Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	distance_n	file_n	rank_n	1,730	5	11.1963	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29760	The description and use of the carpenters-rule together with The use of the line of numbers commonly called Gunters-line : applyed to the measuring of all superficies and solids, as board, glass, plaistering, wainscoat, tyling, paving, flooring, &c., timber, stone, square on round, gauging of vessels, &c. : also military orders, simple and compound interest, and tables of reduction, with the way of working by arithmatick in most of them : together with the use of the glasiers and Mr. White's sliding-rules, rendred plain and easie for ordinary capacities / by John Brown.	Brown, John, philomath.	1688 (1688)	Wing B5040; ESTC R37165	60,566	214

been but 24 in rank and file PROB. II. Any number of Souldiers being propounded to order them into a double battle of Men that is which may have twice as many in rank as file Find out the square-root of half the number given for that root is the number of men to be placed in file and twice as many to be placed in rank to make up a double Battle of Men. Examp. Let 1368 Souldiers be propounded to be put in that order I find by the 12 aforesaid that 26 c. is the square-root of 684 half the number propounded and therefore conclude that 52 ought to be in rank and 26 in file to order so many Souldiers into a double Battle of men PROB. III. Any number of Souldiers being propounded to order them into a quadruple battle of men that is four times so many in Rank as File Here the Square-root of the fourth part of the number propounded will shew the number to be placed in File and four times so many are to be placed in Rank So 2048 being divided by 4 the quotient is 512 whose root is 22 6 and so many are to be placed in file and 88 in Rank being four times 22 c. PROB. IV. Any number of Souldiers being given together with their distances in Rank and File to order them into a Square battle of ground Extend the Compasses from the distance in File to the distance in Rank this done that extent applyed the same way from the number of Souldiers propounded will cause the moveable point to fall upon a fourth number whose square-root is the number of men to be placed in file by which if you divide the whole number of Souldiers the quotient will shew the number of men to be placed in Rank Examp. 2500 men are propounded to be ordered in a Square-battle of ground in such sort that their distance in File being seven foot and their distance in Rank 3 foot the ground whereupon they stand may be a just square To resolve this question extend the Compasses upon the Line of Numbers downwards from 7 to 3 then because the fourth number to be found will in all likelihood consist of 4 figures if you apply that extent the same way from 2500 in the second part among the smallest divisions the moveable point will fall upon the fourth number you look for whose square-root is the number of men to be placed in file By which square-root if you divide the whole number of Souldiers you have the number of men to be placed in Rank As 7 to 3 so 2500 to 1072 whose biggest square-root is 32 then as 32 is to 1 so is 2500 to 78. PROB. V. Any number of Souldiers being propounded to order them in Rank and File according to the reason of any two numbers given This Problem is like the former for as the proportional number given for the file is to that given for the Rank so is the number of Souldiers to a fourth number whose square-root is the number of men to be placed in Rank by which if you divide the whole you may have the number to be placed in File Examp. So if 2500 Souldiers were to be martialled in sueh order that the number of men to be placed in File might bear such proportion to the number of men to be placed in Rank as 5 bears to 12 I say then as 5 is to 12 so is 2500 to 6000 whose square-root is 77 the number in Rank then as 77 is to ● so is 2500 to 32 c. The number of men to be placed in File CHAP. IX The use of the Line in questions of Interest and Annuities PROB. I. A summ of Money put out to Use and the Interest forborn for a certain time to know what it comes to at the end of that time counting Interest upon Interest at any rate propounded Take the distance with your Compasses between 100 and the increase of 100 l. for one year which you must do very exactly and repeat it so many times from the principal as it is forborn years and the point of the Compasses will stay on the Principal with the Interest and increase according to the rate propounded Examp. I desire to know how much 125 l. being forborn 6 years will be increased according to the rate of 6 l. per Cent. reckoning Interest upon Interest or Compound Interest Extend the Compasses from 100 to 106 that extent being 6 times repeated from 125 shall reach to 177 l. the Principal increased with the Interest at the term of 6 years at the rate propounded But if it were required for any number of months then first find what 100 is at one month then say thus If 100 gives 10 s. at one month what shall 125 be at 6 months end facit 75 s. And the work is thus First say If 100 gives 10 s. at one months end what shall 125 and it makes 12 s. 6 d. then say If one month require 12 s. 6 d. what shall 6 months require facit 75 s. that is three pound fifteen shillings the thing required to be fonnd PROB. II. A summ of money being due at any time to come to know what it is worth in ready money This question is only the inverse of the other for if you take the space between 106 and 100 and turn it back from the summ proposed as many times as there are years in the question it shall fall on the summ required Examp. Take the distance between 106 and 100 and repeat it 6 times from 177 and it will at last fall on 125 the summ sought PROB. III. A yearly Rent Pension or Annuity being forborn for a certain term of years to find what the Arrears come to at any rate propounded First you must find the Principal that shall answer to that Annuity then find to what summ the Principal would be augmented at the rate and term of years propounded then if you substract the Principal out of that summ the remainder is the Arrears required Examp. A Rent or Annuity or Pension of 10 pound the year forborn for 15 years what will the Arrears thereof come to at the rate of 6 per Cent. Compound Interest The way to find the Principal that doth answer to 10 l. is thus If 6 l. hath 100 for his Principal what shall 10 have facit 166 l. 16 s. or 166 l. 8 s. for the extent from 6 to 10 will reach from 100 to 166.8 which is 166 l. 16 s. Then by the first Problem of this Chapter 166 l. 16 s. forborn 15 years will come to 398 l. then substract 166 l. 16 s. out of 398 l. and the remainder viz. 231 l. 4 s. is the summ of the Arrears required But note in working this question your often turning unless your first extent be most precisely exact you may commit a gross errour to avoid which divide your number of turns into 2 3 or 4 parts and when you have turned over one