mid-line two other Lines Run these Lines also as far as you can into the wood keeping them just one yard distant and setting up stakes as you proceed into the wood with large whites all of a bigness as half a sheet of white Paper on every Stake spread abroad when any of these three Lines come to a Tree run on the other two till you are past the Tree and then set him off again in its place parallel to his fellowes and so proceed till you be through the Wood marking that wood which must goe down then when your under-wood is stocked up run out your Line again still when you come to a Tree set off Parallels and when past set off into your true Line again This way I cut a straight Line through the Wood-walk at Cashiobury from the North front over one wall and several Hedges neer a mile long and when I came to stake it out true there was at the very end not four foot difference as the ingenious Hugh May Esq can witness and several others This way of staking out a walk by three Lines is worth your practising in setting out of Walks that go through Hedges or Bushes be sure to carry on the Mid-line of the walk and the two Lines where the Trees must goe together now and then measuring to see if they keep their equal distances and that which is amiss you will soon find and may as soon rectifie it again There is another way of carrying a straight Line through a Wood which Reason taught me and by Experience I have found true the place where the middle of the walk should poynt to being given there hang up a large Candle and Lanthorn and having found the Mid-line some 20 30 or 40 yards from that there hang up another they must both hang pretty high but let that next the House or Center be the higher having thus placed your two Lights and in a clear calm night but not too light goe with your Man to the further side of the wood till you make both these Lights in one Line and then walk on keeping them so marking the Trees on each side of you quite through the Wood order them to be cut down at leisure so shall you have a straight Line cut through the Wood. But if you are to make a walk from Gate to Gate so that you are tied to such a Center at each End if your walk be so that you can see from End to End it is then but setting up two Stakes one at each end by the sight of which cause a third to be set up in the middle But if you cannot see to the far End for Hill Wood or the like then you must cause an high Pole with a white on the top to be set up at the End by that and your Centre-stake cause your Assistants to set up as many as you think convenient in the mid-Mid-line but if that wood be so high that you cannot see a high Pole at the End then run it over as near as you can by ghess take notice of the Length and of your Error at End and ¼ and ½ and ¾ each at a Quarter of the Length of your walk set off a quarter of your Error c. And thus bring your Line till it ranges exactly from one point to another from Gate to Gate then set off the two Lines where the Trees must goe as is before shewed by the square and if for three walks then the four Rows of Trees if there be three Walks let the Middle-walk be just as broad as both the other which is the best Form or else all three of equal breadth so may you set your Trees not onely square but they will answer one another several wayes beside as square from A. to B. and other wayes as B. to C. and to D. so that every Tree must keep his Row Range Square and equal Distance c. See Fig. 14. The pricked Lines shew how the sight will take the Trees as square from A. to B. and Angle-wayes from C. to B. or C. to D. c. Thus have I shewed you how to stake out the Mid-line and the two side-lines of your walk I wish Sir E. T. Sir W. B. and Sir R. B. had seen these Directions before they had planted their walks I do judge they then would have done them better For Errors in planting make too many worthy Persons forbear Now as for the Figures which walks ought to end in I have named them before and if you observe most Plants especially Trees which make your Walks the most of them end in a Circular figure and therefore I will shew you some wayes how Walks ought to end in a Circle For a walk ending bluntly without any Figure or entring into another may be compared to a Tree with the Head off and what difference there is let those which well observe the Objects of Nature judge Let the Circle be three times the Breadth of your walk if conveniently you can or bigger if you have Room After you have found the Mid-line and resolved upon the Centre as at A. and of the Bigness of your Circle next consider of the Distance of your Trees round the Circle run that distance
Figures and how they are to be measured TO speak of all sorts of Figures will be far beyond my intentions there being so very many irregular Figures which have many unequal sides and angles but they may all be brought into parts of some of the Figures following and Measured like them I shall shew you one Useful Prob. especially to make your Ovals by whether they be made from two Centres or four and then I shall touch at some Superficial Figures See Fig. 30. Suppose three pricks or points given so they be not in a strait line to find a Centre to bring them into a Circle This may be done several ways viz. either by Circles or by raising Perpendiculars as if the points at A. B. C. were to be brought into a Circle Draw a line from A. to B. and in the middle of that line raise a Perpendicular as the line D. E. which you may soon do for if you open your Compasses to any convenient distance and set one point in B. draw the Arch 1. and 2. then setting one point in 4. draw 3. and 4. where these cross draw the line E. D. Do the same with the points B. C. and where the two Perpendicular lines meet is the Centre as at F c. Superficial Figures that are irregular and right-lined are such whose Sides or Angles are un-equal of which some are triangles or triangular Figures and here Note that there are five sorts of triangles which are thus Named and known 1. Isocheles hath two of the sides unequal 2. Scalena hath the three sides unequal 3. Orthygone hath one Right and two Acute Angles 4. Ambligone hath one Obtuse and two Acute Angles 5. Oxygone hath three Acute Angles or Equilateral triangles See Fig. 31. Every triangle is half of a square whose Length and Breadth is equal to the Perpendicular and Side cut by the Perpendicular as is plain in the first Figure shewed by the pricked lines therefore to Measure any triangle raise a Perpendicular from the Base to the greatest Angle Then Multiply the whole Base by half the Perpendicular or the whole Perpendicular by half the Base and the Product is the Content Or thus take the whole Base and whole Perpendicular and Multiply one by the other the half of that Summe is the Content of the triangle c. Square or Quadrangular Figures are these following 1. A Geometrical square this hath Right Angle and sides equal 2. An Oblong-square which hath equal opposite sides and Rectang 3. A Rhombus hath equal Sides and unequal Angles 4. A Rhomboides having unequal Sides and Angles opposite equal 5. Trapezia Are all other four-sided Figures See Fig. 32. The first is Measured by Multiplying one of the Sides in its self In the Second the length Multiplyed by the breadth gives the Content The three last may be turned into two triangles each and so Measured as is before said Polygones are these Figures following as the end of a Tree hewed into five equal sides this is called a Pentagone of six sides Hexagone seven sides Heptagone eight sides Octagone nine sides Enneagone ten sides Decagone twelve sides Dodecagone To Measure any of these take half the perimeter that is half the Compass about and the perpendicular drawn from the Centre to the middle of any one of the sides Multiply the one by the other and it giveth the Content Circular Figures are these which be thus Named 1. The Circle is near Equal to a square made of ½ Diameter and ½ Circumference 2. The Semi-Circle to a square made of half the Arch line and ½ Semi-diameter 3. The Quadrant or fourth part of a Circle 4. The Segment Arch or part of a Circle The first is Measured by Multiplying the Semi-circumference by the Semi-diameter The second by Multiplying the Radius or Semi-diameter by ¼ of the Circumference of the whole Circle The third by Multiplying the Radius by ⅛ of the Circumference of the Circle that it was made of The fourth by Multiplying the Radius by ½ the length of that Arch-line thus have you the Content or Area of each To find the Diameter of any Circle or the Circumference by having one given the lowest Number is as 7 is to 22. so is the Diameter to the Circumference or as 22 is to 7. so is the Circumference to the Diameter To find the Length of an Arch-line Geometrically This Problem is Useful to be known for to Measure the Quadrand Segment of a Circle or Oval for the Oval is made of parts of the Circle First Divide the Chord-line of the part of the Circle into four equal parts then set one of these parts from one End of the Chord-line also set one of the four parts from the Angle in the Arch-line then from one point to the other draw a Line the length of this Line is half the length of the Arch-line See Fig. 33. Examp. A. B. the Chord-line Divided into 4 parts one of the 4 parts set from B. to C. and one part set from A. to D. then draw the Line C. D. which Line is half the length of the Arch-line A. D. B. which was to be found out Thus may you Measure this part of a Circle or the like but if the part of a Circle be greater than a Semi-circle then Divide the Arch-line into two Equal parts and find the length of one of these as is afore-said which doubled giveth the length of the whole Arch-line This Rule will assist you to Measure the Oval whether it be made from two Centres or four c. There is no regular Figure but may be Reduced into some of these Figures afore-said therefore I shall shew you the Use of some Geometrical Figures which are very Useful not Questioning but that you Understand the first Rules in Geometry as to draw a parallel Line to Raise a perpendicular-line from another c. for those things are out of my intended Discourse therefore if you be to seek in them consult with Euclid and others How to Raise a Perpendicular at the end of a Line by which you make a Square very Vseful also to set off a square-line from a strait-line in any Garden Walk house-House-end or the like See Fig. 34. Examp. If you be desired to set off a square-square-line at B. from the Line A. B. take six Foot Yards or Rod and Measure from B. to C. in your strait-strait-line then take eight of the same Measure and set from B. to D. and ten of the same holding one end at C. bring the Line B. D. till it just touch the Line C. D. at D. so have you an Exact Square made by 6. 8. and 10. See Euclid first Book Prob. 47. and p. 35. Math. Recreations p. 93. See Fig. 35. This you may do in other Numbers that bear the like proportion for Euc. tells you that the square made of the side subtending the Right Angle is Equal to the squares made of both the sides containing the Right
was Round But several men have demonstrated this false Rule to be false near ⅓ as Mr. Wing Mr. Philips and others Yet Custom doth and will keep its Road. I have already shewed how to measure Timber by the Customary way by the Line of Numbers in Chap. 35 and 36. before-going and for further satisfaction I referre you to these Tables following A Table shewing the solid Content of one foot Length of any piece of Timber according to the superficial Content taken at the End thereof The Inches at the End f. pts 1 0.007 2 0.014 3 0.021 4 0.028 5 0.035 6 0.042 7 0.049 8 0.056 9 0.062 10 0.069 20 0.139 30 0.208 40 0.278 50 0.347 60 0.417 70 0.486 80 0.556 90 0.625 100 0.694 200 1.389 300 2.083 400 2.778 500 3.472 600 4.167 700 4.861 800 5.556 900 6.250 1000 6.944 2000 13.888 3000 20.833 4000 27.778 5000 34.722 6000 41.666 7000 48.711 8000 55.555 9000 62.500 10000 69.444 20000 138.888 Finding the superficial Content at the End of your Timber-stick or Stone c. let it be Round or Square so it hath but the same Compass from one end to the other against that Number is the feet and parts of one foot Length and by multiplying that by the Length of your Stick sheweth the Content in square feet Example The superficial Content at the End being 200 Inches and 5 foot long against 200 is 1 foot 389 parts which multiplyed by 5 the Length yieldeth 6 foot and 945 parts that is near 7 foot of Timber But if the Number that is at the End be not in the Table then adde two Numbers together and then take the Number which answereth them and adde them together and multiply the Length by that summe as before c. A Table shewing the true Quantity of one foot length in any true squared piece of Timber for Inches and half Inches from half an Inch square to 36 Inches square I. fo pts  0.002 1 0.007  0.016 2 0.028  0.043 3 0.062  0.085 4 0.111  0.140 5 0.174  0.210 6 0.250  0.293 7 0.340  0.390 8 0.444  0.502 9 0.562  0.627 10 0.694  0.765 11 0.840  0.919 12 1.000  1.085 13 1.174  1.266 14 1.361  1.460 15 1.562  1.668 16 1.778  1.891 17 2.007  2.127 18 2.250  2.377 19 2.507  2.641 20 2 778  2.918 21 3.062  3.210 22 3.361  3.516 23 3.673  3.835 24 4.000  4.166 25 4.340  4.513 26 4.694  4.877 27 5.063  5.250 28 5.445  5.670 29 5.840  6.043 30 6.250  6.460 31 6.673  6.890 32 7.111  7.333 33 7.562  7.780 34 8.028  8.263 35 8.507  8.750 36 9.000 If you would enlarge this Table further the Rule is this As the square of 12 Inches which is 144 is to 1000 So is the square of another Number to another Example As in 36 the Square of it is 1296 then as 144 is to 1000 So is 1296 to 9 foot c. as is in the Table The Vse of the Table The Square of a piece of Timber being found in Inches and the Length thereof in Feet to know the Content take the Number answering to the Square of Inches out of the Table and multiply it by the Length in feet Example A piece of Timber 18 Inches square and 25 foot long the Number answering to 18 Inches square is Which multiplyed by 25 the Length Which is 56 foot and one quarter A piece 18 Inches square at the End and one foot long is 2 foot and 1 40. A Table shewing by the Compass of Round Timber what is contained in a Foot length thereof Co. fo pa. 10 0.055 11 0.066 12 0.079 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 0.716 37 0.756 38 0.798 39 0.840 40 0.884 41 0.929 42 9.974 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 61 2.056 62 2.124 63 2.193 64 2.264 65 2.335 66 2.406 67 2.480 68 2.555 69 2.631 70 2.707 71 2.785 72 2.864 73 2.945 74 3.026 75 3.108 76 3.191 77 3.276 78 3.362 79 3.449 80 3.537 81 3.625 82 3.715 83 3.807 84 3.866 85 3.990 86 4.084 87 4.183 88 4.279 89 4.377 90 4.475 91 4.576 92 4.677 93 4.780 94 4.882 95 4.987 96 5.093 97 5.200 98 5.307 99 5.416 The Vse of this Table is as followeth Look for the Compass of the Tree in Inches and in the Column annexed you have the Quantity of Timber in one Foot length which multiply by the Number of feet that the Tree is in Length and the Product is the Content thereof Example The Circumference or Compass of a Tree 47 Inches and 12 foot long the Number against 47 Inches is 1.220 So there is so much in one foot Length Which multiplyed by 12 gives the Content That is 14 foot and above half a foot This Table shews how many Inches in Length make one Foot of Timber according to the Compass of the piece of Timber from 10 Inches Compass to 100 Inches Compass Co. In. pts 10 217.15 11 179.46 12 150.80 13 128.49 14 110.79 15 94.312 16 84.822 17 75.137 18 67.020 19 60.151 20 54.286 21 49.228 22 44.865 23 40.904 24 37.690 25 34.743 26 32.122 27 29.787 28 27.697 29 25.820 30 24.127 31 22.596 32 21.206 33 19.936 34 18.784 35 17.736 36 16.755 37 15.862 38 15.038 39 14.276 40 13.572 41 12.916 42 12.310 43 11.744 44 11.211 45 10.723 46 10.262 47 9.830 48 9.425 49 9.044 50 8.686 51 8.349 52 8.030 53 7.730 54 7.447 55 7.178 56 6.924 57 6.684 58 6.455 59 6.238 60 6.030 61 5.836 62 5.649 63 5.471 64 5.301 65 5.140 66 4.985 67 4.837 68 4.696 69 4.561 70 4.432 71 4.308 72 4.198 73 4.075 74 3.965 75 3.861 76 3.760 77 3.663 78 3.569 79 3.479 80 3.393 81 3.310 82 3.230 83 3.152 84 3.078 85 3.006 86 2.936 87 2.869 88 2.804 89 2.742 90 2.681 91 2.622 92 2.566 93 2.511 94 2.458 95 2.406 96 2.356 97 2.307 98 2.261 99 2.216 100 2.171 The Vse of this Table Having taken the Circumference of the Tree in Inches look that Compass in the Table and against it you may see how many Inches or parts of an Inch make one Foot of Timber then with a Ruler or a pair of Compasses which are better measure how many times you can find that in the Length of the piece of Timber and so many Foot is in that piece of Timber This is a most usefull Table to measure your Timber-trees by Example The Compass of a Tree being 84 Inches about then
true Scale thus having shewed you several hints of this Line of Numbers I will here shew a few more CHAP. XLVI The Description of the Line of Numbers or Gunters Line THis Line commonly on your two foot Rule is in two parts and each of these two parts divided into 9 unequal parts which be called Primes or Integers or whole Numbers and are distinguished by these Figures the first part to the left hand hath 1 2 3 4 5 6 7 8 9 and 10 Now this Middle one which I call 10 is also but one as the line may be read and then the second part to the Right hand is also 1 2 3 4 5 6 7 8 9 10 Now this last part I shall for distinction call the Second Part and then each of those Integers from the first one to the middle is subdivided into 10 unequal parts and from the middle one to 10 at the end of the Second part between every two Figures according to the same order that the other were divided into 10 parts and each of these 10 parts should be divided into 10 parts more if the Rule were long enough to bear them but on every two-two-foot Rule that hath this line well made on it they be from the Middle one to two in the Second part first divided into 10 parts and then each of these into 10 other parts and were the Rule long enough these should be divided into 10 other parts but to read a summe of a Thousand you must estimate or ghess at the Unite so that you may read any summe under a thousand expressely from the first one to 10 in the Second Part you may read 199 expressely the middle one being 100 then 9 tenths is 90 and 9 tenths of them tenths is 9 that is 199 which is the Division next to 2 in the second part of your Rule By this you may observe that the longer your Rule is the more exactly you may number or read a great summe especially if you understand Arithmetick as may be seen more fully in the Rules of Arithmetick following CHAP. XLVII Numeration on the Line or to read a summe on the Line of Numbers YOu may observe that the Figures on this line as in the preceding Chapter are 1 2 3 4 5 6 7 8 9 and 1 2 3 4 5 6 7 8 9 10 Now the same poynt or Division on the Rule which hath 1 2 3 4 5 c. may be read 10 20 30 40 50 c. or they may be called 100 200 300 400 500 By this you may perceive that the larger Numbers you have to number any of those Figures will admit of a larger Denomination so that if you be to read any summe from one to 10 you have it in the Second part for then the first one is one tenth the middle one is one the End one is 10 but if you be to read a Number of three Figures as any is under 1000 then the first one is 10 the middle one 100 the End one 1000. Example To find 144 I take the middle one for the 100 then 4 of the great Divisions forward for 40 then 4 Divisions forward still to the Right hand for 4 and that poynt is 144 which may also be called fourteen and 4 10 or 1450 or 14500 then must the middle one be 10000 and 4 tenths forward 4000 and 5 tenths forward 500 this poynt wants but five small Divisions of the long poynt which is 15 or 150 or 1500 or may be 15000 according as your summe is in greatness Example To find the poynt 12 first I read the middle one 10 then 2 tenths forward for 2 that is the poynt 12 where in many Rules there is a Brass Pin because it is a Poynt much used as you will find hereafter now this poynt 12 is also 120 or 1200 for the first one being one then the middle one is 10 and two tenths forward is the poynt 12 c. but if you read this poynt 120 then the first one is 10 the middle one 100 and two tenths forward 20 which is 120 and if it be read 1200 then the middle one is 1000 and two tenths forward 200 which is 1200 c. Example To find the Number 1728 being the Cube-Inches in a foot of Timber the middle one is 1000 then 7 tenths forward is 700 and two tenths of them forward is 20 Now the Divisions on the Rule do not shew the 8 that remains therefore you must estimate the place for 8 which is almost one tenth more so having found that place 't is the poynt which is for 1728 so in many great summes you must estimate or ghess at the Unite but Decimal summes do shew themselves more plainly as you may well perceive hereafter especially when they end with a Cypher or Cyphers I hope you now plainly see the use in Reading or numbering any summe under 10000 and that you see also that this is a Decimal Line and is taken from that excellent Rule of Decimals the Canon of Logarithmes and that you may read any Decimal Fraction as one tenth one of 100 or one of 1000 or 2 10 3 10 4 10 or 15 100 26 100 71 100 c. that is if the Integer be in 10 parts you may find out any of these parts or if in 100 parts you may find out any part from one to 100 readily Ex. If the Integer be 10 that is if 10 make one foot yard pound or the like I would know the poynt of one and 5 10 or one and ½ take either the middle one or the first one extend the Compass poynt to 5 which is the longest Division between 1 and 2 that is the poynt of one and 5 tenths or one and a half Example If it were required to find the point of 100 50 100 or 100 and half 't is the same point or it is 1000 and a half Example If it be to find the point of 60 of 100 then the middle one is the 100 and the figure 6 in the first part is the figure that is 60 of a 100 or 60 100 or as decimal fractions commonly are writ 60 the prick before shewing it to be a decimal fraction Example To find 1560 take the middle one for 1000 and five tenths for 500 and 6 tenths of them tenths for 60 which is the point 1560 c. Also if it be desired to find the fraction 1560 of 10000 that is the same point and may thus be writ 1560 10000 or it is the point that represents the fraction 156 1000 c. Be perfect to read the Line well then will the other Rules be easie CHAP. XLVIII Addition on the Line of Numbers THe Rule is first find one of your numbers then count so many as the number or numbers are forward that is to the right hand and that is the Sum. Take notice that your sum or sums must if they be fractions be Decimal fractions Example In whole numbers 55
THE Manner of Raising Ordering AND IMPROVING Forrest-Trees ALSO How to Plant Make and Keep WOODS WALKS AVENUES LAWNS HEDGES c. WITH Several FIGURES proper for Avenues and Walks to End in and convenient Figures for Lawns Also RULES and TABLES shewing how the Ingenious Planter may measure Superficial Figures with Rules how to divide Woods or Land and how to measure Timber and other Solid Bodies either by Arithmetick or Geometry shewing the Use of that most Excellent Line the Line of Numbers by several New Examples with many other Rules usefull for most Men. By M. COOK LONDON Printed for Peter Parker at the Leg and Star over against the Royal Exchange in Cornhill 1676. TO HIS EXCELLENCY Arthur Capell Lord Lieutenant and General Governour of the Kingdom of IRELAND Earl of Essex Vicount Maldon Lord Capell Baron of Hadham Lord Lieutenant of Hartfordshire and one of the King 's most Honourable Privy Council c. May it please your Excellency DID I not very well know your great Understanding in and Love to the Subject of the ensuing Discourse I durst not assume the Boldness to implore your Honours Patronage of it But being well assured that you have not been onely a Spectator but an Actor in most of what is treated of in the ensuing Lines for to your Eternal Prayse be it spoken there is many a fine Tree which you have Nursed up from Seeds sown by your own hands and many thousands more which you have commanded me to raise Therefore my Lord I humbly crave your Pardon for the Presumption and Imperfection of the Pen-man and though your Excellency knows full well how to prune young Trees yet I hope you will pass by the impertinent and superfluous Lines in this my Plantation which though I have endeavoured to keep as well pruned from Errors and as clean from Weeds as I could yet 't is possible there may be some things in it which some may term as ill But to You all things in it are so well known that I hope both it and I shall find such shelter and support by your favourable Aspect as that we need not to fear the Storms of the ignorant or negligent Planters And my Lord since the Art of Raising and Improving of Trees hath ever been esteemed amongst the truly Noble Wise Ingenious and most refined Spirits of the World from Age to Age and chiefly maintained and practised by them and since this Property is Naturally inherent in You you being not onely a great Lover of this Art but also most skilfull in it I humbly presume to Dedicate these my Observations to your Lordship not being ignorant that he who is most knowing in any thing is the best able to judge of the same and that this my Opinion of your Honours Ability and Promptitude in promoting the Planting and Improving of Forrest-trees is surely grounded the Large Plantation you have made will abundantly testifie But I humbly beg your Lordships Pardon for this Presumption not without hopes that my good Meaning may obtain it and since my good Wishes and the best of my Services is all I can contribute to You these shall never be wanting from My LORD Your Excellencies most Humble and most Obedient Servant to serve You whilest I bear the Name of Moses Cook TO The Courteous READER AMongst the many Books that are sent into the world in this Age I have adventured to increase the Number by this one I know there be many Pamphlets prodigious Histories and Romances invented by mens Fancies which abuse many Noble Spirits in reading of which they spend their time in vain and dull their Wits Which Books are more fit for Women than Men. For they will furnish them with strange Stories and a few fine words Also there be many Books of Disputes in Divinity which tend more to make our Differences the greater than any wayes to edifie or unite us therefore if your Genius leads you to read such Books this is not for your Fancy But if you take delight in Planting or Gardening or to raise and improve Forrest-trees or to make Walks Avenues or Lawns to plant or improve your Woods Hedges c. or to measure most sorts of superficial or solid Figures either by Arithmetick or Geometry with several other Rules of the same Nature as the Titles of each Chapter but especially the Chapters themselves will more fully inform you then I hope this Book will be of good use to you For here are several Rules approved of by several Noble and Ingenious Men which are as faithfully delivered as they are really intended for the good of this Nation and all those that will put them in practice which if you please to doe you will employ your time so well that you will never have cause to say it is ill spent and if once you do but step forward one step and see but any success of your Labours you will need then no Logicians Arguments nor no Rhetoricians Eloquence to perswade you to proceed And for your better Encouragement know that it hath been and is the Delight and Practice of Kings Princes Philosophers and all Noble spirited and wise Men For have not many of them quitted their great Employs and taken upon them this pleasing Art of Planting and Gardening as is proved by several See the Prefaces of Perkinson's Gerard's the Curate of Henonville's and several others For Almighty God hath Imprinted in the Hearts of most wise men such a Love to Plants in part as their Father Adam had in his state of Innocency that those noble and usefull Works which the Almighty made for the use of Man and his Glory should be the more common for their excellent use to the Sons of Men and that they should take care of those which are tender and want the more care lest they should be lost and also that both their Vertues and their Beauties should be known in several parts of the World that he might be the more Admired and Glorified For I do believe that the Blessing of God is much Assisting to those who Love and endeavour to Improve and Preserve his Works for God's Works and his Word are no such different things and also it hath been and is observed that those that are Wasters and wilfull Spoylers of Trees and Plants without just Reason so to doe have seldom prospered in this World See this confirmed by Esquire Evelyn in his Preface to his Discourse of Forrest-trees Therefore you that are Lovers of Trees and Plants if once you have them let your Love be shewed in the Care you take of them to keep them from Cattel and other Inconveniencies then will you not onely have Pleasure and Profit of them but others by being defended from the malignant and sharp Air by their Heads and Bodies and also shaded from the violent Heats and their sweet Flowers and their refreshing Fruit will be usefull to several men Also Planting and Gardening addes much to the Health and
So doth your Walnut Chesnut Horse-Chesnut Peaches Almonds Apricocks Plumbs c. and the onely difference from Beans and Pease is that these Stone-fruits put forth at the small ends and the other alwayes at the sides In like manner there be several sorts of Trees and most sorts of Plants that be small which put forth Root at the small end and as soon as that Root hath laid hold of the ground they then send out two false Leaves nothing like those that grow on the Tree or Plant which two false Leaves are the seed which divides into two parts and so stand some small time on the top of the ground and then between these two false Leaves comes forth a Shoot which produceth leaves like those of the Tree or Plant from whence it came Of this way of growth there be an infinite number both of Trees and Plants as the Elm Ash Sycamore Maple Pear Apple Quince and the most sorts of the seeds of Trees which are not environed by Stones or Shells of seeds the Melon Parsnip Carrot Carduus Angelica and indeed most sorts of seeds CHAP. V. Of the several wayes to raise Forrest-trees or others and how to perform the same by Laying THose sorts of Trees which will grow of Cuttings are the easiest to raise by Layings some of which sorts you may see in the next Chapter Now touching the best time for laying your Layers of Trees observe that if they be Trees that hold their Leaf all Winter as Firres Pines Holly Yew Box Bayes Lawrels Elix c. Let such be laid about the latter end of August But if they be such as shed their Leaf in Winter as Oak Elm Line Sycamore Apple Pear Mulberry c. let such be laid about the middle of October I do grant that you may lay at any time of the Year but these times I take to be the best for then they have the whole VVinter and Summer to prepare and draw Root in at that time of the year the Sun having so much power on the sap of the Tree as to feed the Leaf and Bud but not to make a shoot and if that little sap that rises be hindred as it is by some of the following wayes of laying the Leaves and Buds yet gently craving of the Layer makes the Layer prepare for Root or put forth root a little to maintain it self being it finds it cannot have it from the Mother-plant and being it wants but little Nourishment at that time of the Year I think it is better to lay Layers of Trees and to set Cuttings than at other times In Summer when the sap is much abounding or in VVinter when the sap stirres little or in the Spring when the sap begins to rise for then it comes too suddenly to draw sap from the Layer before it hath drawn or prepared for root for Nature must be courted gently though I know in small Plants the Spring or Summer doth very well for they being short-lived are therefore the quicker in drawing root and besides that Trees are many times laid as they are not As for those Trees that are apt to grow of Cuttings take but some of the boughs and lay them into the Ground covering them about half a foot with fresh fine Mould leaving them with the end of your Layer about one foot or a foot and a half out of the ground keeping them moist in Summer and in Twelve Months time you may remove them if rooted if not let them lie longer Another way is take a Bough you intend to lay and cut it half way through right cross the wood then slit it up towards the end half a foot or according as your Layer is in bigness lay the slitted place into the ground and you shall find that slitted place take root if laid as the former and so ordered This way you may encrease many fine Flowers and small Plants but they being out of my Element at this time I shall not speak of the ordering them for fear I seem tedious to some Another way to lay a Layer of a Tree is take a piece of VVyer and tie it hard round the bark of the place you intend to lay into the ground twisting the ends of the VVier that it may not untie prick the place above the VVier thorough the bark with an Aul in several places then lay it into the ground as the first A fourth way of Laying of trees is Cut a place round about one Inch or two where you find it most convenient to lay into the ground and so proceed as is shewed in the first way of Laying A Fifth way to lay some sorts of Trees is to twist the place you intend to lay into the ground as you do a withe and lay it as is shewed in the first way of Laying by this way and the first you may furnish your Woods and Hedges For they being easie any ordinary man will perform the same Thus you may from one Stub as a Sallow or the like between one Fall and another of your VVood for a Rod square of Ground and more if that one Stub produce but strong shoots fill it well with Wood For when the Stub hath got two or three years shoot then lay round it as before at large is shewed there letting them remain to produce new Stubs But if you would increase by laying some young Trees from an high Standard whence you cannot bend the boughs down to the ground then you must prepare either Box Basket or Pot and fill them full of fine sifted Mould putting a little rotten VVillow-dust with this Earth for that keeps Moysture to help the Layer to draw root then set the Pot or Box thus fill'd with Earth upon some Tressel or Post as your Ingenuity will direct you then lay your Bough by the second third or fourth way of Laying leaving not too much head out because the wind will offend it if you doe and by its own motion be likely to rub off the tender young Root and thus lay your Hops this way These things observed you may raise many choyse Trees as Mulberry Hors-Chesnut c. These Rules may instruct you sufficiently concerning the propagation of Trees by Laying but let me tell you it is hard to raise a fine straight Tree by a Layer or Cutting I have hinted at the Reasons before Note the smaller your Boughs be Set them the less out of the ground and keep them clean from VVeeds that they spoyl not your Layers Alsonote that the harder the VVood is then the young VVood will take root best laid in the ground but if a soft VVood then older boughs will take Root best Now you that be Lovers of wood make use of these sure Directions and if you repent then blame me CHAP. VI. Of those sorts of Trees that will grow of Cuttings and how to perform the same IF your Ground be moist you may Set with success any sort of Willow Sallow or Osier
they were never Transplanted before for there is a great deal of Reason to be given that the oftner you Remove a Tree the likelier 't is to grow when it is Removed again provided it be not too great Besides Experience doth plainly shew the same for I have often found that a Walnut-Tree set of a Nut and never-removed in its Minority but still keeping his place of Situation till it is six or seven Foot high that in Removing such a Tree you shall find near as much hazard in the growing of that Tree as in Removing an Oak of the same stature provided the Oak hath had his Abode in open Air and not been tenderly Nursed up in a Wood for such Trees let them be of what kind you will are nice to be removed out of their warm Habitation But at this I have hinted before Now to shew you some Reason why any Tree being Removed before is the likelier to grow when removed again Observe these few Rules First 'T is the Nature of all Trees to put forth one Root first and then some side-roots according to the Kind and Nature of the Ground and this most stately Tree doth commonly run to the bottom of the Soyl that is fit for his Nourishment before it puts forth many side-roots especially in a loose hollow Ground and then at the end of the tap-root it puts forth feeding Roots and when this Tree comes to be pretty big it having few feeding Roots near home the Tree can hardly be taken up well without losing most of them which will be a great hazard to the loss of your Tree Secondly But when a Tree is taken up young as at one two or three years old then there is but small head so that a little Root will maintain that and then this little Root lying not deep and in a little compass of Ground may be taken up with less loss to the proportion of the Head than a greater Thirdly When you have taken up these young Trees in cutting off the end of the tap-root and the ends of the greatest of the others those very ends so cut off with the slope lowermost will at that place put forth many small Roots which lying near to the Body of the Tree are the easier to be taken up with the Tree when 't is Removed again Lastly Custom in Removing of Trees tends somewhat to their growing being Removed for I sansie that if you could get some Acorns of an Oak that had with his Fore-Fathers been accustomed to Removing as our Apple-stocks are I do Judge it would be then as patient of changing his Habitation as they From that which hath been said I hope you will conclude with me that 't is best to Remove either Forest-Trees or others when young for if you Remove them when they be older the better the Ground is the more the Tree runs down with a tap-root therefore if never Removed before the worse to remove off from such a Ground Thus having Ordered these Young Trees till you have Nursed them up to the stature of six or seven Foot high you may afterwards Transplant them into your Walks Wood or where else your Fancy pleaseth onely in Transplanting Observe this Make your holes four Foot wide and two Spade deep at least half a year or a quarter at least before the time of Planting if it be a year 't is the better provided you keep that Mould which you threw out of the holes clean from Weeds and Grass by turning it over as Occasion requires and if you think your Ground be poor or of some contrary Soyl to what your Tree Naturally delights to grow in mix it with some such like Earth as your Tree doth best delight to grow in as for an Oak if your Ground be Gravelly mix it then with the upper Spade of Ground that is a Brick-Earth turning these together with the Earth you did throw out of the holes if Clay mix it then with a light Loom or a fat Sand or small Gravel and if the Ground be poor a little laying of rotten dung in the bottom of your holes but let none be among your Earth when you set your Trees that is to touch the roots of them Having thus prepared your holes for your Tree and your Earth if your Ground be a dry Soyl then begin as soon as you find the Leaf to fall that is in October 'T is not the Hill or Valley North or South Situation which makes the finer or tougher Grain but if there be a seeding Ground on the top of an Hill or on the North side more than there is in the Valley or South-side there then will be the toughest Timber for where a Tree grows most in a year that Oak is the toughest Timber and there that Tree shall have the most sap as on a deep Loomy Ground But let it be Hill or Valley if it be a shallow ground and the bottom Gravel and not mixed with Loom or Clay there Oaks will grow slow and the Annual Circles being close together the Timber must then be the finer Grained and the sap of such Oaks is little as I have many times Observed Experience and Reason which I have alwayes hitherto taken with me as Guides in my Travel and Search after Nature have confirmed me in this A light Brick-Earth or a Loomy-Clay produce the stateliest Oaks soonest and toughest Timber for there they grow quickest Your Clays produce great Oaks for that is a holding Ground although they grow sometimes slow yet they last long Your Gravel produceth many Oaks and streight they grow slow the Timber is fine and they decay while they be young the Reasons of this I have told you before Having made Ready your Holes and taken up your Trees well I Advise you to open the Earth well round your Tree keeping the side of your Spade to the Body of your Tree to prevent Cutting the Roots when you take them up and also to digg deep round the Tree that when you come to pull up your Tree it may come up easily which will prevent those Roots which grow Elbow-like which if they do not break off in pulling up by straining them to pull up they will crack so in the Elbow that they will never grow nor put forth Roots below that place therefore for such Trees as be ticklish to Remove take the more time lest you verifie the Old Proverb which saith Too much haste Oft makes waste Such Roots as you find Bruised or much Cracked cut them off till you come at firm sound Root Such Trees as are slow-growers as the Oak is you may prune up to the smaller Head as if your Tree be taper and streight you may prune up such a Tree to one shoot but if your Tree be not taper then leave two side-boughs or more to receive some of the Sap which will make the shoot that you intend shall lead to make the body of the Tree the smaller and so
I have shewed you that it is not the mixing of Earth with other Plants that will make them change into such Plants as you mix the Earth with or make the Plant alter to any purpose for the main alteration of all Plants is from their Seed though it may be mixing such Plants or Shavings with the Earth you sow Seed in may cause them to have some quality of the Physical use of the Plant in them as is the Opinion of the Learned that Misceltoe on the Oak and Polipody of the Oak and Elder on the Willow c. do partake of the Physical uses of those Plants on which they grow for in Nature you may find that many Bodies do not onely by their Qualities Affect their Adjacents but also infuse their Virtue into them and endue them with the same faculty as the Loadstone doth not onely attract Iron but Communicates its Virtue to it and makes it Magnetical by touching c. But I shall leave the Stones and return to the Walnut-tree Let your Nuts be very Ripe and when they begin to fall then beat the rest off from the Tree and lay them by that the outward Husk may Crack then peel them but do not wash them for wet doth make the Kernel Crack and Mould and spoyls it When you have taken off the Husk lay them thin to dry in some dry open Room turn them sometimes with a Broom When they have sweat and are dry about the beginning of October put them into Sand a little moyst making it a little wetter about Christmas for then they will begin to spear and then will digest it Sow them not in their Husks neither steep them as some Advise Set or Sow them about the latter end of January or beginning of February in good fresh Ground minding the aforesaid Rules and you shall not lose one in a hundred and cover them about an Inch and a half or two Inches keep them well Weeded on their first bed and when they have stood two Summers then Remove them into other beds setting them about a yard asunder one Row from another and about a foot and a half one from another in the Rows Cut the Tap-root and all bruised Roots off and the side-boughs but cut not off the Head of a Walnut-tree Keep them with digging and hoing and pruning up till you have got them five or six foot high then bud them it will make them bear sooner and then you are certain of a good Kind for I presume you will not bud them with a bad Kind if you know it If you do not bud them let them Head about six foot high a year or two and then Remove them but keep them not long in the open Air for the Roots being of a spongy Nature will take in the Air so fast that they will soon Mould and Kill your Tree therefore set them as soon as you can when once taken up Remove them young off from the Seed-bed as is before Advised for if you let them stand to be great on the place where they were first sowed they will be much more dangerous to Remove and not so likely to thrive The Ground they Love is a deep Soyl and of a dry Nature on a sharp Gravel if the Ground be shallow they will not prosper but if the Gravel be mixed with Loom they will do well They Love not a stiff Clay but if it be mixed Naturally with stones or Chalk and not too shallow then they will thrive on it It is a proper Tree to set in Woods for it will run up if the side-boughs be taken off to a great height and yield very good Timber for many Uses CHAP. XV. Of Raising and Ordering the Chesnut TOuching the Kinds of this Nut there may be several but I know but three one of them is very good which ought to be the more Increased For the time of Gathering Observe the same as before is said of the Walnut When you have gathered them and taken the Husks off lay them to dry and sweat but not too thick Do not steep them in Water as some Advise you for it is not good to steep any sort of Seed unless some Annuals and to steep them is good especially if lated in sowing but to steep Stones Nuts or Seeds that are not of quick growth watering them may Kill them by making the Kernel swell too hastily and so crack it before the spear causeth it or it may Mould and stupifie the spear therefore let no Seeds whatsoever that are not quick of growth have too much wet at first You must put your Chesnuts then in Sand a little moist about the beginning or middle of November make it a little moister about the beginning of January and at the latter end or beginning of February sow them on beds and cover them about two Inches or you may set them by a Line as you set Beans or you may sow them in drills as Beans or you may sow them where you intend they shall stand and in any of these ways or places keep them clean from Weeds the first or second year then you may Remove them into your Nursery off from the Seed-bed prune off the side-boughs and Roots They are Subject to put forth many side-boughs near the Ground whereby they may be increased by Laying very easily to do which see Chap. 5. But the best way is to Raise them of Nuts Set them in Rows in your Nursery and Order them as is shewed of the Walnut The Soyl they Love is such as the Walnut takes delight to grow in They be Excellent to set in Coppices or Woods the Timber is very Useful and they will grow to be large for under-wood if the Tree be much crooked fell it it will yield great store of strong shoots from the stemme some of which it will be convenient to Lay whereof you may leave some Layed to thicken the place and others to Plant where you please and may have great shoots from the stemme for several Uses also CHAP. XVI Of Raising and Ordering the Sarvice-Tree AS for the Kinds of the Sarvice they may be many there is one whose Fruit is much better than the other but whether it is the Ground makes it so I cannot positively say We have them grow at Hadham on very stiff Ground the Trees bear well and the Fruit is good and at Cashiobury we have them on a sharp Gravel the Fruit naught and the Trees bear very badly It may be Raised of the Seed or Stone that is in the Berries which when they are rotten are then Ripe that is about the latter end of September or beginning of October eat off the Fleshy part or rub it off by Rolling them in Sand then dry them in the open Aire and keep them in moyst Sand till the beginning of January then sow them on moist Ground or in the shade keep them from weeds then let them stand two or three Years and then
the Roots begin to rot they then come up best then stock them all up the other Wood will grow the better and they will pay you well for your Charge they will cost you about 6 s. a Stack and here they will be worth 12 s. or more when stocked up When you fell your Woods or Coppices cut them smooth and close to the Stub and a little slanting upwards as I advised you about Lopping Pollards the oftner you fell your Woods Coppices or Hedges the thicker they will grow for every felling gives way to the young Seedlings to get up and makes the weak Plants shoot strong Those Woods which increase by running Roots as Elm Cherry Popler Maple Sarvice c. which thicken your wood much And Felling makes the Roots of a tree to swell as Lopping doth the Body and so it produceth the greater shoots and comes sooner to perfection Whereas great wood and old and ill taken off from the Stub many times kills all When you fell your Woods leave young Trees enough you may take down the worst that stand next fall especially neer a great tree that you judge may go down next fall for by its fall it may spoyl some The Statute saith you are to leave twelve score Oaks at every Fall on an Acre for want of them so many Elms Ashes Beeches c. But leave according to the thinness of your wood and where underwood sells well there let your Timber-trees stand the thinner and in such Countreys where Coals are cheap and Timber sells well there let your Timber-trees stand thick and then they will need but little pruning up Endeavour to plant in your Woods such sorts of Wood as the Ground is most proper for if wet then Alder Sallow Willow Withy c. if shallow and dry Ash Cherry Beech Popler c. if shallow and wet Hornbeam Sallow Sarvice c. but remember that the Oak and Elm be entertained in all places If your Woods or Coppices be in Parks where you lye open to Deer then at every Fall plant in them such woods whose Barks the Deer do not much love such are the Hornbeam Hasel Sycamore c. When Trees are at their full growth there be several Signs of their Decay which give you warning to fell it before it be quite decayed As in an Oak when the top-boughs begin to die then it begins to decay In an Elm or Ash if their head dies or if you see they take wet at any great Knot which you may know by the side of the Tree being discolour'd below that place before it grows hollow or if hollow you may know by knocking it with the head of an Axe of which you may be the surer satisfied by boring into the middle of it with a small Auger or if you see the Nighills make holes in it these be certain Signs the Tree begins to decay but before it decayes much down with it and hinder not your self CHAP. XXXVII How to take the heighth of a Tree several wayes the better to judge the worth of them c. HAving shewed you how you may judge of Timber whether it be sound or not in the last Chapter I will now shew you how to take the heighth that you may the better know the worth of it for where you have a Rule to go by you may then the better ghess There be several wayes to take the Altitude of a Tree or Building that is perpendicular as by a two-foot Rule or two Sticks joyned in a right Angle that is square as the Figure A. B. C. having at A. a pin or hole to hang a Thred and Plummet on Suppose you were to take the height of X Y first then hold that end of your square marked with C. to your Eye then goe backward or forward till the Thred and Plummet hang just upon the middle of your Square perpendicular and your eye looking through two sights or two Pins at A. and C. or over the ends of the Square thus look to the very top of the Building at X. See Fig. 8 9. Which found with a Line and Plummet from your Eye at C let fall to the Ground at D measure the length of that Line and adde it to the height that Length to E then measure the distance from E. to the foot of the Altitude as at Y and that if your Ground be level is the height of of X. Y. Or take the Level from your Eye to the height and adde that which is below the Level to the Height c. as the Line C. F. sheweth To find the height of a Tree c. by a straight Staffe or by a Line and Plummet the Sun shining the Altitude perpendicular and the Ground Level if not you must make the end of both the shadows level to each foot which is soon done As if I should take the Level of B. at C. finding the very top of the shadow to End there I measure the Distance from C. to B. and find it 60 foot then at that very instant I set up a stick perpendicular as E. D. 12 foot long which I find to cast a shadow just 9 foot and then the Rule orders it self thus As 9 foot to 12 so 60 foot to 80 which you will find true if you work it by Logarithmes or by Rule and Compass thus Set one point on 9 extend the other to 12 that Extent will reach from 60 to 80 Or if you work it by Natural Arithmetick as 9 is to 12 so 60 to 80. See Fig. 10. The same may be done by Line and Plummet To take the Altitude or height by a Bole of Water or by a Lookingglass placed parallel to the Horizon Place on the Ground a Bole of Water or a Looking-glass at a convenient distance from the Building or Tree as far as you think the height is then go back till you espie in the middle of the Water or Glass the very top of the Altitude which done keep your standing and let a Plum-line fall from your Eye till it touch the Ground which gives the height of your Eye from the Ground 2. Measure the distance from your Plummet to the Middle of the water 3. The distance from the middle of the water to the foot of the Altitude Which Distances if you have measured exactly straight and level by Proportion you may find the Altitude required thus As the distance from the Plummet level to the Center of the Water or Glass Is to the height of your Eye from the Ground which is the Length of your Plum-line So is the distance from the Center of the Water to the Base or foot of the Altitude exact perpendicular to the very top of the height which gave the shadow to the Altitude for if your Object be not upright and you measure straight and level and just under the top that gave the shadow If you miss in any one of these you are quite out in taking the height
I take the mean Diameter to be 9 In. As 7 to 22 so 9 to 28 and 2 7 the Circumference of the hollow ¼ is 7 In. then as 12 to 7 so 12 foot to 4 and ¼ near which taken from 39 foot and ½ leaves 35 foot and ¼ for the sound Timber of that piece CHAP. XXXVIII Of making Walks Avenues or Lawns AS for making of Walks in Gardens I shall not speak of that in this place because I have resolved to keep my walk without the walls there are several Books of Gardening that have many Drafts and Knots in them but they be all done by ghess and none of them fitted to a scale to inform what Ground they be most proper for so that they be as fit for Butter-Prints as for Knots in a Garden Most Walks that are made abroad they either terminate or end or lead to the Front of a House or Door or Garden-gate or other Gate High-way or Wood c. Now if you would make a Walk from any one of these and have resolved upon the Center or Middle Line of the Walk as the Middle of a Door in the Front of a house or the like there pitch up a straight stake and then from the square of the Front c. raise a Perpendicular from this Stake and at a convenient distance in this perpendicular Line set up another stake let these two stakes be two little stakes at first but that at the Centre alwayes the highest these two stakes being thus fixed and you fully concluding them to be in the Mid-line then come to the Centre-stake and having in readiness a Quantity of Stakes according to the Length of your Walk bid one of your assistance go as far as you can well see back-sight and fore-sight and there by the motion of your hand or hat and his own back-sight let him fix upright one stake as exactly as may be in the Line then take up the two little stakes and at the Centre fix in a stake six foot high straight and upright with paper on the top and exactly in the place where the little stake stood Thus having got two stakes placed the Middle-stake and the Centre-stake you may if your Walk be level and the ground clear and the Walk not above one mile long set up one stake at the End in the mid-Mid-line looking over the head of that stake and the other moving it till these three stakes be in a Right Line so may you have the middle line of your walk by these three stakes exacter than by more for the fewer stakes you use in your mid-line the better because that if you be but once a little amiss the more stakes are used you will be so much the further out of the right way And note it is better to take your sight over the head of your stakes than to look by their sides therefore you must have the Center stake highest the next a little shorter and so the next shorter than that c. but if your Ground be not level then order your stakes accordingly as thus And if your Ground be not level or be of such a length that you cannot well see from End to End then you must place down more stakes viz. between the Middle-stake and Centre-stake one and between the Middle and End-stake one if need require more I have oft made use of a sight-stake which I had only to find the place where my other stakes should stand this stake was made with a slit in the head half a foot deep which I looked through over the heads of the rest till I found the place where to set my stake right in the Mid-line It is of good use and Fig. 13. may somewhat represent it you may make it to slide up and down the better to come to the Level of the head of the stakes See Fig. 13. When you take sight to set any stake true in a Line with others stand at a little distance with your Eye from the head of the stake so shall you set it Exacter in the Line than when your Eye touches the head of the stake set your stake so that you may onely see three stakes in a Line let your Walk be of what length it will Having thus staked out your Mid-line strain a Line in this Mid-line and lay a square to that Line so set off the breadth of your Walk exactly square to your Middle-line then set up stakes as you did against every stake in the Middle of the Walk and when you have got the Lines true where your Trees must stand then drive down Oak-stakes in the Line to the head and then it is but putting down high stakes by these when you come to set your Trees Then having resolved on the distance to set your Trees at and provided good store of small stakes take your Chain and not a Line for that will retch and shrink and with your help set little stakes downright in this Line and square where you would have every Tree to stand these stakes are to make your holes by which I would have at least three foot wide and two foot deep and the holes made a Quarter of a Year before you set your Trees if it were a year 't were the better keeping the Mould turn'd over now and then and mixing it with Earth or Dung if need be then when the time of Planting is come begin betimes however on dry ground set up Stakes by every Oak-stake you left in the Row before having pruned the Roots and Heads to an equal height set them right one Tree against another square And if your Trees be not all of one Size set the greatest first right one against another and so lesser and lesser by degrees minding that both Rows go on square together and be sure you mind to let your Trees be at equal distance from End to End then if you have a point fixed at both Ends you must run over that distance you resolve to plant your Trees at before you set your Stakes and if you find it is over or short of equal distances then must you adde or substract this odde open to or from the rest to make them all of equal distance See Chap. 33. Now having your Trees and all things in Readiness set them by the Stakes standing in the Rows minding to set every Tree to range with the Stakes by back-sight and fore-sight Cover and part the Roots with fine Mould and when they be all covered lay on some Rotten Dung over that Mould and then cover that Dung with a little Mould this Dung will keep them from friezing in Winter and from drying too much in Summer and also well prepares the water for the Roots Thus having set them take care to fence them in at such places where need is so will you as well as I reap a great satisfaction if you let not the Dung touch the Roots Do not mask a fine Front nor vail a
a mile two Trees as at Figure 2 is ½ a mile three Trees as at Figure 3 is ¾ of a mile See Fig. 21. Though the Figure doth not show well because the smallness of the Paper will not allow Room to draw the distance of miles as the Trees are according to Scale though my scale is here for the distance of the Trees 160 foot for one Inch yet I presume where this is really acted in Walks it will do well I here begin at the Centre-tree in the Semi-circle and in the Right-hand Row shewing how the ¾ of the mile may be set out and shewed by the Semi-circles on the sides at the other End I begin at the Centre of the Circle and so shew the ¼ ½ and ¾ how they may be set out on the other side Or if you please you may have a Tree in the mid-Mid-line of your Walk at every quarter of a mile with a Circle to break round that Tree three times the breadth of the Walk which Tree must be pruned up high or else it will hinder the Prospect of your Walk I fansie the other way is best as let a Tree stand at every ¼ of a mile as you see in the Figure See Fig. 22. Thus having shewed you how Walks may end in Circles or Semi-circles I shall now shew how Walks may end or come into an Oval and how it sometimes happens that an Oval is the best Figure that Walks can End in If three Walks meet acutely at one place then it will be necessary to have the mid-Mid-line of the three Walks meet at a Tree in the side of an Oval for if you make that poynt the Centre of a Circle it will be too large 't is possible larger than your Ground will permit as at Cashiobury where the three Walks meet by Hemsted High-way for if I had made the Circle from the aforesaid Centre and made the Semi-di3ameter so large as to have in the Circumference the two Trees marked A. A. which rangeth for both Walks then would this Circle have been too great and beside could not be made within the Pale Now I having Orders from my Lord that the Mid-line of these three Walks should meet at a Tree as in Fig. 23. they doe at B. and that I should make the Figure so large as that the Wood which is between the Middle-walk and the two out-side Walks should end at a Tree which should stand exactly in the Range of Trees for the Middle-walk and also for the in-side Rows of the two out-walks by considering I found the Oval to suit best with this ground so I having these two Trees as at A. A. and the Poynt as at B. which I took for the Breadth of the Oval accordingly I made it See the Figure Length of the Oval is 205 foot Breadth 124 foot Middle-walk 50 foot the side-walks each 40 foot wide having wood between the VValks and round the Oval See Fig. 23. Now having the two Trees as at A A. and the Centre-tree of the three Walks B. from the Mid-line of the middle-walk and in the middle of that Line between A A. and B. draw a perpendicular Line which sheweth the Length of the Oval at each End set a Tree as C. C. then divide the distance between the Centre-tree at B. and the End-trees at C. C. which let be at such a distance as may best suit with the six Trees between D. and C. on each side here the Trees between B. and C. are ten foot ten Inches distance and the Trees between D. and C. are 10 foot 9 Inches distance Let alwayes the Trees that make either Oval or Circle stand pretty nigh they shew this or any other Figure the better For this no certain distance can be given but they must be set at such a distance as the Arch-line can be divided into c. I shall shew you how to know the Length of an Arch-line and how to make an Oval or other Figure hereafter This Oval and Walks are surrounded with Wood and also between the Walks ending at a Tree as at A A. you may make broader at your pleasure or you may alter the Oval in shape or bigness as your Ground and Fancy shall direct you Your Oval may be surrounded with a double or treble Row of Trees if you fansie it and indeed if it be in a place where it is not encompassed with wood it is very proper An Oval or a Circle are very good Figures for Ponds though they be not in use Now for making Walks to end in a Triangle this may be several wayes according to your Fancy or Ground But I confess I never yet saw or heard of any Walk in England or elsewhere that ended in such a Figure But why may not the best of Figures be neglected by the Ingenious Survey or both at home and abroad as well as we see many Excellent things known to several ingenious men which are practised by few Having made at the End of Walks Semi-circles Circles and Ovals of several sorts and notwithstanding that I had at the end of the three VValks that goe from the Garden to the Bowling-green that end next the Garden a Figure given me by a worthy person but how proper for that place I shall not now speak I nevertheless neglected that and made the Triangle as is shewed by Figure 24. The trees I set the closer because this being a Front of the house intended to be hid at a distance all but the breadth of the VValks therefore I chose this Figure as much proper for such a design See Fig. 24. This Line according to Scale is the Length of the Garden-walk the Break in the middle against the great Walk is a Grate which is intended to front it This Figure might be much improved if it were made a little larger so that the inner Row of the Triangles might range a little without the End of the Garden wall and at that end a walk to take it to goe by the Garden-side so might you have a convenient by-way without the VValls from the 20 foot VValk along either VValk of the Triangles to the walk by the Garden-side c. There are several other sorts of Triangles proper for VValks to end in but for Shade I preferre this or the next following if you would have the Trees to shew the shape of their heads then a single Row is best as the out-Row of the Triangle-walk See Fig. 25. For a Court you would have shaded with Trees this Figure will do well In this last Figure you may let the little VValk end Parallel with the VVall and have no VValks by the side-walls or you may make onely one VValk on each side As for making of the Triangle at the End of your Walk it may be Analogically according to your Ground though these two be made obtuse the perpendicular half the Length of the Base there be several sorts of Triangles or triangular Figures
Angle for 10 times 10 is a 100. and 6 times 6 is 36. and 8 times 8 is 64. so 36 and 64. make 100. equal to the subtended square There be several other ways to Raise a Perpendicular at the end of a Line but this being so easie and the most useful I shall not name any other CHAP. XL. To Divide a Right Line given according to any Proportion Required and how to Divide Land or Woods with some Vses of the four-pole Chain THE Line A is Required to be Divided into two such parts which shall have proportion the one to the other as the Line B. hath unto C. See Fig. 36. Make an Angle of any Quantity as A. B. C. and let the side A. B. be Equal to the given Line A. then set the Line C. from A. to E. and the Line B. from E. to C. and from the point E. draw the Line E. D. parallel to C. B. cutting the Line A. B. in D. so shall B. D. bear the same proportion to D. A. as the Line B. hath to the Line C. this is the Golden Rule by Lines To Divide a Right Line in Power according to any Proportion given See Fig. 37. Draw the Line C. D. Equal to the two Lines A. B. then Divide the said Line in the point F. in proportion as A. to B. then in the middle of the Line C. D. Describe the Semi-circle C. E. D. and on the point at F. Raise the Perpendicular F. E. cutting the Semi-circle in E. from that point draw the lines E. C. and E. D. which two Lines together shall be equal in power to the given Line and the power of the Line E. C. shall be in such proportion to the power of the line E. D. as A. to B. Many Men when their Woods are felled sell their Wood by the Acre or half-Acre or sometimes two or three Acres and sometimes Men Let their Land to Plow by the Acre and sometimes Men purchase part of a Field by the Acre I will here shew you how you may cut off parts of an Acre or several Acres from a Field or how far you must go in a VVood or Field to make an Acre more or less of several Figures which will be Useful to be known of most Men for several other Occasions Suppose a VVood or part of it should be in a Triangle as the Figure following which should contain 745 pole 42 100. that is 4 Acres 105 Pole and near a ½ Of this VVood there is Sold 2 Acres which is to be taken off from the Angle C. and to cut the line A. B. having Measured your Triangle and found it as above-said and also the Base-line to be 84 pole then by the Rule of Three work it thus See Fig. 38. If 745 ' 42. the Content of the whole Triangle have for its Base 84 Pole or Rods what shall 320 pole have for its Base that is 2 Acres See it wrought by Logarith Here you see that this Log. gives 36 pole and 6 100. so that you must go 36 pole and little more on the Base-line A. B. from A. to D. for your 2 Acres then the Angle A. C. D. is the two Acres or 320 Pole and the Angle C. D. B. is 2 Acres 105 pole and near ½ a pole By the same Rule may you cut off what Number of poles you please from the Angle D. to fall upon the Line C. B. or to fall upon the Line D. B. having but the length of the Lines given you But if it be Required to take off a part from a Triangle according to any proportion given by a Line drawn parallel to any of the sides assigned As let A. B. C. be a Triangle containing 5 acres and it is desired to cut off 2 acres by a Line drawn parallel to A. B. first on the Line A. C. draw the Semi-circle A. E. C. and the Diameter C. A. Divide into 5 equal parts and from the point of 3 of these parts of that Line draw the perpendicular D. E. to cut the arch-line in E. then set the length of C. E. from C. on the Diameter-line and it will reach to the point F. then from that point at F. take the nearest distance to the Line A. B. and set that distance off from B. to G. then draw the Line F. G. exactly parallel to A. B. so will the Triangle C. G. F. be 3 acres and G. B. A. F. 2 acres the thing propounded See Fig. 39. This Rule in it self is exact but in a large Field or Wood it is difficult to be done because the Semi-circles and other Lines are very hard to be drawn exactly But if your Field or part of it be a square and you are to take off some parts of it you may do it to any Number of Rods desired easily and exactly thus Let the Field be never so great Measure you onely that side of the Square whence you are to take off your part exactly See Fig. 40. Examp. It is Required to cut off 2 acres or 320 Pole from a Field or part of one that is in form of the Square A. B. D. C. with a Line drawn parallel to the side A. B. Now finding the side of the Square to be 32 Pole Divide 320 the parts you are to cut off by 32 the side of the Square and the Quotient will be 10 then set off 10 Pole from A. to E. and from B. to F. and the Square A. B. F. E. is 2 acres as was Required This is very Useful for several Men and readily to be performed but if these sides A. C. or B. D. do not go Square from the end A. B. then must you find the mid-mid-line of the Square you are to take and Divide the Summe of Poles you are to take off by that the first Example will assist you to find this mid-line and somewhat help you in the working This being such an usefull Prob. I shall shew you how to perform it another way as in the last Examp. the side of the square 32 Pole and you know 160 Pole make one Acre then divide 160 by 32 the side of your Square the Quotient is 5 which tells you that you must measure 5 Rod or Poles from the side of your Square on each End to make one Acre 10 Pole for two Acres 15 Pole for three Acres c. which you see agrees with the former Rule But if it be required to take off the parts of a Square and to have those parts in a Triangle then the first and second Figures will assist you how to perform that To divide an Irregular Figure into any parts required that is to take what number of Rods you please from such a Figure As if A B C D E. be the Figure of a Field or Wood and it is desired to take off the half of it from the Angle at A. the whole Figure is 705 Pole then the half is 352.50 and the Triangle A
D E. is but 290 Pole which wants 62 Pole and a half of the half of the Field therefore take 62. 50 from the Triangle A C D. by the Rules delivered in the 38 th Fig. and there will be added the Triangle A D H which being added to the Triangle A D E will divide the Figure into two equal parts the thing desired See Fig. 41. Thus may you take half from any irregular Figure or more or less than half and from what Angle desired which will assist you well how to fell your Woods by the Acre or to know how far you shall go into a Field to take off any parts the fourth Rule which I found by my Practice I commend for very good One Example I shall give you more which shall be according to my fourth Rule I try'd it in a Field near to Cashiobury-Park this I was ordered to doe by my Lords Steward Mr. Sydenham to take off three Acres from a small Field as exactly as I could at one End appointed by him First I measured that End and found it to be 37 pole and ¾ but observing the Hedges I found them to splay off a little so that about 6 Rod and a half or little more would be the middle which I set off at each End and found that Line to be 38 Pole long then I divided 160 the Poles in one Acre by 38 the Poles of the End of the Field the Quotient was 4 and 8 38 which 8 of 38 I must turn into parts of my Chain that is into Decimal parts thus As 38 is to 8 so is 100 to 21 and 2 of 38 which 2 is not considerable So that if the Chain be divided into 100 Links you must then goe 4 Pole and 21 Links at each End for to make one Acre of Ground but if your Chain be a four pole Chain divided into 100 Links then with such a Chain you must goe 4 pole 5 links and ¼ and a little more to make one Acre at 38 Pole long Then for three Acres I must goe in breadth 12 Pole 63 100 to make three Acres and a little more see it proved Here you may see that 12 Pole 63 100 multiplyed by 38 Pole gives 479 Pole and 94 100 which being divided by 160 the Poles in one Acre gives in the Quotient 2 and 159 so then if you adde but 6 of 100 to the 94 it is just three Acres for whereas I take in the Decimal parts but 21 100 I should take the 21 Links and the 22 th part of one of these Links which niceness may be dispensed with From what hath been said you may measure any standing Wood or part thereof especially if these parts be near to a Square or Triangle if not you may Reduce them to one of these Thus having spoke something how superficial Figures are to be measured I shall give an Example or two of the Chain and it shall be of the Four-pole Chain divided into 100 parts as suppose the Figure A B C D. See Fig. 42. This Figure may be measured several wayes as first it may be put into two Triangles and so measured or else you may measure both the Ends and half them and so measure the Length in the middle you may measure also both the sides and half them and then measure the breadth in the middle But for Example First I measure the side A B. and find it to be 15 Chains and 80 Links of the Four-pole Chain the End B C. is 6 Chains 74 Links the other side C D. is 12 Chains 50 Links and the other End D A. is 6 Chains Then adde the two sides together of which take the half that half is the mean Length both sides added together make 28 Chains 30 links half of which is 14 Chains 15 links then adde the Ends together viz. 6 Chains and 6 Chains 74 links the total of both is 12 chains 74 links then half of the Ends added together is 6 chains 37 links Then multiply the mean Length by the mean Breadth and cut off 5 Figures to the Right hand and whatsoever Figures Remain to the Left hand are Acres and those 5 Figures cut off are parts of an Acre Thus may you know the Content of a Field without Division as in the last Examp. 14. 15 multiplyed by 6. 37 gives 901355 then if you take off five figures as the fractional parts there remains 9 which is nine Acres two Pole and above ⅛ of a Pole But you may easily know the fractional part of any Decimal fraction thus This belongs to 100000 for if the Decimal fraction have 5 Figures the Integer is 6 the fraction 4 then the Integer 5. c. Then work it by the Rule of Three or by your Line of Numbers thus As 100000 is to 1355 so is 160 the square Poles in one Acre to 2 Poles and neer ¼ but that you may be the better satisfied in this most useful Rule if 100000 be Equal to one Acre or 160 Pole So that when any Fraction is repair but to these Rules and you may see what Number of poles is equal to it you may proportion it to half-poles c. for Not onely to prove this but also to shew you how much readier this way is than the 100 Links to bring it into Rods or Poles then divide it by 160 to bring the aforesaid Measure to the one Pole Chain and 100 multiply 14. 15 by 4 it gives 56. 60 and 6. 37 multiplyed by 4 gives 25. 48 which being multiplyed one by the other gives 1442 1680 10000 I will neglect the Fraction as being not ¼ of a Pole and divide 1442 the Poles in that Measure by the sq Poles in one Acre 160 Pole and the Quotient is 9 and 2 over that is 9 Acres 2 Pole and a little more as before But how much the other way is readier than this I leave the Reader to judge Example the Second How to measure a Triangle with the Four-pole Chain and never use Division As in the Triangle A B C. the Base A C. is 40 Pole and the pricked Perpendicular Line is 20 the half is 10 Pole Now when you have even Poles as in this Examp. you must adde two Cyphers to the length and two to the breadth or else you cannot take off the 5 Figures or 5 Cyphers as is before shewed then taking the 5 Cyphers off after Multiplication there remains 40 which sheweth you that such a Triangle that hath such a Base and such a Perpendicular containeth four Acres of Ground And if you work it the common way you will find it to be true See Fig. 43. But to assist you yet further to turn  M. C. X.  ac ro p. ac ro p. ro po 1 6. 1. 0 0. 2. 20 0. 10 2 12. 2. 0 0. 1. 0 0. 20 3 18. 3. 0 1. 3. 20 0. 30 4 25. 0. 0 2. 2. 0 1. 0 5 31. 1. 0 3. 0. 20 1. 10
three Inches and 078 1000 make one Foot take with your Compasses three Inches 078 from off a Scale and so many times as there is that Length in your Tree so many foot of Timber are there c. If any Tree be above 100 Inches Circumference then take half that Circumference and find the Number belonging thereto in the Table then take one fourth part of it and that makes one foot of Timber Suppose a Tree to be 146 Inches about the half of it is 73 against this in the Table is 4 Inches 075 parts one quarter thereof viz. one Inch 019 parts makes one foot of Timber at that Circumference These Tables with what hath been before said will be sufficient to measure any Cylinder by and how to measure a Cone I have shewed already A Cone is such a Figure as the Spire of a Church having a Circular Base and ending in a sharp point It is measured by the superficial Content of the Base multiplyed by one third part of the Altitude or Length A Pyramid or Pyramis is such a Figure as hath an angular Base and ends in a sharp point which is measured as the Cone is A Sphear or Globe is a solid Figure every where equally distant from the Centre it is measured by cubing the Diameter and multiplying that by 11 and dividing that product by 21 the Quotient sheweth the solid Content of the Sphere There be several other sorts of solid Figures as several parts of the Sphear but they all depend on the proportion of a Circle and its Diameter Also the Hexaedron which hath 6 Bases Octaedron 8 Bases Dodecaedron 12 Bases and several other which to name I shall forbear CHAP. XLIII Of the Oval how to make it and how to measure it with other Observations thereon HAving the Length and Breadth of the Oval given you you may take the whole Length and half the Breadth as is shewed before in bringing three Pricks into a Circle and from the Centre of these three poynts draw half the Oval and so likewise the other half as you see the Oval in the Figure drawn for the poynt F. is the Centre of the Arch A B C and the Arch A G C is made by the same Rule and where the Line F H. crosseth the Line A E C as at K there is the Centre of the breadth B G and the End A from the Centre K may you make the Ends of your Oval Round as you please so that from four Centres you may make the Ends of your Oval round as you please but if they be made from two Centres as that is then will the Ends be more Acute Or you may make your Oval thus Having resolved on the breadth draw the sides from Centres in the mid-Mid-line of the breadth as before then set up two sticks exactly in the Mid-line of the Length at equal distance from each End then hold the Line at one and turn the Line to the side of the Oval and then on the other side the stick with the same length so may you make the Ends of your Oval as Round as you please for the nearer you place these sticks in the Centre of the length and breadth of the Oval the nearer Round your Oval is made even till you come to a Circle This way your Ingenious Work-men make their Ovals in small works as your Plaisterers Joyners c. and it is a good way and so common that I need not say more to teach how to make an Oval of any bigness but here I shall take occasion to shew the Figure of one at Cashiobury now made See Fig. 46. To measure this Oval which is 28 Rod long and 19 Rod broad as 't is now staked out at Cashiobury intended for a Kitchen-Garden This Oval being made of 2 Segments of a Circle whose Semi-diameter is 15 Rod as 't is found by making the Oval it being the Centrepoynt of each Arch-line of this Oval as the lines F A. F B. and F C. Now to find the length of one of these Arch-lines is shewed before which I find to be 18 Rod the half length of one which is shewed by the line D D. so the whole length of one Arch is 36 and both Arches round the Oval is 72 Rod. Now take the ½ of one of the Arch lines which is 18 and the Semi-diameter of that Arch which is 15 Rod Multiply the one by the other and it is 270 Rod which is the Figure A. B. C. F. that is half of the Oval and the Triangle A. F. C. which must be substracted out of the 270 then the Semi-Oval will be 192 Rod. For the Base A. C. is 28 Rod which is the length of the Oval and the Perpendicular of the Angle which is E F. is 5. 57. Now half the Base which is 14 Multiplied by the whole Perpendicular 5 57 100 gives 77 98 100 which is 78 Rod ferè this taken from 270 the Area of the Figure A. B. C. F. there then remains 192 Rod which is half of the Oval that doubled is 384 Rod which being Divided by 160 sheweth that the Content of this Oval will be 2 Acres and 64 Rod. But if your Oval be round at the end as your Ovals are that be made with 4 Centres then they be more difficult to be Measured however these Rules are sufficient An Oval is no ill Figure for a Garden for if the Garden-wall be an Oval and the length of the Oval point North and South as the afore-mentioned Oval doth A. being the South point C. the North then may such a Wall be Planted with Trees both in-side and out-side and have never a Tree stand to the North Aspect for it you make your going in at the South end of your Oval then will those 2 Trees or Tree that stood on the in-side or were to stand there be removed from the North aspect to the North-East and North-West according to the largeness of your Gate so will every 2 Trees on the in-side of your VVall tend nearer the South-point till they come to the point C. which is South and then the Trees on the out-side every 2 Trees will fall nearer the North-point at C. till you leave that point of the Oval between 2 Trees so will not one Tree stand to the North aspect and but few near the North aspect the like whereof no other Figure can do that I can think of An Oval with the ends pointing East and VVest is no ill Figure for a Garden for the walls in this as in the other are not so subject to oppose the winds as straight walls be therefore not so blasting as you may well conceive 2. Ovals on each side the Front of your House would be no ill Prospect but in many things very convenient these being at equal distance from the middle of your Front and poynting upon your Lawn c. CHAP. XLIV Suppose you have a Plat to draw on one or many Sheets of
is the Root divide the Distance from 64. to one into 3 equal parts one third part of that distance will reach from one to 4 the Root for the first third part will reach from 64 to 16 the square the 2d third part from 16 to 4 the Root the third part from 4 to one for 4 times 4 is 16 and 4 times 16 is 64 the same Rule observe for any other number Thus may you find the square of any Circle or the end of a tree the square equal to that Circumference and so measure it as is before shew'd Example 12. Having the Circumference of a Tree you would know the side of a Square equal to that Circumference as in the 10th Example the Circumference was 60 Inches now to find the Content in superficial Inches of such a Circle the Rule is as is before shewd as 22 is to 7 so is the Circumference to the Diameter now if you Extend your Compasses from 22 to 7 that Extent will reach from 60 to 19. and 2 22 the Diameter this Fraction may be turned into a Decimal Fraction and so wrought but being so small it is not worth minding in such operations as this then if you take half the Diameter and ½ the Circumference and multiply one by the other or if you Extend your Compasses from one to 9 and ½ that Extent will reach from 30 to 285 the superficial content in Inches then to find the square by the Line of Numbers that is to finde a Number which if Multiply'd in its self makes this Summe the Rule is Extend your Compasses from 285 to one and the middle between these 2 Numbers is 16 882 1000 very near as here you may see but first note that if your Rule have but the Lines on it that most of your ordinary Rules have that is but 2 Lines on it as 1. 2. 3. 4. 5. 6. 7. 8 9 and 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 then this Question may be some trouble to work on such a Rule but if your Rule hath 4 parts or 6 parts as a 6 foot Rule may have then this Question may be performed very readily as you may hereafter better perceive for if you take 285 in the second part of the Rule then is the middle figure one a 100 and the figure one at the end is 10 and the Rule is that you must take the middle between 1 and 285 which here you cannot for if you count the first one one the middle one is then 10. and the end one is 100 so then 285 is off from the Line whereas if your Rule had another part added to it then might you work and read it very readily But to work it by this Rule you must take the distance from 100 to 285 that is from the middle one to 285 then take half of this distance and add it to half the length of the Line and the Compasses will reach from 10 in the middle to near 17 the side of a square equal to 285 as you may see it here proved by the pen. Here you may see that 16 882 1000 Multiplyed by 16 882 1000 gives 285 and 001924 1000000 which Fraction being so small is not considerable Many other wayes there be to measure a Cyllinder but this after you have found the side of a square equal to the Circumference Multiplyed by the length is sufficient c. CHAP. LI. Division on the Line THe Rule is as one is to the Divisor so is the Dividend to the Quotient or as the Divisor is to the dividend so is to 1 to the Quotient Example 280 being to be divided by 5 set one foot of the Compasses on 5 and Extend the other to one that Extent will reach from 280 to 56 the Quotient Or thus Extend the Compasses from 5 to 280 that distance will reach from 1 to 56 the Quotient Example 2. 260. divided by 5 2 10 Extend the Compasses from 5 2 10 to 260 that Extent will reach from 1 to 50 the Quotient By these Rules may you work any other Question in Division for Division is easier than Multiplication for in this having the Sums given you look for less and in Multiplication the Sums being given you may seek for greater CHAP. LII The Rule of Three on the Line THis Rule which by most is called the Golden Rule for its Excellent uses is performed with much ease only by 2 turns of your Compasses and in working differs little from Division The Rules are if 4 Numbers are proportional their order may be so transposed that each of those terms may be the last in proportion in this manner 1. As the first is to the second so is the third to the fourth 2. As the third is to the fourth so is the first to the second 3. As the second is to the first so is the fourth to the third 4. As the fourth is to the third so is the second to the first See Mr. Oughtreds Circles of proportion pag. 77. So that four proportional Numbers being desired to be known if any three be given you may find the fourth As if 2 8 6 and 24. be the Numbers given these Numbers may be so varyed as is aforesaid that if any three be given you may find the fourth Note First If 2 costs gives or requires 8 then 6 costs gives c. 24. Secondly If 6 gives 24 then 2 will give 8. Thirdly If 8 require 2 then 24 will require 6. Fourthly As 24 is to 6 so is 8 to 2. Fiftly Or thus it may be as 2 to 6 so is 8 to 24. Here are five wayes that will teach you if you have three Numbers given to find out the fourth proportionable to them but the first and last are most useful and are many times good proofs one of the other Example If 2 of any thing cost 8 sh then 6 will cost 24. s. for if you Extend your Compasses from 2 to 8 that same distance will reach from 6 to 24 the Question or if you Extend your Compasses from the first Number to the third Number that same Extent will reach from the second number to the fourth which was the thing sought Extend your Compasses from 2 to 6 that same Extent will reach from 8 to 24 the Question as before c. Example 2. If you sell your timber by the Load that is 50 foot to the Load ' at any price to know what it is a foot as if you sell for 25 shillings the Load what is that a foot First know how many pence is in 25 shillings because your foot will cost pence and not a shilling 25 shillings is 300 pence then the Rule orders it self thus as 50 to 300 so is one to 6 therefore Extend your Compasses from 50 to 300 that distance will reach from 1 to 6 so then one foot costs 6 pence the Question If you would know the price of 2 Foot then set one poynt of your Compasses on