Selected quad for the lemma: water_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
water_n	according_a	false_a	great_a	21	3	2.1433	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A96647	Willsfords arithmetick, naturall, and artificiall: or, decimalls. Containing the science of numbers, digested in three books. Made compendious and facile for all ingenious capacities, viz: merchants, citizens, sea-men, accomptants, &c. Together with the theorie and practice united in a sympathetical proportion betwixt lines and numbers, in their quantitites and qualities, as in respect of form, figure, magnitude and affection: demonstrated by geometrie, illustrated by calculations, and confirmed with variety of examples in every species. / By Thomas Willsford, Gent.	Willsford, Thomas.; Vaughan, Robert, engraver.	1656 (1656)	Wing W2874; Thomason E1584_1; ESTC R204128	162,697	364

as before answering the state of the question for the lesser number which being discovered the other is easily found this question will be performed by the Rules of single position if you take proportionall numbers answering the state of the proposition Question 3. To divide a given number into any two parts and those in any quantity assigned as to part 10 in two and so as that the greater divided by the lesse the quotient shall be 20. In all questions of this kinde suppose any one number the other is the remainder as here I suppose 2 the other must be 8 both numbers being 10 and according to the state of the question the greater should contain the lesse 20 times then consequently 20 times the lesse would be equall unto the greater number so 2 multiplied by 20 produceth 40 and should have been equall to 8 the error is 32 too much then take a second supposition as admit 1 the other part must be 9 and the second error 11 and both too much which note and then multiply them into their contrary suppositions the products will be 22 32 the difference 10 for the Dividend the difference of errors 21 the Divisor the Quotient 10 21 for the lesser part which subtracted from 10 the remainder will be 9 11 21 which is 20 times the other and consequently 9 11 21 or ●00 21 divided by 10 21 the Quotient will be 20 the thing required and for triall by the first Rule of False positions as 21 to 32 so 1 unto 1 11 21 which according to the same Rule subtracted from 2 the first supposition the remainder will be 10 21 for the true number as before Question 4. A vessell of 63 gallons was filled with French wine of two sorts the one was at 2 s. the gallon the other at 2 s. 6 d. the gallon the wine in the hogs-head thus filled did come unto in money 7 L. 4 s. and it is here demanded how much there was of either sort The quality here and the number of gallons in either supposition will solve this question the denominations being the same in both as in respect of the quality that is supposing the best or worst sort or price in either yet to avoid any great number the quantity of gallons being odde as 63 and the meanest price or quality being even I take that in both and presuppose 23 gallons of the meanest sort then there was 40 gallons of the best which at 2 s. 6 d. the gallon comes unto 5 L. and the other sort unto 2 L 6 s. in all 7 L 6 s. the price was 7 L. 4 s. from whence it is apparent that the first error was ● s. too much● then suppose 33 gallons or what you please which granted there must be 30 gallons of the best which comes unto 3 L. 15 s. and 33 gallons of the worst at 2 s. the gallon amounts unto 3 L. 6 s. the summe 7 L. 1 s. the error 3 s. defective these errors multiplied crossewise by the suppositions will produce 69 66 and according to my former directions being the signes are unlike their summe is 135 for the Dividend the summe of the errors 5 for the Divisor the Quotient 27 the number of gallons of the worst sort of Wine then must there be 36 gallons of the best the totall quantity 63 gallons the price of the worst is 2 L. 14 s. and the best comes unto 4 L. 10 s. the just summe of 7 L. 4 s. according unto the proposition And by the second Rule the proportion is as 5 unto 2 so 10 to 4 which 4 if it be added unto 23 the first supposition the summe will be 27 gallons as by the former operation in the figure does appear Question 5. Hiero King of Sicylia caused a Crown of Gold for to be made in weight 10 lb. and it was conceived that the Work-man had put a great Allay of Silver unto it which abuse of the Artificer Archimedes detected and by False positions may be thus discovered lb lb 1 lb lb As 10 Gold to 2 water so 6 Gold to 6 5 water As 10 Silver to 3 water so 4 Silver to 6 5 water The totall of these fourth proportionalls 2 ⅖ lb lb 2 lb lb As 10 Gold to 2 water so 7 Gold to 7 5 water As 10 Silver to 3 water so 3 Silver to 9 10 water The totall of these proportionals is 2 3 10 Admit by putting the Crown into the cistern of water the quantity run out was 2 ⅕ lb. the masse of pure gold avoided but 2 lb water and that of silver 3 lb. which in the first place shewed the difference of mettalls for they being of equall weight that most compacted and heaviest of nature will have the lesser body and consequently possesse the lesser room by this a great allay appears and will be explicitly known as thus suppose there was 4 lb of silver then was there 6 lb of gold here institute the Rule of proportion twice for either mettall as in the first Table viz if 10 lb of gold voyded 2 lb of water how much will 6 lb of gold voyd which will prove 1 ⅕ lb of water and so according to the supposition finde how much water the silver will avoyd which is here also 1 ⅕ lb the summe is 2 ⅕ whereas the water which the Crown forced out was 2 ⅗ lb. the difference onely ⅕ lb for the first error then suppose there might be 3 lb of silver in the Crown there must be of gold 7 lb. and according to the second Table the fourth proportionall number will be 14 10 or 7 5. then again as 10 s. to 3 W. so 3 lb silver to 9 10 lb of water the summe of these is 2 3 10 lb water the difference of this 2 3 ●0 and 2 ⅕ is 1 10 too much for the second error These multiplied by their contrary suppositions will produce ⅖ ⅗ and according to my former directions the difference is ⅕ for the Dividend the difference of errors 1 10 the Quotient 2 lb of silver the quantity of the alay and 8 lb the weight of gold that was in the Crown the thing required The examen or triall For the proof of this or the like take the quantities of both mettals found and likewise the quantity of the thing or masse propounded then institute twice the Rule of proportion if 10 lb of gold forced out 2 water how much will 8 of gold put forth facit 1 ⅗ lb water then by the second Rule if 10 lb of silver expelled 3 lb of water then 2 lb of silver will force out of the same cistern ⅗ lb of water the summe of these is 2 ⅕ lb of water and so much did the Crown it selfe put forth or by the first canon to this double Rule of False positions as 1 10 to ⅕ so will 1 be to 2 which according unto the same Rule if subtracted from the first

supposition the remainder will be 2 lb the quantity required as before this question may be solved by any lesse quantity of mettall in either sort for by finding how much one ounce or any other quantity shall force out of a cistern by the common Rule of proportion you will easily finde what quantity of water shall be expulsed by any greater or lesser masse of the same mettall therefore I will write no more of this Truth by these two last Paragraphs is extracted from False positions and grosse errors multiplied and divided by errors more and lesse obsurd in themselves yet in these the thing lies involved which is inquired after though benighted in obscurity and by correcting the errors will be brought to light the Aenigma's solved the Objections cleered and I discovered in my intentions a friend to the Truth and really wishing this for the common good reflecting upon honest ingenious men to whose candid and mercifull censure I referre my self and for instructions in the Rules of false because it is so generally belov'd and daily put in practice I will recommend this Breviate to their memories as a Directorie whereby to avoid some errors of this kinde in future and thus conclude the second Book The Rule of False Positions to discover the Truth or by erroneous suppositions to finde things really true a paradox and no hyperbole AXIOMES in Rules of False are briefly these Take two convenient numbers as you please Two errors will arise from what you guesse Which note with signes as whether more or lesse Then multiply those errors you disclose Crosse-wise by both the numbers you suppose If in your work two signes alike you make Diffrence of errors then all numbers take If signes unlike as ✚ this doe Adde both the errors and the numbers too The summe or difference th' errors must divide Which quotient then the riddle will decide Unlesse both numbers sought it does contain Or both products alike th' Aenigma's vain Where naught is to divide you may descrie The Question 's false or but a fallacie If more than two positions you must need The Rule of false will then be false indeed Some other notes and queries might be shown Whose use is best to Cossick-numbers known The Rules prescribed here will guide you true Yet take these caveats too along with you Though many say and will my counsell shun What need we Rules when as this Work is done To which I answer All I here impart Are but the grounds and principles of Art Some Rules search tracts that various wayes doe winde Yet leave not inquisition 'till they finde Errors Maeanders are in which we 're led That none can well return without a thread Make no positions errors to maintain As blinde sects doe who seek for truth in vain With miscall'd Lights pretend to guide men right They 're Faux his lanthorns a snuff's their light 'T is not to such my labours I intend But to the good or those that would amend The new but false inspired Saints suppose All things of truth are now reveal'd to those He that from them can any truth descrie By false positions hath more art than I These I as errors shun and doe implore To be Christ's servant and I wish no more The well-dispos'd amend will what 's amisse And finde their errors as I doe in this Which found correct they 'l vanish then away And Truth will rise from thence like break of day Errors are mists that doe benight our Spheres Withdraw those vapours and the day appears Man did by errors fall whence Art in vain Labours in part for to restore again By false positions you may errors finde Who cannot see their faults are very blinde By what is false I hope you 'll finde what 's true I wish your Errors small and so Adieu All that I know I know was given to me For others good so this I give to thee And for my labours give if you be eas'd All glory unto God and I am pleas'd To be the Servant Vnto his Servants THOMAS WILSFORD Artificiall Arithmetick OR NUMBERS Divided into SECTIONS And these in CHAPTERS Containing Decimall Arithmetick with the Definition Reduction Annotation Numeration and Construction of these fractions with their severall rules in Addition Subtraction Multiplication and Division with Decimall Tables of the Coins Weights and Measures commonly used in England Also one of Minutes and Seconds THE THIRD BOOK LONDON Printed by J. G. for Nath Brooke at the Angel in Cornhill 1656. THE THIRD BOOK Containing Decimall Arithmetick SECT I. CHAP. I. The Definition of Artificiall Arithmetick with the Reduction of the Decimall fractions and the art of framing those numbers The Definition ARtificiall Arithmeticke by Decimall fractions doth Adde Subtract Multiply and Divide with whole numbers and fractions commixt together in one summe and their Totalls Remainders Products and Quotients shall produce mixt numbers as integers and fractions in one totall summe these Decimall fractions have alwayes for their Denominators an Unite with Cyphers annext unto that Unite towards the right hand as 1 10 2 190 3 1000 or 1 1000 c. but if any Fraction propounded shall not have such a Denominator it must be reduced unto it by art from whence this kinde of Arithmetick derives it exordium or name originally Rule 1. The reduction of common or vulgar fractions unto Decimalls with the first grounds thereof Any vulgar fraction may be reduced unto a Decimall by division or very neer the same quantity without any sensible error as thus unto the Numerator of the fraction given annex cyphers as in extracting the Quadrat root Lib 2. Parag 1. Example 5. but in all these cases at pleasure as 1 2 or 3 cyphers c. this done divide the whole by the Denominator of the fraction propounded the Quotient will be the Numerator of the fraction whose Denominator shall be an Unite with so many Cyphers as the Numerator hath places of these there are two kindes viz Rationall and Irrationall those are called Rationall whose Numerators are just quantities without having any remainder as all the others have and yet those Decimalls retaining a proportion so neer their vulgar fractions as that humane works can require no more exactnesse as shall be instanced in some following examples Example 1. Of some vulgar fractions reduced to Decimalls retaining true proportions The Denominator of every fraction is in proportion unto the Numerator as are the Integers to their parts according to the Rule of Fractions Lib 1. Sect 2. Parag 1. Paradig 9. then by the first of these 4 Examples ½ is a fraction propounded for to be made a Decimall of which suppose 10 to be the integer then say by the Rule of Three As 2 is to 1 so 10 unto 5 which are proportionall numbers Lib 2. Parag 7 Ax 11. that is as the Denominator of the given fraction is unto its Numerator so shall 10 100 1000 c. the Decimall Denominator be

reigne who changed the value of those Pence unto 3 Pence the piece as now they stand so a Grain of Wheat as a fraction of a fraction to 1 Pound-Troy the Integer will stand thus viz 1 24 of 1 29 of 1 12● that is by reduction 1 5760 parts Averdupois weight 24 Graines of wheat 1 Scruple 3 Scruples make 1 Dragme 8 Dragmes make 1 Ounce Averdup 16 Ounces make 1 Pound Averdup 14 Pound Averdup 1 Stone 2 Stone or 28 lb ¼ Of an Hundred 4 Stone or 56 lb ½ a Hundred 8 Stone 112 lb 1 Hundred weight 5 Hundred lb 1 Hogshead 10 Hundred lb 1 Butt or Pipe 20 Hundred lb 1 Tunne or Loade This is called Civill or Merchants weight with which is weighed all grosse commodites and Merchandizes Malynes lex Mercat pag 49. 252. of these there are two kindes viz the lesser and the greater these proceed originally from a Graine of Wheat Georgius Agricola de pond mens and so in severall parts and denominations they encrease to a pound the lesser weight by which are sold commodities by retaile as Butter Cheese Flesh Tallow Wax and what hath the name of Garbell and whence issueth Wast or Refuse of this a Pound is the Integer and the least of the greater weight whose Integer is 1 C that is 112 lb and as fractions they may be thus exprest the lesser weight proceeding from a grain of Wheat viz 1 24 of ⅓ of ⅛ of 1 16 which if reduced is 1 9216. and the greater weight proceeding from a pound thus 1 14 of ½ of ½ of ½ that is if reduced 1 1●2 or thus ● 14 of ⅛ which is the same 1 stone being ⅛ part of a hundred Long or radicall measures 4 Barley corns 1 Inch or finger 4 Fingers or Inches 1 Palme or hand 12 Inches or 3 Palmes 1 Foot 18 Inches or 1 ½ Feet 1 Cube 3 Feet or 2 Cubes 1 Yard 3 Feet and 9 Inches 1 Elle 5 Feet 1 Pace Geometricall 6 Feet or 2 yards 1 Fathome 5 ½ Yards or 16 ½ Feet 1 Pearch or Pole 40 Perches 132 Paces 1 Furlong 8 Furlongs 320 Pole 1 Mile English 3 Miles 1 League These are named long or radicall by reason the superficies of divers things are measured by the Squares composed of their sides commonly called Roots vide 33 Edw 1. 25 Eliz in Geometrie the least of these is a Barley corn in breadth being ¼ of an Inch from whence all the other measures are derived as in the Table the Integers of these are Feet Yards Paces Poles c. the fractions as to the greatest denomination may be thus exprest ¼ of ¼ of ⅓ of ⅓ of 2 11 of 3 40 of ⅛ of ● 3 these fractions reduced into a single fraction will be 1 760320 which may be made out of fewer compositions or more for these proceed from a Barley corn and so to a Palme a Foot a Yard a Pole a Furlong a Mile and a League the greatest denomination here Of concave drie measures 2 Pints or pounds 1 Quart 2 Quarts 1 Pottle 2 Pottles 1 Gallon 2 Gallons 1 Peck 4 Peckes 1 Bushell Land measure 5 Peckes 1 Bushell Wat. measure 4 Bushels 1 Coombe 2 Coombes 1 Quarter 4 Quarters 1 Chalder 5 Quarters 1 Tunne or Wey These measures are derived from a Pint which of Wheat is supposed to weigh 1 pound Troy from hence proceeding unto Gallons 8 of them making 1 Bushell usually called Land measure and 5 pecks doe make 1 bushell of Water measure 5 quarters is the greatest denomination containing 1 Tunne Wey or sized Load the Measures here proceeding from a Pinte may be expressed in broken numbers or fractions of fractions thus ½ of ½ of ½ of ½ of ¼ of ¼ of ½ of ⅕ and these fractions by reduction will be made a single fraction as 1 512 if 1 quarter were the Integer but if a Tunne it must be ⅕ more and then it will be 1 2560 the fraction required proceeding from a Pinte unto a Wey by these are measured drie commodities viz all kindes of Graine Salt Lime Sea-coale c. Of concave liquid measures 2 Pints 1 Quart 2 Quartes 1 Pottle 2 Pottles 1 Gallon 8 Gallons 1 Firkin of Ale Soape or Hering 9 Gallons 1 Firkin of Beer 2 Firkins 1 Kilderkin 2 Kilderkins 1 Barrell 36 Gallons 42 Gallons 1 Tierce 63 Gallons 1 Hogshead 2 Hogsheads 1 Pipe or Butt 2 Butts 252 Gallons 1 Tunne By these all liquid substances are measured proceeding from a Pint unto a Tunne the Integer containg 252 Gallons or 2016 Pints which will be expressed by fractions of fractions thus ascending by these particulars excepting the Ale Firkin Kilderkin and Pipe viz ½ of ½ of ½ of 1 9 of ¼ of ● 7 of ⅔ of ¼ which is 12 24192 or reduced 1 2016 the fraction made of a Pinte and a Tunne the Integer A Table of Time 60 Seconds makes 1 Minute 60 Minutes 1 Houre 24 Houres 1 Day naturall 7 Daies 1 Week 4 Weekes 1 Moneth 13 Moneths 1 Day 6 Houres 1 vulgar Yeare   Or 365 D. 5 H. 48 M. 55 S. The magnitude of a common Year This is a Table of Time but not of these from hence the Worlds infancy derives a pedegree with a continuall succession of Dayes Moneths Years unto this declining Age proceeding here from a Second and terminated with a Yeare wherein I will conclude being there is a time for all things I could have derived these from Thirds and Fourths c. but doe conceive Seconds are sufficient for common use 60 making a Minute as in the Table not perfectly true errors encreasing as the times an Hour unlimited in humane understanding and is onely known to GOD the sole Creator of all as I will instance in a Naturall day generally conceived for to consist of 24 Houres just which opinion is reprehensible in humane sense and found to containe 57 Seconds more yet one Day not equall unto another some being greater and others lesse for which I have inserted at the bottome of the Table the magnitude of a common Intercalary yeare according to the opinion of divers learned men the fractions are not here subscribed being written as the last and so pronounced their termes respectively considered besides the year is also divided into 12 Solar months each containing 30 equall parts and by some into 30 dayes 5 12 or 10 houres which is 4 seconds and more to little so fearing I should write too much of this and consequently lose time I will here conclude this Chapter and proceed to the next Sect. I. Chap. VII Of Decimall Tables calculated to 7 places according to the fractions before in Number Weight and Measure with Time made apt for use in this kinde of Artificiall Arithmetick I. The Decimall Tables of reduction of English Coines unto sevenths are these An explanation THis Decimall Table of English Coines is divided into 4 columnes or denominations each of those in