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-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-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-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
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
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-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
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