Selected quad for the lemma: order_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
order_n	distance_n	foot_n	rank_n	8,037	5	11.9661	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08582	The circles of proportion and the horizontal instrument The former shewing the maner how to work proportions both simple and compound: and the ready and easy resolving of quæstions both in arithmetic, geometrie, & astronomie: and is newly increased with an additament for navigation. All which rules may also be wrought with the penne by arithmetic, and the canon of triangles. The later teaching how to work most quæstions, which may be performed by the globe: and to delineat dialls upon any kind of plaine. Invented, and written in latine by W.O. Translated into English, and set out for the public benefit, by William Forster.	Oughtred, William, 1575-1660.; Forster, William, mathematician.; Oughtred, William, 1575-1660. Addition unto the use of the circles of proportion. aut	1633 (1633)	STC 18899B; ESTC S120820	74,822	159

the diligent Practizer 6 To finde the Weight of a Sphaere of Tinne at any other Diameter assigned Multiply the Cube of the Diameter giuen by 1216 if it be in inch measure or by 2101 ⌊ 248 if the measure be by decimall parts of a foot and the product will be the weight of that Sphaere And contrariwise to find the Diameter of a Sphaere of Tinne by the weight giuen in graines Diuide the weight giuen in graines by 1216 if you would haue inch measure or by 2101 ⌊ 248 if you would measure by decimall parts of a foot and the quotient shall be the Cube of the Diameter 7. To finde the Weight of a Sphaere of any Mettall at any Diameter giuen either in Inch measure or in decimall parts of a foot First by Sect. 6 seeke the weight of a Sphaere of Tinne at that Diameter then by Sect. 4 say As the proportionall number of Tinne is to the proportionall number of that other Metall so is the weight of the Sphaere of Tinne now found to the weight of the Sphaere proposed Example Suppose a Sphaere of Iron whose Diameter is 3 inches what shall be the weight thereof First the weight of a Sphaere of Tinne of 3 inches Diameter will be found to be 32832 graines Then say 1554 · 1680 ∷ 32832 · 35494 ⌊ 054 graines the weight of the Sphaere proposed 8 To finde the Diameter of a Sphaere of any Metall in inch measure or decimall parts of a foot the weight thereof being giuen First by the contrary of Sect. 6 seeke the Cube of the Diameter of a Sphere of Tinne of that weight Then by Sect. 4 say reciprocally As the proportionall number of that other Metall is to the proportionall number of Tinne so is the Cube of the Diameter now found to the Cube of the Diameter of the Sphaere proposed Example A Sphaere of Iron weigheth 35494 ⌊ 0●4 grains how many inches is the Diameter thereof First the Cube of the Diameter of a Sphere of Tinne of 35494 ⌊ 054 graines weight will be 29 ⌊ 18910695 then say reciprocally 1680 · 1554 ∷ 29 ⌊ 18910691 · 27 The Cubic root whereof is 3 the Diameter of a Sphaere of Iron of that weight proposed CHAP. XI Concerning the Ordering of Soldiers in any kinde of rectangular forme of battaile 1 BAttailes are considered either in respect of the number of men or in respect of the forme of ground As asquare battaile of men is that which hath an equall number of men both in Rank and File though the ground on which they stand bee longer on the File then on the Ranke And a square battaile of ground is that which hath the Ranke as long as the F●le though the men in Ranke be more then in File 2. In respect of the number of men it is called either asquare battaile or a double battaile or a battaile of the grand front which is quadruple or a battaile of any proportion of the number in Ranke to the number in File 3. If it bee asquare battaile of men Extract the quadrat root out of the whole number of men and the same shall be the number of Souldiers to be set in a Ranke Example 576 Souldiers are to bee martialled in a square battaile that so many may be in Ranke as in File Take the quadrat root of 576 which is 24 the same shall be the number to be placed in a Ranke 4. If it be a double battaile of man Extract the quadrat root out of halfe the number of men and the same doubled shall bee the number of Souldiers to bee set in a Ranke Example 1458 Souldiers are to be placed in a double battaile so that twise so many may be in Rank as in File Take halfe the given number 1458 which is 729 the quadrat root whereof is 27 double it and you shall haue 54 men to be placed in a ranke 5. If it be a quadruple battaile which is called of the great front Extract the quadrat root out of one quarter of the number of men and the same quadrupled shall be the number of Souldiers to be set in a ranke Example 1024 Souldiers are to bee martialled into a battaile of the grand front so that fower times so many be in ranke as in file Take one quarter of 1024 the number given which is 256 the quadrat root whereof is 16 quadruple it and you shall haue 64 men to be placed in a ranke 6. If a battaile bee required of any other forme that is if a Ratio be given according to which the number of men in Ranke shall be to the number in file Multiply the two termes of the Ratio given Then say As the product is to the quadrat of the terme which is for the ranke or As the terme which is for the file is to the terme which is for the ranke so is the whole number of Souldiers to the quadrat of the number of men to be placed in a ranke Example 1944 Souldiers are to be martialled so that the number of the ranke be to the number of the file as 8 vnto 3 that is for 8 men in ranke 3 are to be set in file First multiply the two termes of the Ratio 8 and 3 the product whereof is 24 also quadrat 8 the terme of the ranke which will be 64. Then say 3 · 8 ∷ 1944 · 5184 · out of which extract the quadrat root 72 and it will giue you the true number of the ranke 7. In respect of the forme of ground the battaile is either a square of ground or longer one way then the other For the distance or order of Souldiers martialled in array is distinguished either into Open order or Order Open order is when the very centers of their places are distant 7 feet asunder both in ranke and file Order is when the centers of their places are distant 3 feet and a halfe in ranke and so much in file Or else 3 feet and a halfe in ranke and 7 feet in file which last order and whatsoeuer order else there is in which the distance of the rankes one from another is greater then the distance of files causeth that a square of men maketh not a square of ground but the ground is longer on the file then on the ranke 8 If it be a square battaile of ground the centers of the distances being feet 3½ in ranke and 7 feet in file Because 3½ is halfe of 7 the ratio of the distances is as 1 unto 2. And seeing the number in ranke to the number in file is reciprocall to the distances the ratio of the number of men in ranke to the number of men in file shall be as 2 unto 1. And so the Rule shall be the same with that in Sect. 6 namely As the terme of the file is to the terme of the ranke so is the whole number of Souldiers to the true number of the ranke Example 1352 Souldiers are to bee set in a

square of ground that their distances may be feet 3½ in ranke and 7 feet in file The Ratio of the ranke to the file shall reciprocally be as 7 to 3½ that is as 2 to 1. Say therefore 1 · 2 ∷ 1352 · 2704 the quadrat roote whereof 52 is the number of men to be set in a ranke 9 If a battaile wherein the distance in ranke is vnequall to that in file be longer one way then the other according to any Ratio giuen there is to be considered a double ratio one reciprocall in respect of the distances the other according to the forme of the ground Wherefore to finde the Ratio of men in rank to the men in file Multiply the two termes of the ranke for the ranke and the two termes of the file for the file And then the Rule shall bee the same with that in Sect. 6 namely As the terme of the file is to the terme of the ranke so is the number of Souldiers to the quadrat of the true number of the ranke Example 10290 souldiers are to be set in a battaile so that they may stand onely 3 feet asunder in ranke and 7 feet in file and the length of the ground for the ranke to the length of the ground for the file shall haue the ratio of 5 vnto 2. First in respect of the distances the Ratio of Rank to file reciprocally is as 7 vnto 3. Secondly in respect of the ground the ratio of rank to file is as 5 to 2. Wherefore by multiplication of like termes the true ratio of rank to file shall be 7 × 5 to 3 × 2 that is as 35 to 6. Say therefore 6 · 35 ∷ 10290 · 60025 the quadrat root whereof is 245 the number of men to be set in ranke 10 If 1000 Souldiers may be lodged in a square of 300 feete how many feete must the side of a square be which will serue to lodge 5000 Say 1000 · 5000 ∷ 300 × 300 · 450000 · the quadrat roote whereof 671 is the square side sought for And this is the order for resolution of all other questions of this sort CHAP. XII A collection of the most necessarie Astronomicall operations 1 BEfore wee deliuer the Rules of such operations it will not be inconuenient to set downe certaine Reductions wherof we may haue frequent vse To reduce sexagesime parts into decimals Diuide the sexagesimes giuen by 60. Example How many decimals are 34′ 12″ Here are required two reductions first of the seconds into decimals of minutes then of the minutes with their decimals into decimals of degrees Thus 60 · 1 ∷ 12″ · 0 ⌊ 2 Againe 60 · 1 ∷ 34 ⌊ ′ · 0 ⌊ 57° Wherefore 34′ 12″ are equall to 0 ⌊ 57 of a degree And contrariwise to reduce decimall parts of degrees in sexagesimes Multiply the decimall part giuen by 60. Example How many sexagesime parts are 0 ⌊ 57° 1 · 60 ∷ 0 ⌊ 57° · 34 ⌊ ●′ Againe 1 · 60 ∷ 0 ⌊ 2 · 12″ To reduce houres into degrees Multiply the houres with their decimall parts by 15. Example How many degrees are 8 Ho 34′ 12″ that is by the former reduction 8 ⌊ 57 Ho thus 1 · 15 ∷ 8 ⌊ 57 · 128 ⌊ 55 Wherefore Houres 8 34′ 12″ doe containe 128 ⌊ 55 degrees And contrariwise to reduce degrees into houres Diuide the degrees with their decimall parts by 15. Example How many houres are in degrees 128 ⌊ 55 15 · 1 ∷ 128 ⌊ 55 · 8 ⌊ 57 2 It is to be vnderstood that if foure numbers are proportionall their Order may be so transposed that each of those termes may bee the last in proportion In this manner I. As the first is to the second so is the third to the fourth II. As the third is to the fourth so is the first to the second III. As the second is to the first so is the fourth to the third IIII. As the fourth is to the third so is the second to the first Wherfore euery proportion doth implicitly containe foure Orders two descending and two ascending as may be seene by their combinations By one of which orders if of foure proportionall numbers any three be giuen that other which is vnknowne may be found out Example To finde out any of these termes 1 As the Sine of the complement of the suns declination 2 is to the Sine of the compl of his altitude 3 So is the Sine of the Sunnes Azumith from the meridian 4 to the Sine of the horary distance from the meridian If the first second and third termes be giuen the fourth shall be found out by the I order If the first third and fourth termes be giuen the second shall be found out by the II order If the first second and fourth termes bee giuen the third shall be found out by the III order If the second third and fourth termes be giuen the first shall be found out by the IIII order 3. To finde out any one of these termes 1 As the Radius or totall Sine 2 is to the Sine of the distance or longitude of the Sunne in the Ecliptic from the next Aequinoctial point 3 So is the Sine of the Sunnes greatest declination which is the angle of the Ecliptic with the Aequinoctial 4 To the Sine of the Sunnes declination in that longitude 4. To finde out any one of these termes 1 As the Radius 2 is to the Sine of the Sunnes right ascension from the next aequinoctiall point 3 So is the tangent of the Sunnes greatest declination 4 to the tangent of the Sunnes declination in that place 5. To finde out any one of these termes 1 As the Radius 2 is to the Sine of the compl of the Sunnes greatest declination 3 So is the tangent of the longitude of the Sunne from the next aequinoctiall point 4 to the tangent of the Right ascension of the Sunne from the same aequinoctial point 6. To finde out any one of these termes 1 As the Radius 2 is to the Sine of the compl of the longitude of the Sunne from the next aequinoctiall point 3 So is the tangent of the Sunnes greatest declination 4 to the tangent of the compl of the angle of the Ecliptic with the Meridian 7. To finde out any one of these termes 1 As the Radius 2 is to the Sine of the Sunnes greatest declination 3 So is the Sine of the compl of the Sunnes right ascension from the next aequinoctial point 4 to the Sine of the compl of the Angle of the Ecliptic with the Meridian 8. To finde out any one of these termes 1 As the Sine of the compl of the Poles height 2 is to the Radius 3 So is the Sine of the Sunnes declination 4 to the Sine of the Sunnes Amplitude ortiue that is the arch of the horizon from the place of the Sunnes rising or setting to the true East or West point 9.