Selected quad for the lemma: land_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
land_n	line_n	page_n	read_v	2,533	5	12.1252	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29761	The description and use of the trianguler quadrant being a particular and general instrument, useful at land or sea, both for observation and operation : more universally useful, portable and convenient, than any other yet discovered, with its uses in arithmetick, geometry, superficial and solid, astronomy, dyalling, three wayes, gaging, navigation, in a method not before used / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5041; ESTC R15524	175,812	507

what ibid. Circles of Position what ibid. Of Terms in Astronomy What a Sphear is Page 50 Of ten Points and ten Circles of the Sphear Page 51 The 2 Poles of the World or Equinoctial ibid. The 2 Poles of the Zodiack Page 52 The 2 Equinoctial-points ibid. The 2 Solstitial-points Page 53 The Zenith and Nadir Page 54 The Horizon the Meridian the Equinoctial the Zodiack the 2 Colures the 2 Tropicks and 2 Polar Circles Page 55 56 58 Hours Azimuths Almicanters Declination Latitude Longitude Right Ascention Page 59 60 Oblique Ascention Difference of Ascentions Amplitude Circles and Angles of Position what they are Page 61 62 To rectifie the Trianguler Quadrant Page 63 To observe or find the Suns Altitude Page 64 To try if any thing be level or upright Page 66 To find what Angle the Sector stands at at any opening or to set the Sector to any Angle required Page 67 68 The day of the Month given to find the Suns Declination true Place Right Ascention or Rising and Setting by inspection only Page 71 To find the Suns Amplitude and difference of Ascentions and Oblique Ascention Page 73 To find the Hour of the Day Page 74 To find the Suns Azimuth Page 75 The use of the Line of Numbers and the use of the Line of Lines both on the Trianguler Quadrant and Sector one after another in most Examples To multiply one Number by another Page 78 A help to Multiply truly Page 85 A crabbed Question of Multiplication Page 90 Precepts of Reduction Page 94 To divide one Number by another Page 95 A Caution in Division Page 97 To 2 Lines or Numbers given to find a 3d in Geometrical proportion Page 98 Any one side of a Figure being given to find all the rest or to find a proportion between two or more Lines or Numbers Page 99 To lay down any number of parts on a Line to any Radius Page 100 To divide a line into any number of parts Page 102 To find a Geometrical mean proportion between two Lines or Numbers three wayes Page 104 To make a Square equal to an Oblong Page 107 Or to a Triangle ibid. To find a Proportion between unlike Superficies Page 108 To make one Superficies like another Superficies and equal to a third Page 109 The Diameter and Content of a Circle being given to find the Content of another Circle by having his Diameter Page 111 To find the Square-root of a Number ibid. To find the Cube-root of a Number Page 113 To find two mean Proportionals between two Lines or Numbers given Page 116 The Diameter and Content of a Globe being given to find the Content of another Globe whose Diameter also is given Page 118 The proportion between the Weights and Magnitudes of Metals Page 119 The Weight and Magnitude of a body of one kind of Metal being given to find the Magnitude of a body of another Metal of equal weight Page 121 The magnitudes of two bodies of several Metals having the weight of one given to find the weight of the other Page 122 The weight and magnitude of one body of any Metal being given and another body like unto the former is to be made of any other Metal to find the diameters or magnitudes of it Page 123 To divide a Line or Number by extream and mean proportion Page 124 Three Lines or Numbers given to find a fourth in Geometrical proportion Page 128 The nature reason of the Golden Rule Page 129 The Rule of Three inversed with several Cautions and Examples Page 132 The double and compound Rule of Three Direct and Reverse with Examples Page 139 The Rule of Fellowship with Examples Page 148 The use of the Line of Numbers in Superficial measure and the parts on the Rule Page 154 The breadth given in Foot-measure to find the length of one Foot Page 156 The bredth given in Inches to find how much in length makes one Foot ibid. The bredth given to find how much is in a Foot-long Page 157 Having the length and bredth given in Foot-measure to find the Content in Feet ibid. Having the bredth given in Inches and length in Feet to find the Content in Feet Page 158 Having the length bredth given in Inches to find the content in superficial Inches Page 160 Having the length bredth given in Inches to find the Content in Feet superficial Page 161 The length and bredth of an Oblong given to find the side of a Square equal to it Page 163 The Diameter of a Circle given to find the Circumference Square equal Square inscribed and Content Page 164 The Content of a Circle given to find the Diameter or Circumference Page 166 167 Certain Rules to measure several figures Page 108 A Segment of a Circle given to find the true Diameter and Area thereof Page 169 A Table to divide the Line of Segments Page 170 The use of it in part Page 171 The measuring of Triangles Tapeziaes Romboides Poligons and Ovals Page 172 173 A Table of the Proportion between the Sides and Area's of regular Poligons and the use thereof for any other Page 174 175 To make an Oval equal to a Circle and the contrary two wayes Page 175 176 The length and bredth of any Oblong Superficies given in Feet to find the Content in Yards Page 177 The length and bredth given in feet and parts to find the Content in Rods Page 179 The nearest way to measure a party Wall Page 180 To multiply and reduce any length bredth or thickness of a Wall to one Brick and a half at one Operation Page 183 Examples at six several thicknesses Page 184 To find the Gage-points for this reducing Page 185 At one opening of the Compasses to find how many Rods Quarters and Feet in any sum under 10 Rods Page 186 The usual and readiest equal wayes to measure Tileing and Chimnyes Page 187 Of Plaisterers-work or Painters-work Page 188 Of particulars of work usually mentioned in a Carpenters-Bill with Cautions Page 189 190 At any bredth of a House to find the Rafters and Hip-rafters length and Angles by the Line of Numbers readily Page 191 The price of one Foot being given to find the price of a Rod or a Square of Brick-work or Flooring by inspection Page 193 At any length of a Land given to find how much in bredth makes one Acre Page 194 A useful Table in measuring Land and the use thereof in several Examples Page 196 197 The length and bredth given in Perches to find the Content in Squares Perches Poles or Rods Page 200 The length and bredth in Perches to find the Content in Acres ibid. The length and bredth given in Chains to find the content in square Acres Quarters and Links Page 201 To measure a Triangle at once without halfing the Base or Area ibid. To reduce Statute-measure or Acres to Customary and the contrary ibid. A Table to make Scales to do it by measuring or inspection with Examples Page

stor'd As first with Gunters Sector and his Quadrant eke also By Foster altred after and with Gunters Rule and Bow The Traviss Quadrant and Cross-staves the Davis Quadrant too Their uses all to more than halfs this Instrument will do With this advantage more beside of lying in less room A fault that Saylors must abide when they on Ship-board come In the next place the Rudiments of Geometry exact The right Sines ●heir complements and how they lie compact Within a Circle and the rest the Chords and versed Sines About a Circle are exprest the Tangents Secants Lines And how their use and place is seen in Round and Plain Triangles Which serve to deck Urania Queen as Iewels Beads and Spangles In the next place Arithmetick by Numbers and by Lines In wayes that won't be far to seek by them that use their times Because the Precepts are explain'd by things of frequent use That for the most part are contain'd in City Town or House As Land and Timber Boards Stones Roofs Chimneys Walls and Floor Computed and reduc●d at once in Thickness Less or More The cutting Platoe's Bodies five which are not yet made six And them the best way to contrive and Dials on them fix Their Measure and their Magnitude in Circle circumscribed Whose Properties by old Euclide and Diggs have been described Then also in Astronomy are many Propositions Which fitly to th' Rule I apply avoiding repetitions And after in the pleasant Art of Shadows I do wander To draw Hour-lines in every part both upright over and under And all the usual Ornaments that on Sun-Dials be Which are describ'd to the intent Sol's travels for to see As first his Place and Altitude his Azimuth likewise His Right Ascention Amplitude and how soon he doth Rise The same also to Moon and Stars is moderately appli'd Whereby the time of Night appears the Moons Age and the Tide Then Heights and Distances to take at one or at two Stations Performed by those wayes that make the fewest Operations And also ready Rules to use the Logarithmal Table Which may prove ready Hints to these that are in those most able And many other useful Thing is scattered here and there Which formerly by Me hath been accounted very rare And lastly for the Saylors sake I have spent many an Hour Th' Trianguler-Quadrant for to make more useful than all other Sea Instruments that they do use at Sea for Observation And sure I am it won't abuse them in their Operation As in the following Discourse to them that willing be It will appear with easie force if they have eyes to see The Method and the Manner us'd as neer as I was able To follow the old Wayes still us'd and counted warrantable And in this having done my best 〈…〉 up my male Ascribing to my self the least would have the Truth prevail And give the honour and the praise to him that hath us made Of willing minds his Fame to raise by his assisting aid To whom be honour now and eke henceforth for evermore Ascribed by all them that seek the Truth for to adore J. B. ERRATA PAge 28. line 8. for Rombords read Romboides P. 73. l. last f. 337 r. 247. p. 75. l. 1. f. 7. r. 8. p 87. l. 14. r. multiplied by p. 89. l. 14. f. 5 371616. r. 538.1616 l. 21. f. 537 r. 538. p. 90. l. 4. f. 537 r. 538. l. 5. add being better done with a parallel answer p. 100. l. 2 add the Thred p. 128. l 2. dele 10 min. p. 133. l. 6. f. 60 r. 16. p. 143. l. 10 11. f. from 12 to 7 r. from 7 to 12. p. 146. l. 22. f 12 Section r. 13 Section p. 158 l. last dele and. p. 160. l. 11. f. 72 r. 720 also in line 15 23. p. 164. l. 19. f. Diameter r. Area p. 165. l. last add to 707. p. 184. l. 10 f. foot r. brick l. 20. f. ½ r. 1 ½ p. 187. l. 17. f. Ceiling r. Tileing p. 201. l. 11. f. 52 Links r. 55 Links l. 12. f. 48 Acres r. 4 Acres 3 Roods 8000 Links p 102. l. 5. f. 21 Acres 42 Links r. 2 Acres 0 Roods but 14760 Links read so likewise in l. 11. of the same page p. 204. l. 1. f. 16 ½ r. 18 ½ p. 205. l. 8. f. 55 r. 50. r. 50 f. 55 in l. 21 22. p. 206. l. 19. f 4-50 r. 4-50000 l. 21. f. 1 Chain 25 r. 11 Chains 23. p. 229. l. 16. f. 8-10 th r. 8-100 p. 231. l. 15. f of r. at p. 234. l. 22. f. 1 of a foot r. 1.10 th of a foot p. 236 the 3 lines over 134-5 are to come in after 134-5 Also the two lines over 3-545 should come in after 3-545 p. 257. l. 13. f. ●496 r. 249-6 p. 370. l. 3. f. sine r. Co-sine p. 383. l. 22. add by the general Scale p. 384. l. 14. f. = S. ☉ r. = Co-sine p. 414. l. 11. f. or r. on p. 420. l. 22. f. 71 r. 31. p. 429. l. 15. f. Declination r. Suns Right Ascention The Description and some Uses of the Triangular Quadrant or the Sector made a Quadrant being an excellent Instrument for Observations and Operations at Land or Sea performing all the Uses of the Fore-staff Davis-Quadrant Gunter's-Bow Gunter's-Cross-staff Gunter's-Quadrant and Sector with far more conveniency and as much exactness as any or all of them will do The Description thereof 1. FIrst it is a joynted Rule or Sector made to what Length or Radius you please as to 6 9 12 18 24 30 or 36 inches Length when it is folded or shut together the shorter of which Lengths is big enough for Land uses or Paper draughts the four last for Sea uses or Observations To which is added a third Piece of the same length of the Sector with a Tennon at each end to fit into two Mortice-holes at the two ends of the inside of the Sector to make it an Aequilateral Triangle from which shape and its use it is properly called a Triangular Quadrant 2. Secondly as to the Lines graduated thereon they may be more or less as your use of them and as the cost you will bestow shall please to command But to make it compleat for the promised Premises these that follow are necessary to be inscribed thereon as in the Figure thereof And first you are in order hereunto to consider The outer-edges of the Sector or Instrument the inner-edges the Quadrantal-side the Sector-side and the third or loose-piece also the fixed or Head-leg the moving-leg the head and the end of each leg also the head and leg center of which more in its proper place 1. And first on the outer-edge is placed the Lines of Artificial Numbers Tangents Sines and versed Sines to as large a Radius as the Instrument will bear 2. Secondly on the in-side or edge on short Rules is placed inches foot measure the line of 112

there being 30 degrees in one Sign Fiftly Next above this is a Kalender of Months and Dayes every single Day being exprest and three or more Letters of the name of every Month being set in the Month and also at the beginning of each Month and every 10th day noted with a Prick on the top of the Line representing it as is usual in such work Sixtly Next over the Months is the Line to find the Hour and Azimuth in a particular Latitude Put alwayes on smaller Instruments and very rarely on large Triangular Quadrants for Sea Observations the lowest Margent whereof and next the Months is numbred from the end toward the Head with 10 20 30 40 50 60 70 80 90 100 110 120 130 near the Head Center For the Semi-diurnal Ark of the Suns Azimuth and in the Margent next above this with 4 5 6 7 8 9 10 11 12 near the end for the Morning hours then the other way viz. toward the Head on the other-side the Hour Line with 1 2 3 4 5 6 7 8 for the Afternoon hours Seventhly On the same Quadrantal-side and Moveable-leg on the spare places beyond the Months toward the end is set an Almanack and the Names of 12 or more Stars to find the hour of the Night which 12 Stars are noted with 1 2 3 4 5 6 7 8 9 10 11 12. among the degrees in small Figures as in the Figure Eightly Next of all to the in-side is the Line of Natural versed Sines drawn to the Center with his correspondent Line on the other or Head-leg Exprest sometimes in a pricked Line for want of room Ninthly On the Head-leg and next to the versed Sines last mentioned is first the Line of Equal Parts or Line of Lines and on the same common Line wherein is the Center is the Line of Natural Sines whose length is equal to the measure from the center at C to 600 on the moveable-leg so that the Line of degrees is a Tangent and the measure from C to any Tangent a Secant to the same Radius of the Natural Lines of Sines and Lines Also beyond the Center C on the same common middle Line is another smaller Line of Natural Sines whose length is equal to the measure from C to 60 on the loose-piece then if you count from the Center pin at 60 on the loose-piece toward the end of the movable-leg they shall be Tangents to the same Radius and the measure from the Center C to those Tangents shall be Secants to the same Radius which may be well to be ordered to a third or fourth part of the former from the Center downwards These two Lines of Sines are best figur'd with their Sines and Cosines the other way with a smaller figure and the Line of Lines from the Center downward from 1 to 10 where 90 is which Lines of Sines may be called a general Scale for all Latitudes Tenthly Next to this toward the outer-edge is another Line of Natural Sines fitted to the particular Line of Hour and Azimuths for one particular Latitude noted Pert. Scale of Altitudes or Sines Eleventhly Next to this is the Line of 29 ½ for so many dayes of the Moon 's age in short Rules of the whole length but in longer not being easily known by the single strokes and Figures annexed to those strokes Twelfthly Next the outer-edge is a Line of 24 hours 360 degrees or 12 Signs or in most Rules inches also used together with the former Line of 29 ½ and as a Theory of the Sun and Moon and ready way of finding the Hour by the Moon or fixed Stars Thirteenthly To this Instrument also belongs a Thred and Plummet and Sights as to other Quadrants and a pair of Compasses as to other Sectors a Staff and Ball socket also if you will be curious and accurate And for large Instruments for Sea a Square and an Index which makes it a perfect sinical Quadrant and two sliding sights also which makes it a fore and back-staff and bow as will appear more at large afterward Some Uses of the Trianguler Quadrant for Land and Sea Observations and Operations CHAP. I. Numeration on the Lines graduated on the Instrument IN the first place it will not be amiss to hint a few words as to the reading the Lines or more properly Numeration on the Lines wherein take notice That all Lines of Equal Parts or Lines applicable to Arithmetick as the Line of Lines the Line of Numbers the Line of Foot-measure and the like wherein Fractions of Numbers are requisite they are most commonly accounted in a Decimal way and as much as may be the small divisions are numbred and counted accordingly But in the Lines of Sines Tangents Secants and Chords being Lines belonging properly to a Circle in regard that the Sexagenary Fraction is still in use the intermediate Divisions are as much as may be fitted to that way of account viz. by whole degrees where they come close together or the Line of no great use And if more room is to half degrees or 30 minuts and sometimes to quarters of degrees or 15 minuts but toward the beginning of the Line of Natural Sines or the end of the Natural Tangents and Secants where the degrees are largest they are divided to every 10th minute in all large Rules as by considering and accounting you may plainly perceive Take two or three Examples of each kind 1. First On the Line of Lines to find the Point that represents 15. In the doing of this or any the like you must consider your whole Scale Radius or length of the Line may be accounted as 1 as 10 as 100 as 1000 or as 10000 and no further can be applicable to any ordinary Instrument Wherein observe That if the whole Line be one then the long stroke by every Figure doth represent one tenth of that Integer and the next shorter without Figures are hundredth parts of that one Integer and a 1000th part is estimated in smaller Instruments and sometimes exprest in larger But the hundredth thousand part is alwayes to be estimated by the eye in all Instruments whatsoever 2. But if the whole Line of Lines shall represent 10 as it usually doth and as it is figured then the long stroke at every Figure is 1 and the next longer are tenths and the shortest are hundred parts and the thousand parts as near as can be estimated 3. But if the whole Line represents a hundred as here in our present Example then the long stroke by every Figure represents 10 and every shorter stroke is one and the shortest strokes are tenths and the hundredth parts as much as can be estimated 4. But if the whole Line shall represent a 1000 then the long stroke by the Figure shall represent a hundred and every shorter 10 and every of the shortest strokes is one Integer and a 10th part as near as can be estimated 5. But lastly if the whole Line represent 10000 then

part 2 shillings and 6 pence or every 10th part 2 shillings because 8 half-crowns or 10 two shillings is 20 shillings Example Right against 6 Inches and a half for 6 l. ●0 s. on this other Line I find ● pence 3 farthings the price of one Foot at 6 l. 10 s. per Rod And at 7 farthings per Foot I find near 40 shillings or 2 pound per Rod. Also at 40 shillings per Square found at 40 on Foot-measure is 4 pence 3 farthings 1 ● per Foot found just against it on the Inches CHAP. VIII The use of the Line of Numbers in measuring of Land by Perches and Acres Problem I. At any length of the Land to find the breadth of the Acre IN the Answering of this Question it is not amiss but very needful to premise how many Square Inches Feet Yards Perches or Chains I mean a Chain of ●6 ●oot long is contained in a Square Acre of Land for which purpose have recourse to the Table annexed which is drawn with great care and exactness for that purpose By which Table you may perceive That 6272640 Square inches are contained in one Square Acre And 100000 or one hundred thousand Square Links of a 4 Pole Chain make a Square Acre And 43560 Square Feet make a Square Acre And 4840 Square Yards make a Square Acre And 1742 4 Square Paces make a Square Acre And 160 Square Perch make a Square Acre And 10 Square 4 Pole Chain make one Acre As in the Table you may see And 3097 1 ● Square Ells make one Acre of Land Statute measure The Table   Inch Links Feet Yards Pace Perch Chain Acre Mile Inch 1 7.92 12 36 60 198 792 7920 63360 Link 62.720 1 1.515 4.56 7.575 25 100 1000 8000 Feet 144 2.295 1 3 5 16.5 66 660 5280 Yard 1296 20.755 9 1 1.66 550 22 220 1760 Pace 3600 57.381 25 2.778 1 3.3 13.2 132 1056 Perch 39204 625 272.25 30 25 10.89 1 4 40 320 Chain 627264 10000 4356 484 174.24 16 1 10 80 Acre 6272640 100000 43560 4840 1742.4 160 10 1 8 Mile 4014489600 64000000 27878400 3097600 1115136 102400 6400 640 1 Square Inches Links Feet Yards Pace Perch Chain Acre Mile Then as the length of the Land given in Feet Yards Paces Perches or Chains is to the number of Square Feet Yards Paces Perches or Chains in a Square Acre So is 1 to the breadth of the Land in that measure the length was given to make a Square Acre See the Examples of all these measures in their order viz. of Feet Yards Paces Perches and Chains Suppose a piece of Land be 660 Feet long or 220 Yards or 132 Paces or 40 Perches or 10 Chains in length which several measures are all of the same quantity I would know how much in breadth I must have to make a Square Acre Extend the Compasses from the length given viz. 660 Feet or 220 Yards or 132 Paces or 40 Perches or 10 Chains to 43560 for Feet or to 4840 for Yards or to 1742 for Paces or to 160 for Perches or to 10 for Chains To the Number in the Table for that measure in a Square Acre the same Extent applyed the same way from 1 shall reach to the Feet Yards Paces Perches or Chains required Note the Work 1. As 660 to 43563 the Feet in a Square Acre So is 1 to 66 the breadth in Feet required 2. As 220 the length in Yards to 4840 the Square Yards in a Square Acre So is 1 to 22 the breadth in Yards required 3. As 132 the length in Paces to 1742 So is 1 to 13-2 the breadth in Paces sought 4. As 40 the length in Perches to 1●0 So is 1 to 4 the breadth in Perches 5. As 10 the length in Chains to 10 So is 1 to 1 the breadth in Chains required 6. As 176 the length in Elles to 3097 ⅓ So is ● to 17-6 the breadth in Elles required To work this by the Line of Lines say 1. As the 43560 to = 660 So is = 10 to 66 Latterally 2 As the Latteral 220 to Parallel 4840 So is Latteral 1 to Parallel 22 single double or four-fold 3. As 132 doubled is to = 1742 likewise doubled because it falls near the Center So is 1 quadrupled viz. 4 to = 13-2 quadrupled viz. 52-4 4. As 160 to = 40 So is = 10 for 1 to 4 Perch 5. As 10 to = 10 So is = 1 to 1 the breadth required If you would know how much breadth at any length shall make 2 3 or 4 Acres Then say As the length given to the quantity of one Acre in that measure according to the Table So is 2 3 4 or 5 to the breadth required Example at 30 Perch in length The Extent from 30 to 160 shall reach the same way from 4 to 21 Perch and 34 of 100 or 5 Foot 06 Inches the breadth of 4 Acres at 30 Perches in length Problem II. The length and breadth given in Perches to find the Content in Perches of any piece of Land The Extent from 1 to the breadth in Perches shall reach the same way from the length in Perches to the true Content in Square Perches Example As 1 to 50 so is 179 to 8950 the Content in Square Perches Problem III. The length and breadth being given in Perches to find the Content in Square Acres The Extent from 160 to the breadth in Perches shall ●each the same way from the length in Perches to the Content in Square Acres Example As 160 to 50 so is 179 to 5-58 Acres or 5 A●res 2 Rood and 13 Perches Problem IV. The length and breadth of a piece of Land being given in Chains to find the Content in Acres The Extent from 1 to the breadth in Chains and 100 parts which are Links shall reach the same way from the length in Chains and Links to the Content in Square Acres Example As 1 to 5 Chains 52 Links the breadth So is 8 Chains 72 Links to 48 Acres and 3960 Square Links Problem V. Having the Base and Perpendiculer of a Triangle given in Chains or Perches to find the Content in Acres The Extent from 2 if you use Chains or from 320 if you measure by Perches to the whole Base shall reach the same way from the whole Perpendiculer to the whole Content of the Triangle or if it be a Trapezia joyn both the Perpendiculers in one sum Example As 2 for Chains to 3-63 the whole Perpendiculer So is 11-80 the whole Base to 21 Acres 42 Links the Content of the whole Triangle Or in Perches As 320 to 14-55 the Perpendiculer in Perches So is 47-20 the length or base Line in Perches to 21 Acres 24 Links the Content in Acres Problem VI. The Area or Content of a piece of Land given that was measured by Statute-Perches to find the Content of the same piece of Land in Wood-land measure or Customary Acres or Irish Acres For the better understanding of this Problem

for if you shall turn the Extent between 100 and 106 ten times backward from 257 it will stay at 143 ½ the worth in ready Money Or to make use of the former remedy Multiply 0253058 the Logarithm of 106 by 10 then this Extent taken and laid the decreasing way from 257 shall reach to 143 ½ For Note That the Line of Lines is the Scale of equal parts that makes the Line of Numbers and 10 or 7 or 15 or any other Number multiplied by the Logarithm of 106 taken from that Scale of Lines all at once is equal to so many repetitions and consequently more exact because of the difficulty of taking the 10 12 or 15th part of any Number whatsoever and observe That so much as you err in the first it will be 10 12 or 15 or 20 times so much at last which may be considerable in this Problem IV. A yearly Rent or Annuity being forborn a certain number of years to find what the Arrears thereof will amount unto according to any rate propounded First you must find out the Principal-Money that answers to the Rent or Annuity in question then find the sum of that Principal and Use at the end of the term given at the rate propounded then the Principal taken out of this sum both of Arrears and Principal the Arrears do remain which is the sum you look for Example Suppose a Landlord live far from his Tennant and yet judging his Tennant honest and able is content to take his Rent once in every fourth year which should be paid every year or every quarter of the year and suppose the Rent be 10 l. per annum and the rate of profit for the forbearance be 8 per cent First to find the Principal for 10 l. per annum at the rate of 8 l. per cent Say If 8 l. have 100 for his Principal what shall 10 l. have The Answer will be 125 for the Extent from 8 to 100 shall reach from 10 the same way to 125 then by the 2d Problem of this Chapter 125 l. forborn for four years will come to 170 l. which is 170 l. 0 s. 0 d. from which sum if you substract 125 l. there remains 45 l. the Arrears for 10 l. per annum forborn four years at the rate of 8 per cent But if you would have the profit of these Arrearages supposing 2 l. 10 s. the 4th part of 10 l. per annum to be paid quarterly and to count Use upon Use at the rate abovesaid then you will find the Principal and Arrears to be 171 l. 10 s For if you multiply 0086 the log of 102 l. the Interest and Principal of 100 l. for a quarter of a year by 16 the quarters in four years it will be 1376 which Number taken from the Line of Lines and laid from 120 on the Line of Numbers shall reach to 171 ½ or 171 l. 10 s. being 30 s. more than the former sum when 150 l. the Principal is taken away the residue Arreares is 46 l. 10 s. Or If you turn the distance on the Numbers between 100 and 102 16 times from 125 which you may help thus turn first 4 times then take them 4 times in one Extent and turn 3 times more and you will stay at 271 ½ the Answer required Problem V. A yearly Rent or Annuity propounded to find the worth thereof in ready Money at any rate whatsoever First by the 4th Problem find the Arrears that shall be due at the end of the term and at the rate propounded then by the 3d Problem find what those Arrears are worth in ready money which shall be the worth of the Annuity or Rent required Example There is a Lease of a House or Land worth 12 l. per annum and there is 16 years yet to come which Lease a man would buy provided he may lay out his money to gain after the rate of 10 l. per cent the question is What is it worth First by the last if 10 l. have 100 for his Principal What shall 12 the Answer is 120 Then by the second part of the second 120 l. forborn 16 years comes to 551 l. the Principal and Interest from which sum taking 120 l. the Principal there remains 431 the Arrears Then by the third Problem find what 431 due 16 years to come is worth in ready money and the Answer will be at 10 in the 100 93 l. 14 s. Also herein observe That if there be any Reversion of a Lease to be expired before it may be injoyed then you are to find the worth of 431 l. after so many years more as suppose it be 5 years before the Annuity begin then find the worth of 431 forborn 21 years which will be 58 l. 4 s. Problem VI. A sum of Money is propounded and the rate whereby a man intends to Purchase to find what Annuity and how many years to continue that sum of money will buy Take any known Annuity at pleasure and find by the last the value of that in ready money then this proportion holds As the value found is to the Annuity supposed So is the sum of money to be improved to the Annuity required Example What Annuity to continue 16 years will 500 l. Purchase whereby a man may gain after the rate of 10 l. per cent By the last Problem I find That 93 l. 14 s. will purchase 12 l. a year for 16 years at 10 per cent Therefore The Extent of the Compasses from 93 l. 7 to 12 l. per annum shall reach the same from 500 to 64 l. per annum For such an Annuity to continue 16 years will 500 l. purchase to gain 10 l. per annum per cent for your Money Problem VII Or first rather Lands or Houses sold at any certain number of years Purchase to find what the value of the whole will be The usual way of valuing Land or Houses is by the years Purchase and Land Fee-simple is usually vallued at 20 years Purchase Coppy-hold-Land at 15 or 16 years Purchase and good strong and new Houses at 12 13 or 14 years Purchase for Fee-simple But a Lease of 〈…〉 of 21 years about 7 years Purchase and a Lease of 31 years about 8 years Purchase rather less than more and a Lease of 60 or 100 not worth above 8 ½ years Purchase Again The usual profit allowed for Land in Fee-simple is not above 5 l. in the 100 per annum because of the certainty thereof for Coppy-hold Land full 6 l. in the 100 per annum for the best Houses 7 and 8 l. in the 100 Fee-simple But in laying out Money on Leases either of Land or Houses Men shall hardly be savers if they gain not 8 9 or 10 in the 100 per annum for their Money The reason and demonstration whereof you may read at large in Mr. Phillips his Purchasers Pattern Thus the number of years Purchase agreed on which ought to be cleer