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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	low_a	part_n	upper_a	1,487	5	9.1326	5	false

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A77649	The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.	Brown, John, philomath.; Gaywood, Richard, fl. 1650-1680.	1667 (1667)	Wing B5039D; ESTC R173095	73,644	256

they lengthen by degrees gradually therefore the Winter and Summer 12 and consequently the rest of the hour lines run sloping upwards and downwards as the days lengthen or shorten This being premised and considered an easier Dial all things considered cannot be had Now for an Example or two Having found out the parallel of Declination for so is it called if there be 25 lines or of the Suns rising if there be but 19 you may easily know it by the name at the end of it or by being a prick-line or the next to or the 2 next to a prick line c. hang or hold the Dial up as was taught in the 1 Problem and you shall have the exact hour of the day among the Summer or Winter hours according to the time of the year Example On the 2 of Aug. 1656. I look for A in the lower line of the months because the days shorten and laying a string or causing a shadow to fall from the centre upon the 2 of August which if it hath not a particular stroke for it is a little beyond the long stroke by the A and toward the S and I observe the thred to cut upon the line of Declination called 15 and also it is a prick line in one of 25 lines but almost midway between the first beyond a prick line and may be called the line of the Suns rising at 4. and 41 min. then I hold up my Dial and find at 8 a clock the shadow to cross the 8 of clock line just in the prick line and at the same instant the Suns altitude is 30.15 and the quadrat is 29 and the line of shadows is 1. and 7 tenths that is the shadow of a yard or any thing held upright is the length of the yard and 7 tenths more of another length or yard and note that at 4 a clock the same day the shadow will fall in the same place exactly as was hinted before for equal hours from 12. the Sun hath the like altitude at all times of the year and if it is morning the height increases if afternoon then it decreaseth so that two observations will resolve the question But note First for the months of June and Decemb. where the days are close together the reason is because the days at that time lengthen or shorten but a little so must their spaces be on the instrument if you should miss 3 or 4. days there it makes no sensible error take near as you can and it sufficeth Also note the hours of 11 and 12 are neer together therefore you must be so much the more cautious in observing to hold the Dial wel and to look just on or between the parallel of declination or rising and at 12 of the clock you may look in the Kalender for the day of the month for just on that day will the shadow be at 12 of the clock and short of it increasing before but decreasing after 12. Note also on the 10 of March and 13 of September you must observe in the upper line but on the 11 of June and 11 of December on the lowest line as the rules rehearsed make manifest Lastly if you meet with a Dial that hath the Kalender of Months on the backside then it is but laying a thred over the day and on the line of Declination the thred cuts the correspondent number of Declination as before also the rising and true place and amplitude as I hinted before Then having the number look for the line on the other side that shall have the same number and proceed as before Thus much shall suffice for the Dial particular for one latitude The use of the other line to make it General as also of a Joynt-rule to find the hour and azimuth I shall refer you to the Book of the Joynt-rule a book of this volume fit to be bound up with it being a very useful peice for Dialling Geometry Astronomy and Navigation and many other Mathematical Conclusions and a portable universal Sea-Instrument as any whatsoever extant CHAP. III. The Description of a Universal Dial for all Latitudes from 0 to 66. 30 of North or South Latitude 1. First the Dial it self is an oblong made of Box Brass or Silver or the like and at the shortest side it hath two sights either of it self or fitted into it parallel to one of the shortest sides 2. It hath a Bracheolum with a Thred Bead and Plummet fastned to it that is 3 pieces of Brass so fitted together that being pinn'd on the middle will reach to any of the lines of Latitude and it may be cut away after the work is on to a very comely Form or left Square as shall best please the Fancy 3. Thirdly for the lines on the Dial consider first the centre on the 6 of Clock line where the tangents of Latitude begin and pass on to 66.30 being straight parallel lines drawn cross the oblong to every single Degree of Latitude and you have them numbred with 10.20.30 40.50.60.65 at both ends of those lines 4. Then you have from the Centre aforesaid long streight sloping lines drawn to every 5 or 10 Degr. of the signs and on that end next the sights on the middle line you have ♈ and 🝞 from thence toward the left hand you have 10.20 ♉ and ♍ and then onwards the same way still 10.20 ♊ and ♌ then 10.20 ♋ on the other side to the right hand you have 10.20 ♓ and ♍ and 10. 20. ♒ and ♐ and 10.20 ♑ In all 12 signs 5. Also adjoyned to them you have a Kalender of months and days that knowing the day of the month you have the sign answering thereto 6. You have the same signs as was above pourtrayed on the right side and 5 and 10 parts reciprocal to the former signs and parts on the top 7. You have the hour lines parallel to the length of the oblong and numbred with 12. 1.2.3.4.5.6.7.8.9.10.11.12 on the upper end of them and with 12. 11.10.9.8.7.6.5.4.3.2.1.12 at the lower end 8. About the 2 sides opposite to the right upper corner you have Degrees of Altitude and Declination to find the Latitude the use of which followeth with as much brevity and plainness as may be PROB. 1. To find the Latitude Having the Suns Declination and his Meridian Altitude to find the Latitude When the Sun is just on the Meridian observe his Altitude and set it down then find his Declination for that day and consider whether it be North or South for if it be North Declination you must substract it from it if South you must adde it to the Meridian Altitude found and the Sum or remainder shall be the comment of the Latitude sought for Example I am on the first of August in a place where the noon Altitude is 50 the Suns Declination the same day is 15.18 North which taken out of 50. there remains 34.40 whose complement to 90 is 55.18 the Latitude sought The Degrees

half 3 Inches is one quarter 9 Inches is the quarters 4 Inches is one third 8 Inches is two thirds and 1 Inch is somewhat less than one tenth on Rule on the other or second side then right against the length found on the first on the second is the Content required Example At 3 Foot 3 Inches broad and 9 Foot 9 Inches long you shall have 31 Foot 8 Inches ½ near the very same is for Foot-measure only much easier because the divisions on the Line of Numbers and on the Line of Foot-measure on the edge do agree together This being premised as to the using of it you may apply all the former precepts and examples to this Rule as well as the other CHAP. III. To measure Timber by the Sliding-rule PROB. 1. To measure Timber by this Rule is nothing else but to work the Double-Rule of Three As for Example At 8 Inches square and 20 Foot long I would know the Content Set 12 if the side of the square be given in Inches or 1 if in Foot-measure on the first side to 8 the Inches square on the second then right against 12 on the second side on the first is 18 the fourth proportional part Then for the second work set 18 the fourth proportional last found to 8 the Inches square on the second then right against 20 the length is 9. the Content required Or rather thus Set 12 against 8 then right against 20 on the same side 12 was is 13.5 neer on then look for 13.5 fere on the first side and right against it on the second is 9 foot the Content required PROB. 2. To measure a piece that is not square Set 12 if you use the Inches or 1 if you use Foot-measure on the first side to the Inches thick on the second then right against the Inches broad on the first side on the second is a fourth proportional then in the second operation set 12 on the first side to the fourth proportional on the second then right against the length on the first side on the second is the Content required Example At 8 Inches thick and 16 broad and 20 Foot long you shall find 18 Foot ferè PROB. 3. The Square given to find how much makes a Foot Set the Inches square on the first side to 12 on the second then right against 12 on the first on the second is a fourth proportional number then in the second work as the Inches square to the fourth proportional so is 12 to the number of Inches required to make a Foot of Timber Example At 6 Inches square set 6 to 12 then against the other 12 is 24 then set 6 to 24 then right against 12 you shall have 48. the length in Inches required After the same manner are other questions wrought but the Compasses are easier and more ready therefore I shall say no more to this but only refer you to the former rules in the third fourth and fifth Chapters Only note that in those Sliding-rules made for Glasiers use the one half of the Line of Numbers is on one side of the Rule and the other on the other and whatsoever leg or piece of the rule is the first on the one side the same leg or piece is the first when the Rule is turned on the other side which must well be observed but note that for measuring of Timber those that use it may have one side fitted for that as I shall more plainly and fully shew in the next Chapter being the easiest speediest and neat way that ever yet was used by any man resolving any Contents by having the length and the diameter circumference or square given A Table of the true Sise of Glasiers Quarries both long and square calculated by J.B. Square Quarries 77.19 gr Ranger Sides breadth length content in Feet content in Inch. in 100 i. 100 I. p. I. pts F. parts Inc. p. 4 20 4 30 5 36 6 70 0.1250 1.50 3 76 3 84 4 80 6 00 0.1000 1.20 3 43. 3 51 4 38 5 47 0.0833 1.00 3 07. 3 13 3 92 4 90 0.0667 0.80 2 80 2 86. 3 57 4 47. 0.0555 0.666 2 66. 2 72 3 39 4 24 0.5000 0.60 Long Quarries 67.22 Ranger Sides breadth length content content In pts I pts I. 100 I. pts F. 100 I. pts 4 09 4 41. 4.90 7.34 0.1250 1.50 3 65 3.95 4.38 6.57 0.1000 1.20 3 34 3.61 4.00 6.00 0.0833 1.00 2 98. 3 23 3.58 5.37 0.0667 0.80 2 58 2 79 3.10 4.90 0.0555 0.666 2 72 2 94 3.27 4.65 0.0500 0.60 Note that a prick after the 100 parts of an Inch notes a quarter and a stroke a half of 100 part of an Inch to make this Table work thus by the Line of Numbers Divide the distance between the content of some known size as square 10 s. or long 12 s. and the content of the inquired Size into two equal parts for that distance laid the right way increasing for a bigger or decreasing for a less from the sices of the known size shall give the reciprocal sides of the inquired size Example for square 12s The half distance on the line of Numbers between 1000 the content of square 10 s. and 0. 833 the content of square 12 shall reach from 6 the length of square 10 s. to 5 47 the length of square 12 s. and from 4. 80 the breadth of square 10 s. to 4 38 the breadth of square 12 s and from 3 84 to 3.51 and from 3 76 to 3 43 and so for all the rest CHAP. IV. The description of the Line of Numbers on a Sliding-rule to measure Solid measure onely according to Mr. White 's first contrivance but much augmented by J. B. First when the figures on the Timber-side stand right toward you fit to read then that half or piece next to your right-hand I call the right-side the other is of necessity the left Secondly the figures on the right side are first at the lower end where the Brass is pin'd fast either 3 or 4 or 5 it matters not much which yet to have 3 there is best then upwards 4. 5. 6. 7. 8. 9. 10. 11 for so many Inches then 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12 under the brass at the top for so many Feet the divisions between to one Foot are quarters of Inches the next above 1 Foot are only whole Inches as you may plainly see Thirdly at 1 Foot you have the word Square at 1 Foot 1 Inch ½ is a Mark and right against it is set TD noting the true Diameter of a round solid body at an Inch further is 12 set which I call small 12 being in small figures Again at 1 Foot 3 Inches better is another Mark and right against it the word Diameter for the Diameter of a piece of Timber according to the usual English allowance Then again at 3 Foot 6 Inches ½ neer is T R for the true circumference of a round Cillender

Lastly at 4 Foot is the word Round noting the circumference according to the usual allowance whose use followeth Note also if you put on the Gage-points for Ale or Wine with the mean Diameter and length you may Gage any Wine or Beer-vessel the Wine at 17 Inches ¼ the Ale or Beer at 18.95 Fourthly the figures on the left side are not much unlike the right for 1 at the beginning is one Inch and so it proceeds by quarters of Inches to one Foot then by figures at the Feet and the divisions all whole Inches to 10 Foot then every whole Foot and half and quarter or 10th to 100 or 140 or 150 Foot and this I call the left-side the other the right side so that from one Inch at the lower end to one Foot every Inch hath a figure from one Foot to 10 Foot every Foot hath a figure and from 10 Foot to a 100 every 10th Foot only is figured I have been very plain in explaining this because I would avoid vain repetitions in the following uses wherein you shall have first the most ordinary and easie questions and then the more hard and critical and less useful The Uses follow PROB. 1. A piece of Timber being not square to make it square Set the breadth on the left side to the breadth on the right then right against the Inch and quarters thick found on the left side on the right is the Inches square required Example At 18 broad and 6 thick you shall find 10 Inch ⅜ the side of the square required For if you set 6 inches against 6 Inches on the right and left-side then right against 18 Inches or 1 Foot 6 Inches on the left on the right you have 10 Inches 1 quarter and half a quarter for the side of the square equal to 18 one way and 6 the other way PROB. 2. The side of the square given to find how much makes a foot For all pieces between 3 or 4 Inches and 42 Inches square which are the most usual this is the best way set the Inches or Feet and Inches square found out on the right-side to one Foot on the left then right against one Foot on the right on the left is the Inches or Feet and Inches required to make a Foot of Timber Example At 8 Inches square set 8 on the right to 1 Foot on the left then right against 1 Foot on the right on the left is 2 Foot 3 Inches the length required To find how much is in a foot long Just as the Rule stands even look for the Inches the peice is square on the right and on the left is the Inches or feet and Inches required Example At 17 Inches square there is 2 foot of Timber in one foot long which if you multiply by the length you shall have the true content A very good way for large peices and very exact PROB. 3. The side of the square and length given to find the Content For all pieces between one Inch or 8 12 part of a Foot and 100 Foot this is the easiest way Set the word square or 1 Foot to the length on the left then right against the Inches or Feet and Inches square on the right on the left you have the Content Example At 9 Inch square and 20 Foot long Set the long stroke by the word square to 20 Foot on the left then right against 9 Inches on the right side on the left-side you have 11 Foot and a quarter the Content required But if it be a very great piece as above 100 Foot then call one Foot on the left side 10 Foot and 2 Foot 20. c. then 10 shall be 100. and 100. a 1000 that will supply to 1500 Foot in a piece but if you would go to a bigger piece then call 2 Foot on the left 200 c. then you shall have it to 150000 Foot in a piece such as I never saw But for all small pieces under 3 Inches square and above 1 quarter of an Inch do thus Set 12 on the top or the small 12 when it is most convenient to use to the length on the left-side then right against the inches or 12 s. of one inch squares sound on the right-side on the left is the true Content required Example At 2 Inches 3 twelves or 1 quarter square and 10 Foot long you shall find 4 Inches and a quarter ferè But note when you use the small 12 the answer is given in decimals of a Foot therefore the top 12 is best PROB. 4. The square of a small piece of Timber given to find how much makes a Foot For all pieces from 12 Inches to 1 Inch square do thus Set the Inches and 12 s. or quarters square counting one Foot on the right side for one Inch and 2 Foot for 2 Inches c. found out on the right-side to 100 on the left then right against the upper or small 12 on the right on the left is the length required to make a Foot of Timber Example At 2 Inches ¼ square you must have 28 Foot 4 Inches to make a Foot PROB. 5. Under 1 Inch square to find the length of a Foot Set 1 Foot 9 Inches 6 Inches or 3 Inches found on the right-side for one Inch ¾ ½ or ¼ of an Inch against 10 on the left-side counted for 100 then right against the small 12 you have the Feet in length required Example At 1 Inch square you find 144 Feet at ¾ square 256 Feet at ½ an Inch square 576 Feet at ¼ or an Inch square you find 2034 Feet in length to make one Foot of Timber Or if you set the former numbers 12 9 6 1 against 1 Inch on the left then right against the upper 12 is a number which multiplyed by 12 is the number of Feet required PROB. 6. A great piece above 3 Foot ½ square to find the length of a Foot Set the Feet and Inches on the right to 100 on the left then right against small 12 is the Inches and 12 s or 12 s of a 12th that goes to make a Foot Example At 4 Foot square you have 9. 12ths or ¾ of an Inch to make a Foot of Timber at 5 Foot square 5. 12ths and 10. 12ths of a 12th to make a Foot Thus you see the Rule as now contrived resolves from 1 quarter square to 12 Foot square the Content or Quantity of a Foot of Timber in length at any squareness without Pen or Compasses CHAP. V. For round Timber PROB. 1. The number of Inches that a piece of timber is about being given to find how much makes a Foot First for all ordinary pieces set one foot on the left to the inches or feet and inches above on the right then right against TR for true measure or round for the usual measure is the feet or feet and inches required to make a foot of timber at that circumference about Example At 4 inches about 113 foot 2 inches is