Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	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

quadrat as on a quadrant you may then move the pin to the hole at the other end of the horizontal line and you shall see that defect to be supplyed Note lastly that by heights we speak only of perpendicular or upright heights and in distances only of levels or horizontals PROB. 5. How to find unaccessable heights by the quadrat at two Observations If the place which is to be measured cannot be approached unto then work thus to find both height and distance first make choice of a place where looking up I find the thred to fall on 50 in the quadrat then the distance will be equal to the height Then make a mark at that Station and go directly backward in a right line with the former distance and make choice of a second Station where the thred may fall on 25 parts of right shadow then this second Station is double to the height and also to the distance departed from the first Station and the half therefore is the height and first distance But if it be so you cannot come to take such a height as 50 and 25 then take as you may as suppose one be at 25 and the other at 20 and suppose the height to be 100. I find that As 25 the parts cut are to 50 the side of the quadrat so is 100 the supposed height unto 200 the distance And as 20 the second Station to 50 the side of the quadrat so is 100 the supposed height unto 250 the second distance wherefore the difference between the Stations should seem to be 50 then if in measuring you find it to be either more or less then this proportion doth hold as from the supposed difference to the measured difference so from the supposed height to the true height and from the supposed distance to the true distance And now suppose the difference between the two Stations were found to be 30 by measuring Then as 50 the supposed difference to 30 the true difference so is 100 the supposed height to 60 the true height And 200 the supposed distance to 120 the true and 250 at the second Station unto 150 the distance the like reason holdeth in all other examples of this kind and if an Index with sights were fitted to the Centre it might serve for all other horizontal distances by the same reason The Vse of the Almanack PROB. 6. Having the Day of the Week to find the Day of the Month for ever First find what day of the Week the first of January is on which is thus done First find the Dominical Letter for the last Leap-year set down in the Almanack the next letter is for the next year following and so till you come to the year you look for And note every Leap-year hath two Dominical letters viz. the next before it till the 24 of February and that over it for the remainder of the year Having found it reckon from A either backwards or forwards always calling A Sunday you shall find what day is the first of January Example For the year 1656 F is the Dominical Letter therefore say A Sunday G Monday F Tuesday and that is the first of January and then make use of that thus On the first Tuesday in the beginning of February I would know the day of the Month Among the Months look for 12 which is for February reckoning from March which is always the first Month and right under ●● you have 5 for the fifth day being the first Tuesday in February and 12 19 26 for the other Tuesdays in February But now for the other Months after March you must say Wednesday the reason is because February hath 29 days and the Leap-year two Dominical Letters viz. F. and E. then reckon from E to A and it falls on Wednesday which use thus in the year 1656 and all other Leap-years As in the beginning of August on Thursday what day of the Month is it August is the sixth Month look for 6 among the Months and right under it you have 6 which is Wednesday therefore 7 is Thursday and the first Thursday in August But now for 1657. I find that Thursday is the first of January saying thus A Sunday B Saturday C Friday D Thursday And so it is all the year long in all the Months for having found the Moneth all the days right under are Thursdays and then reckon onwards or backwards for any other of the Week-days and you have your desire for any yearpast present or to come PROB. 7. To find the Epact and by that the Moons age any day of the Month. On the Leap-year you have it set down in the Almanack for the next year add 11. and you have your desire And for the next year adde 11 to that and so to the next leap-year But if by so adding it exceed 30 then take away 30 and the remain is the Epact Having the Epact add to it the day of the Month and the number of the Month from March also including both the Moneths and if they come not to 30 that is the Moons age but if they exceed 30 and the Month hath 31 days then Substract 30 and the remain is the age but if the month have but 30 days then substract but 29 and the remainder is the age of the Moon required Example In July 1656. on the 20 day the Epact is 14. then 14.20 and 5 added is 39. from which take 30 rest 9 days old on the 20 of July 1656. the Moons age sought for PROB. 8. To find the hour of the day Having found the day of the month by the Almanack you must find the mark or the space between two marks in the Kalender representing that day which do thus Look for the first letter or name of the month in the Kalender according to the time of the year then reckon from thence to the day you are in either by 5 10 15 20 25 30 31 if the parts are so divided as in small Instruments they cannot well be more but if you have single days every fifth and tenth is known from the rest by a longer stroke and the last day by the longest stroke Well having found the day or the place between two strokes representing it lay a thred from the centre over that day or for want of a thred stick a ●in in the centre and cause the shadow to fall upon the day and then observe on which or between which of the 25 or 19 lines the thred cuts the 12 of clock line for on that line must you look for the hour all that day Before I come to example I shall hint a plain word of the reason of this which I find some to marvel at The hour of the day in this and in most Instrumental-Dials is given by the Suns height now all men know the Sun is not so high in Winter as in Summer therefore the Summer hour lines will not serve the Winter and also all men know

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

these or the like means you may come to know all the Stars in the Nocturnal And if you attain to know them with the help of the other paper you may know all in the half-Hemisphere that is between the Pole and Equinoctial Secondly to find when any star comes to the Meridian The Meridian is a line or arch of a Circle conceived to be drawn through or rather by the star in the tail of the little Bear which is the Pole Star right over your head and to make you understand this the better Hang a line with a weight at the end of it out of a window that looks to the North a good way from the house or on a tree or corner of a house and then go to and fro till you see the line cut by the North-star how much and on which side the Nocturnal will shew you and that line then is the meridian-line and then what star soever is under the line and the North-star or Pole for when you use the stars of Cassiopeia the star is the true Pole as by the Meridian-line on the Nocturnal you may plainly see that star I say is exactly on the Meridian be it above or below the Pole for so it be in that direct line with the Pole it matters not so you have the hours divided round about but you may be able in a little practice to guess without the Plumb-line yet it will marvellously rectifie your judgment till you be more ready at it These two being known all the rest is very easie as may be 3. The day of the Month being given and a Star on the Meridian to find the hour of the night Suppose on the 1 of August I see by the means beforesaid the Star in the tip of the great Bears tail to be in the Meridian then bring that Star just under the string and look for the 1 of August and right against it you have 4 a Clock and 8 minutes in the morning Or else set the day of the month to 12 and then keep it fixed all that night then the thred laid over the Star that is in the meridian shall at the same time in the hours shew the hour counting backwards Another Example Suppose on the same night the star in the nose of the Bear were in the Meridian then bring that star under the string and the 1 of August will shew 10.37 that is 37 minutes past 10 at night the like is for any other 4. To find the right ascension of a star bring the star under the thred and the thread sheweth his right ascension in the degrees so you will find the right ascension of the star in the great Bears tail to be 203. 5. To find the declination of a star bring the star under the line then prick a pin thorough the string and just in the middest of the star then keep the pin there and bring the Scale of declination right under the line and pin and the pins point sheweth you his declination or distance from the Pole by these two last you may adde any star whose right ascension and declination you know and so put in all as may be seen in this compass at any time or by the right ascension only being sufficient for this purpose to wit the hour of the night you may add the Buls eye little Dog 7 Stars Orion or any other chief principal sixed star and make use of it to find the hour of the night withal 6. The day of the month and hour being given to know what star is on or neer the meridian Set the day of the month to the hour of the night and the stars that are under the string are all on the meridian and if there be none just you shall see what half or 3 or 4 part between 2 is on the meridian and this is an excellent way to help you to know the stars Also note That to use this Paper peice pasted on a Board and not to turn about do thus Lay a thred on the Star you find to be in the Meridian then with a pair of Compasses measure from the thred to the next 12 the same extent laid the same way in the line of months and hours shall reach from the day of the month to the hour required FINIS The Vse of the LINE of NUMBERS ON A SLIDING or GLASIERS RULE In Arithmatique Geometry AS ALSO A most Excellent contrivance of the Line of Numbers for the Measuring of Timber either Round or Square being the most easie speedy and exact as ever was used WHEREBY At one setting to the length all ordinary peices of Timber from one Inch to 100 Foot is with a glance of the eye resolved without Pen or Compasses First drawn by Mr. White and since much inlarged and made easie and useful by John Brown London Printed in the Year 1656. The Use of the LINE OF NUMBERS ON A SLIDING-RULE For the measuring of Superficial or Solid-measures CHAP. 1. A Sliding-rule is onely two Rules or Rule-pieces fitted together with a Brassesocket at each end that they slip not out of the grove and the Line of Numbers thereon is cut across the moving Joynt on each piece the same divisions on both sides only the placing of the lines differ for on one side of the Rule you have 1 set at the beginning and 10 at the end on each piece but on the other side 1 is set in the middle and the rest of the figures answerably both ways on purpose to make it large and to take in all numbers and the reading of this is the very same with the other for if you pull out the Rule and set 10 at the end right against 1 at the beginning then on both pieces you have the former Line of Numbers completely therefore I shall say nothing as to description or reading of it but come streight to the use On the edges of the Rule is usually set Foot-measure being the Foot or 12 Inches parted into 100 parts and on the flat sides next to the Foot-measure Inches in 8 parts and on the other flat edges on the other side the Line of Board-measure and sometime Timber-measure whose use is shewed in the first Chapter of the Book but note if the Rule be a just Foot when it is shut as Glasiers commonly have it then the Inches are set alike on both sides and the Foot-measure alike on both edges and being pulled out as far as the brasses will suffer it wants about one Inch of two Foot but if you would have it to be two Foot just when pulled out as it is made for Carpenters use then the Inches on one side and Foot-measure on the same reciprocal edge must be figured otherwise as 13. 14. 15. 16. 17. c. to 25. Inches and the Foot-measure with 110. near the end 120 130 140 150 c. with 210 at the very end shewing the measure from end to end being drawn out to any