Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	hand_n	hold_v	left_a	2,273	5	10.0216	5	true

Text snippets containing the quad

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

The Description and Vse OF THE CARPENTERS-RULE Together with the use of the LINE of NUMBERS Inscribed thereon In Arithmatick 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 Vniversal-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 London Printed by W. G. for William Fisher at the Postern-gate neer Tower-hill 1667 To the Reader Courteous Reader whomsoever thou art I Shall intreat thee to take in good part this Collection of The Ules of the Line of Numbers commonly called or best known to Artificers by the name of C●nter's Line I write it not as a new thing but rather as a renovation of an old one and the great motive that provoked and stimed me up to it is this I making and selling Rules with Gunter's Line on them many a one would say to me How shall I come to know the use of this Line I reply that in Mr. Cunter's Book there the Use is set forth but because of the obscurity of the Instructions there as to the reading of the Line and also the dearness of the Book many a one that would gladly learn are deterred from taking pains therein lest they should spend time and oyl to no purpose and also for want of cases fit to their purpose they are apt to think it as to no purpose Therefore that I might be as an ABCdarian to the Instrumental way of working being the most proper for Mechanick Men such as Carpenters Joyners Masons Bricklayers and the like which for the most part are ignorant of Arithmatick and that knowledge might be increased any way I thought it convenient and make no doubt of a good benefit to accrue thereby to them whose capacities and purses in these Critical times cannot well reach to other more difficult and dear Authors I shall not much Apologise for my self as to style or manner of writing being like my self what it is I beseech you accept in as good part as it was offered I might have implored the aid of some more abler Pen but I thought Mechanick men best understand them of their own profession in this and other Discourses because they are men of the same stature in knowledge and expressions Possibly it may provoke some to a more accurate and universal Treatise In the mean time take this as a Harbinger till that come And being apt to think that Ship-carpenters or Sea-faring men may light of it I have added in the conclusion as an Appendix the Vse of a perticular and Vniversal Sun-dial also of a Nocturnal or Star-dial by which the hour of the Day and Night may be had in all places of the North latitude from 1 degree to 66.30 where the day Artificial is 24 hours long In all which I have laboured after b●evity and plainness as much as may be And to the end you may learn to know the Stars I have been at the charge to print a Paper with all the principal Stars in the Northern Hemisphere from the Pole to the Equinoctial so that you may take any in that compass and they that please may do the like for the South Hemisphere So I wish you may reap much profit thereby and remain willing to serve you in what I may J. B. At the Sphere and Dial in the great Minories Lond. 66. The Description and Vse of the Carpenters-Plain-Rule as it is now made CHAP. 1. I Thought good to add this Chapter for the sake of some possibly young beginners and them that would not be ignorant altogether in the way of Measuring therewith though they may seldom have occasion of it and also knowing that they that have the most knowledge once had little enough And farther I find by experience that many there be that can measure by the Plain Rule that cannot use the Line of Numbers and some also know not the use of the plain Rule neither For these Reasons I have added this Chapter of The Description and use of the Carpenters-Plain-rule It is call'd a Carpenters Rule rather-then a Joyners Bricklayers Masons Glasiers or the like I suppose because they find the most absolute necessity of it in their way for they have as much or more occasion to use it than most other Trades though the same Rule must measure all kind of Superficies and solids which two Measures measure every visible substance which is to be measured And it is usually made of Box or Holly 24 Inches in length and commonly an Inch and half or an Inch and quarter in breadth and of thickness at pleasure and on the one side it is divided into 24 equal Inches according to the Standard at Guild-hall London and every one of those 24 Inches is divided into eight parts that is Halfs Quarters and Half-quarters and the Half-inches are known from the Quarters and Quarters from the Half-quarters by short longer and longest strokes and at every whole Inch is set figures proceeding from 1 to 24 from the right hand toward the left and these parts and figures are on both edges of one side of the Rule both ways numbred to the intent that howsoever you hold the Rule you have the right end to measure from provided you have the right side On the other side you have the Lines of Timber and Board measure The Timber-measure is that which begins at 8 and a half that is when the figures of the Timber-line stand upright to you then I say it begins at the left end at 8 and ½ and proceeds to 36 within an Inch and ⅜ of an Inch of the end Also of the beginning end of the Line of Timber-measure is a Table of figures which contains the quantity of the Under-measure from one Inch square to eight Inches square for the figure 9 comes upon the Rule as you may see neer to 8 in the Table On or next the other edge and same side you have the Line of Board-measure and when those figures stand upright you have 6 at the left or beginning end and 36 at the other or right end just 4 Inches of the end unless it be divided up to 100 then it is nigh an inch and half of the end This Line hath also his Table of Under-measure at the beginning end and begins at 1 and goes to 6 and then the divisions on the Rule do supply all the rest to 100. Thus much for Description Now for Use The Inches are to measure the length or breadth of any Superficies or Sollid given and the manner of doing it were superfluous to speak of or once to mention being

not only easie but even natural to every man for holding the Rule in the left hand and applying it to the board or any thing to be measured you have your desire But now for the use of the other side I shall shew it in two or three examples in each measure that is Superficial or Sollid And first in Superficial or Board-measure Example the first The breadth of any Superficies as Board or Glass or the like being given to find how much in length makes a Square Foot or is equal to 12 inches broad and 12 Inches long for so much is a true Foot Superficial To do this look for the number of Inches your Superficies is broad in the Line of Board-measure and keep your finger there and right against it on the Inches side you have the number of inches that goes to make up a Foot of Board or Glass or any Superficies Suppose I have a peice 8 Inches broad How many Inches make a Foot I look for 8 on the Board-measure and just against my finger being set to 8 on the Inch side I find 18 and so many Inches long at that breadth goes to make a Foot Superficial Again suppose it had been 18 Inches broad then I find 8 Inches in length to make a Foot superficial but if 36 Inches broad then 4 Inches in length makes a Foot Or you may do it more easier thus Take your Rule and hold it in your left hand and apply it to the breadth of your Board or Glass making the end that is next 36 even with one edge of the Board or Glass and the other edge of the Board sheweth how many Inches or Quarters of an Inch goes to make a Foot of the Board or Glass This is but the converse of the former and needs no example for laying the Rule to it and looking on the Board-measure you have your desire Or else you may do thus in all narrow peices under 6 inches broad As suppose 3 ¼ double 3 ¼ it makes 6 ½ then I say that twice the length from ½ to the end of the Rule shall make a foot Superficial or so much in length makes a foot Example the second A Superficies of any length and breadth to find the Content that is how many Foot there is in it Having found the breadth and how much makes one Foot turn that over as many times as you can for so many Foot is there in that Superficies But if it be a great breadth then you may turn it over two or three times and then take that together and so say 2 4 6 8 10 c. or 3 6 9 12 15 18 21 and till you come to the end of the Superficies Note that the three short strokes between figure and figure are the Quarters as thus 8 and a quarter 8 and a half 8 and three quarters then 9 c. till you come to 30 and then 30 and a half 31 c. to 36. And if it be divided any further it is to whole Inches only to 100. The use of the Table at the beginning end of the Board-measure First you have five ranks of figures the first or uppermost is the number of inches that any Superficies is broad and the other 4 are Feet and Inches and parts of an Inch that goes to make up a Foot of Superficial measure As for example at 5 Inches broad you must have 2 Foot 4 Inches and 4 Fifths of an Inch more that is 4 parts of 5 the Inch being divided into 5 parts but where you have but two figures beside the uppermost and Ciphers in the rest you must read it thus At two Inches broad you must have six Foot in length no Inches no parts Thus much for the Use of the Line of Superficial or Board-measure The Use of the Line of Sollid or Timber-measure The use of this Line is much like the former For first you must learn how much your piece is square and then look for the same number on the Line of Timber-measure and the space from thence to the end of the Rule is the true length at that squareness to make a Foot of Timber Example I have a peice that is 9 Inches square I look for 9 on the Line of Timber-measure and then I say the space from 9 to the end of the Rule is the true length to make a Foot of Timber and it is neer 21 Inches 3 eights of an Inch. Again suppose it were 24 Inches square then I find 3 Inches in length makes a Foot for so I find 3 Inches on the other side just against 24 But if it were small Timber as under 9 Inches square then you must seek the square in the upper rank in the Table and right under you have the Feet Inches and parts that go to make a Foot square as was in the Table of Board-measure As suppose 7 Inches square then you must seek the square in the upper rank in the Table and right under you have the Feet Inches and parts that go to make a Foot square as was in the Table of Board-measure As suppose 7 Inches square I find in the Table 2 Foot 11 Inches and 2 sevenths of an Inch divided into 7 parts and 8 you find only 2 Foot 3 Inches o parts and so for the rest But if a peice be not just square but broader at one side than the other then the usual way is to adde them both together and to take half for the square but if they differ much then this way will be very erroneous and therefore I refer you to the following Rules But if it be round Timber then take a string and girt it about and the fourth part of this is usually allowed for the side of the square and then you deal with it as if it were just square Thus much for the Use of the Carpenters plain rule I have also added a Table for the Under-measure for Timber Board to Inches and Quarters and the use is thus Look on the left side for the number of Inches and Quarters your Timber is square or your Board is broad and right against it you have the Feet Inches tenth part of an Inch and tenth of a tenth or hundredth part of an Inch that goeth to make a Foot of Timber or Board Example A piece of Timber 3 Inches 1 quarter square will have parts to make a Foot And a Board 3 Inches and a quarter broad must have in length to make a Foot and so of the rest as is plain by the Table and needs no further explication being common to most Artificers A Table for the under Timber-measure to inches quarters A Table for the Vnder-Board-m to inch Qu. Inch. qu. feet inch Iop ●oop   feet inc 10. 100.   1 2304 0 0 0   48 0 0 0   2 576 0 0 0   24 0 0 0   3 256 0 0 0   16 0 0 0 1 1 144 0 0 0 1 12 0 0 0

they are only whole hours But in large Dials there may be put halfs and quarters and then there are 8 prick'd hour lines for 12 being the last needs no pricks for distinction And they are figured above the Aequinoctial with 6.7.8.9.10.11.12 and under the Tropiques with 8. 7. 6.5.4.3.2.1.12 for the same line hath two figures viz. 4 8 7 5 6 6 5 7 4 8 3 9 2 10 1 11 12 12. That is the same line that is for 4 in the morning is for 8 at night and the like is both for winter and summer the reason is look how high the Sun is at 7 in the morning so high is it at 5 in the afternoon and the like 7. Those lines that descend from the Aequinoctial toward the left hand are the winter hours and are figured above as before but below with 12.1.2.3 for in the shortest days the Sun sets before 4 and in large Dials there are halfs and quarters also and distinguished as before but of whole hours at the Tropiques there is but 4 but at the Aequinoctial there be 6 and a point representing the hour of 6. 8. And lastly in the spare room beyond the Aequinoctial you have set a perpetual Almanack whereby if you know the day of the month you may find the day of the week and the contrary Also in some Almanacks you have the Dominical letter Leap-year and Epact to find the Moons-age the largest and uppermost of which ranks of figures are the 12 months the next 5 are the 31 days of the month and the rest if any be are according to their names thus much for description One thing more I think convenient to hint to make it serve for all fashions of Dials of this kind and it is this some Dials of this kind have the Kalender of months and days on the backside in 1 2 or 4 Circles and lines of the Suns declination rising true place and amplitude and the right ascension and the use is only thus Lay a thred on the day of the month and the Centre and it cuts or sheweth all the other in their respective lines It being so easie and also not to our present purpose I shall not give any example but come to the uses of the foreside which are sufficient for the hour of the day the thing promised Note also that by the addition of on line it is made to serve for all latitudes also in the form of a very strong and handsom Tobacco-box CHAP. II. The use of the Dial. PROB. 1. How to hold the Dial in time of Observation Hang the string of the Dial over your thumb on your left hand or you may hold it between your thumb and the middle of your fore-finger and stretch your 4 fingers streight out and let the Dial hang at liberty just touching the palm of your hand that it may be steady then turn your whole body about till the edge of the Dial or your fingers ends be just against the Sun then shall you see the shadow of any thing stuck in the Centre though never so short to reach quite through the Dial and then it is held right PROB. 2. To find the Suns Altitude Stick a pin the smaller the better in the Centre and hold it up as before and the shadow will shew on the limb the Suns Altitude required Example At 8 of the clock on the 11 of June in the morning I wonld know the Suns Altitude I hold it up as before and I find it to be 36.46 that is 36 Degrees and 46 Minutes each Degree being 60 Minutes as in the Tables of Reduction PROB. 3. To find the perpendicular height of any thing by its shadow by the line of shadows Hold up the Dial by the thred as before and look on what division of the line shadows the shadow of the pins cuts that is the true height or length of the shadow by which to get the height of any perpendicular thing or the very top of any leaning thing that causeth the shadow Example On the same 11 of June at neer 9 a Clock in the morning I hold up my Dial and I find the shadow to fall just on 1 on the line of shadows or 45 on the Degrees therefore I say that the height of the object that causeth the shadow and the shadow are both of one length but if it had fallen on 2 that is to say of right shadow then the object is but half the length of the shadow measuring upon a level ground from the end of the shadow to right under the object that causeth the shadow if it falls on 3 the shadow is 3 times as long as the thing is and so to 12 to 12 times longer and the strokes between note one tenth 2 tenths 3 tenths c. more but if it falls beyond 1 on contrary shadow then the shadow is shorter accordingly as will appear very plain with a little practice Or rather thus by the Numbers Count the middle 1 on the Rule as 1 at 45 on the Dial then if the Sun be under 45 count them on the rule toward 10 and if above 45 the contrary then as the parts cut are to the middle 1 so is the length of the shadow to the altitude required PROB. 4. The Use of the Quadrat To use the Quadrat you must have a hole in the other end of the horizontal line and also some where in the Dial square from the Centre to the horizontal line also you must have a thred and plummet then the use is thus Stick a pin in the Centre and thereon hang the plummet then put a pin in the other whole that is perpendicular to the horizontal line and just over the Centre and hold up the Dial in your right hand and make the string to play evenly by the Superficies of the Dial when you see the object right against both the pins then observe what stroke is cut by the thred on the line of quadrat or shadows for that may be used so also for if you go backwards or forwards till you make the thred to fall on 1 in the shadows or on 50 in the quadrat then is the height of the House Steeple Tree or the like equal to the distance between you and it adding the height of your eye to it But if it had fallen on 25 of the quadrat or 2 on the shadows then the distance had been twice as much as the height if right shadow but for contrary shadow the contrary I shall say no more to this only give you a caution that if you look from the height of any place downwards then you must put that pin next the Centre to your eye and look downwards to your object and then the side which before was right shadow will become contrary shadow and the contrary Note one thing further that if your instrument be a Sextance or a Circle and you cannot have all the

distance shall reach from the third to the fourth proportional Example Divide the space between 9 and 72 in three parts that third part shall reach from 8 to 4 or from 4 to 8 as the question was propounded either augmenting or diminishing Also if a cube whose side is 6 inches contain 216 inches how many inches shall a cube contain whose side is 12 inches Extend the Compasses from 6 to 12 that extent measured from 216 in the first part of the line of numbers three times shall at last fall upon 1728 in the second part of the line of numbers for note if you had begun on the second part you would at three times turning have fallen beyond the end of the line and the contrary as above holds here in squares also PROB. 8. Betwixt two numbers given to find a mean arithmetically proportional This may be done without the help of the line of numbers nevertheless because it serves to find the next following I shall here insert it though I thought to pass both this and the next over in silence yet to set forth the excellency of number I have set them down and the Rule is this Add half the difference of the given terms to the lesser of them and that aggregate or sum is the Arithmetical mean required Example Let 20 and 40 be the terms given now if you substract one out of the other their difference is 60 whose half difference 30 added to 20 the lesser term makes 50 and that is the Arithmetical mean sought PROB. 9. Betwixt two numbers given to find a mean musically proportional Multiply the difference to the terms by the lesser term and add likewise the sa●●e terms together this done if you divide that Product by the sum of the terms and to the Quotient add the lesser term that last sum is the Music●● mean required or shorter thus Multiply the terms one by another and divide the Product by their sum and the Quotient doubled is the Musical mean required Example The numbers given being 8 and 12 multiplyed together make 96 that divided by 20 the sum of 8 and 12 the Quotient is 4 80 which doubled is 9-6 10s the Musical mean required This may be done by the line of numbers otherwise thus find the Arithmetical mean between 8 and 12 and then the analogy or agreement is thus As the Arithmetical mean found is to the greater term so is the lesser term to the Musical mean required PROB. 10. Betwixt two numbers given to find a mean Geometrically proportional Divide the space on the line of numbers between the two extreme numbers into two equal parts and the point will stay at the mean proportional required So the extreme numbers being 8 and 32 the middle point between them will be found to be 16. PROB. 11. Betwixt two numbers given to find two means Geometrically proportional Divide the space between the two extreme numbers into 3 equal parts and the two middle points dividing the space shall shew the two mean proportionals As for example let 8 and 27 be two extremes the two means will be found to be 12 and 18 which are the two means sought for PROB. 12. To find the Square root of any number under 1000000. The Square root of every number is always the mean proportional between 1 and that number for which you would find a square root but yet with this general caution if the figures of the number be even that is 2 4 6 8 10 c. then you must look for the unit or one at the beginning of the line and the number in the second part and the root in the first part or rather reckon 10 at the end to be the unit and then both root and square will fall backwards toward the middle in the second length or part of the line but if they be odd then the middle one will be most convenient to be counted the unity and both root and square will be found from thence forwards toward 10. so that according to this rule the square of 9 will be found to be 3 the square of 64 will be found to be 8 the square of 144 to be 12. the square of 1444 to be 38. the square of 57600 to be 240. the square of 972196 will be found to be 986. and so for any other number Now to know of how many figures any root ought to consist put a prick under the first figure the third the fifth and the seventh if there be so many and look how many pricks so many Figures there must be in the Root PROB. 13. To find the Cubique Root of a Number under The Cubique root is always by the first of two mean proportionals between 1 and the Number given and therefore to be found by dividing the space between them into three equal Parts So by this means the root of 1728 will be found to be 12 the root of 17280 is neer 26 the root of 172800 is almost 56 although the point on the Rule representing all the square numbers is in one place yet by altering the unit it produceth various points and numbers for their respective proper roots The Rule of find which is in this manner You must set or suppose pricks to be set pricks under the first figure to the left hand the fourth figure the seventh and the tenth now if by this means the last prick to the left hand shall fall on the last figure as it doth in 1728 then the unit will be best placed at 1 in the middle of the Line and the Root the Square and Cube will all fall forward toward the end of the Line But if it fall on the last but 1 as it doth in 17280 then the unit may be placed at 1 in the beginning of the Line and the Cube in the second length or else the unit may be placed at 10 in the end of the Line and the Cube in the first part of the Line you may help your self as in the first Problem of the 2 Chapter But if the last prick fall under the last but two as in 172800 it doth then place the unit always at 10 in the end of the Line then the Root the Square and Cube will all fall backward and be found in the second part between the middle 1 and the end of the Line By these Rules it doth appear that the Cube root of 8 is 2 of 27 is 3 of 64 is 4 of 125 is 5 of 216 is 6 of 345 is 7 of 512 is 8 of 729 is 9 of 1000 is 10. As you may see by this following Table of Square and Cubique roots Thus you have the chief use of the line of numbers in general and they that have skill in the rule of three and a little knowledge in plain triangles may very aptly apply it to their particular purposes Yet for their sakes for whom it is intended I shall inlarge to some more particular applications in measuring

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