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Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
cause_n	call_v	great_a	world_n	1,652	5	4.2491	3	false

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ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A10530	The grounde of artes teaching the perfect vvorke and practise of arithmetike, both in whole nu[m]bers and fractions, after a more easie ane exact sort, than hitherto hath bene set forth. Made by M. Robert Recorde, D. in Physick, and afterwards augmented by M. Iohn Dee. And now lately diligently corrected, [and] beautified with some new rules and necessarie additions: and further endowed with a thirde part, of rules of practize, abridged into a briefer methode than hitherto hath bene published: with diverse such necessary rules, as are incident to the trade of merchandize. Whereunto are also added diuers tables [and] instructions ... By Iohn Mellis of Southwark, scholemaster.; Ground of artes	Record, Robert, 1510?-1558.; Dee, John, 1527-1608.; Mellis, John, fl. 1588.	1582 (1582)	STC 20802; ESTC S102132	245,945	706

vse of those rules whiche without them can not wel be wrought Maister If my leasure were as great as my will is good you shoulde not néede to vse anye importunate crauing for the attaining of that thing whereby I maye be perswaded that I shal anye waies profite the common wealth or helpe the honest studies of anye good members in the same wherefore while myne attendaunce will permitte me to walke and talke I am well willing to helpe you as I may VVhat a Fraction is Therefore firste to beginne with explication of this name Fraction what take you if to be Scholer Marie sir I thinke a Fraction as I haue heard it often named to be a broken number that is to say to be no whole nūber but a part of a number Mayster A Fraction in déede is a broken number and so consequentlie the part of another number but that muste be vnderstanded of suche an other number as can not bée diuided into any other partes thā Fractions for although I may take the third part of 60 or the fourth part of it and so of other partes diuerslie yet these partes be not properlie nor ought not to be called Fractions bycause they maye be expressed by whole numbers for the third part of it is 20 the fourth part is 15 the twelfth part is 5 and so forth of other parts which all be whole numbers Wherefore properlie a Fraction expresseth the partes or part onelie of an vnit VVhat a Fraction in properlie that is to saye that the number which is the whole or entire summe of anye Fraction may not be greater than one and therefore it followeth that no one Fraction alone can be so gret that it shall make 1 as by examples I will declare as soone as I haue taught you to knowe the forme howe a Fraction is expressed or represented in writing NVMERATION BVt first to begin with the expressing of a Fraction which is the numeration of it you must vnderstand that a Fraction is represented by 2 numbers set one ouer the other and a line drawen betwéene them as thus ⅓ ● 4 ⅘ 10 17 which foure Fractions you muste pronounce thus ● 3 one thirde parte ¾ thrée quarters ⅖ two fifte partes 10 17. tenne seauentéene partes Scho. I vnderstande the forme of theyr expression and pronunciation but their meaning or valuation séemeth more obscure yet I think that by the two first Fractions I vnderstand the valuation of the two later Fractions and so consequentlie of other M. Value them then that I may perceyue your taking of them Scholer ⅖ betokeneth two fifte partes that is to say if one be diuided into 5 parts that Fraction doeth expresse ij of those fifthe partes 10 17 doth signifie that if one be diuided into xvij partes I must take tenne of them And this I gather of the two firste examples for ⅓ that is one thirde parte doth easily declare that if anye one thing be diuided into three partes I muste take but one of them so ¾ that is thrée quarters doeth declare that one being diuided into four quarters I must take for this Fractiō thrée of those quarters If there be no more difficultie in their Numeration thē I pray you go forward to their Addition and Subtraction ☜ and so to the other kinds of workes for I vnderstande that the same kinds of workes be in Fractions that be in whole numbers Maister There are the same kynds of workes in bothe albeit the order of them is diuerse as I will anone declare but yet more in Numeration before we leaue it You muste vnderstande that those two numbers whiche expresse a Fraction haue seuerall names Numerator and Denominator The ouermost whiche is aboue the line is called the Numerator and the other beneath the lyne is called the Denominator Scholer And what is the reason of theyr diuerse names For in mine opinion both bee Numerators séeing both they do expresse the numeration of the Fraction Maister You are deceiued for one onelye whiche is the ouermoste doeth expresse the Numeration and the denominatour doeth declare the number of partes into whiche the vnit is diuided as in this example when I say Diuide a pounde weighte of Golde betwéene foure men so that the firste man shal haue 2 15 the seconde 2 15 the thirde 4 15 and the fourth 6 15. Now do you perceiue the by the denominator whiche is one in al foure Fractions it is intended that the pounde waight shoulde be diuided into so manye partes I meane 15 and by the foure seuerall numerators is limitted the diuerse portion that each man shold haue that is that whē the whole is parted into 15 the firste man shall haue 2 of those 15 partes the second man thrée of them the third man 4 and the fourth man 6. And so may you sée the seueral offices as it were of those two numbers I meane of the Numerator and the denominator And hereby you perceiue that a man can haue no more parts of any thing than it was diuided into nether yet aptlie so many so that it were vnaptly sayd You shall haue 15 15. that is xv fiftéene partes of any thing séeing it were better sayde You shal haue the whole thing Sc. So doth it appeare reasonablye for the labour is vaine to diuide anye thing and than to applie the Diuision to no vse And much lesse reasonable were it to say 16 15 for if the whole be diuided into 15 parts only it is not possible to take 16 of them that is to say more than altogither Maister This is true touching the proper and apte vse of the name of a Fraction ☜ yet improperlye and after a vulgare acceptation for easinesse in worke both those formes be called Fractions because they be writtē like fractions although they be none in déede for 15 15 and generally all suche other where the Numerator and Denominator be equal are not Fractions but the whole thing with all his partes And so 16 12 is not to be called a fraction but a mixt number of a whole number and a Fraction for it is as muche as 1 4 12 that is one whole one and 4 twelue partes as shall be declared in Reduction Therefore they doe abuse the names that call them Fractions where the Numerator is either equall or greater than the Denominator Sc. But is there any néedefull cause why they should so abuse the name Mai. There is cause why they shal sometimes for easinesse in worke write some nūbers after that sorte like fractions but they néeded not to call them fractions but as they be whole numbers or mixt numbers that is whole numbers with Fractions expressed like fractions Nowe must you vnderstande that as no fraction properly can be greater than 1 so in smalnesse vnder one the nature of Fractions doeth extende infinitelye as the nature of whole numbers is to increase aboue one infinitelye so that not onely one may be

men yet am I bolde to put my selfe in preace with such abilitie as God hath lent mee thoughe not with so greate cunning as manye men yet with as great affection as any man to help my countrymen and wil not cease dayly as much as my small abilitie wil suffer me to endite some such thing that shall be to the instruction though not of learned men yet at the least of the vulgare sort whose argument alwayes shall be such that it shall delight al learned wits though they do not learne any great things out of it But to speake of this present Booke of Arithmetick I dare not nor wil not set it foorth with any words but remit it to the iudgement of all gentle readers namelie such as loue good learning beseeching them so to esteeme it as it doth seeme worthie And so either to accept the thing for it selfe either at the leaste to allowe my good endeauour But I perceiue I neede not vse anye persuasions vnto them whose gentle nature and fauourable minde is readie to receiue thankefullye and interpreate to the best of al suche enterprices attempted for lo good an ende though the thing do not alwayes satisfie mens expectation This considered did bolden me to publish abroade this little Booke of the Arte of numbring which if you shal receiue fauourablie you shal encourage me to gratifie you hereafter with some greater thing And as I iudge some menne of so louing a minde to their natiue countrey that they woulde much reioyce to see it to prosper in good learning and wittie Artes so I hope well of all the rest of Englishmen that they wyl not be vnmindeful of his due praise by whose meanes they are helped and furthered in anye thing Neither ought to esteeme this thing of so little value as manye men of little discretion oftentimes do For who so setteth small price by the wittie deuise and knowlege of numbring he little considereth it to be the chiefe point in manner wherby men differ from all bruite beastes for as in al other things almost beastes are partakers with vs so in numbring we differ cleane from them and in manner peculiarlie fith that in manie things they excel vs againe The Fox in craftie witte exceedeth most men A dogge in smelling hath no man his peere To foresight of weather if you looke then Many beastes excel man this is cleere The wittinesse of Elephants doth letters attaine But what cunning doth there in the Beeremaine The Emmet foreseeing the hardenesse of winter Prouideth vitailer in the time of Sommer The Nightingale the Lines the Thrush the Larke In Musical harmonie passe manie a Clarke The Hedgehog of Astronomie seemeth to knowe And stoppeth his caue where the wind doth blowe The Spider in weauing such are doth show No man can him mende nor follow I trow When a house wil fall the Mice right quicke Flee thence before can man do the like Many things else of the wittinesse of beasts byrdes might I heere saye saue that another time I entende to write wherein they excel in manner all men as it is daylie seene but in number was there neuer beast found so cunning that coulde know or discerne one thing from manye as by daylie experience you may well consider when a Bitch hath manie whelpes or a Hen many Chickens and likewise of other whatsoeuer they be take frō them al their yong sauing onlie one and you shall perceiue plainly that they misse none though they wil resist you in taking them away and wil seeke them again if they may know where they bee but else they wil neuer misse hem truelye but take awaie that one that is left and then wil they crie and complaine and restore to them that one then are they pleased againe so that of nūber this may I iustlie say It is the only thing almost that separateth man from beastes He therefore that shal contemne number he declareth himselfe as brutish as a beast and vnworthy to be counted in felowship of men But I trust there is no man so foule ouerseene thoughe manie right smallie do it regarde Therefore wil I now stay to write against suche and returne againe to this booke whiche I haue written in the forme of a Dialogue bicause I iudge that to bee the easiest way of instruction when the Scholer may aske euerie doubt orderlie and the maister may answer to his question plainelie Howbeit I thinke not the contrary but as it is easier to blame an other mans worke than to make the lyke so there wil be some that wil finde fault bicause I write in a Dialogue but as I coniecture those shal be suche as doe not cannot either will not perceiue the reason of right teaching and therefore are vnmeete to be aunswered vnto for such men with no reason wil be satisfied And if any man obiect that other bookes haue bene written of Arithmetike alreadie so sufficientlie that I needed not now to put pen to the booke except I will condemn other mens writings to them I aunswer That as I condemne no mans diligence so I know that no one mā can satisfie euerie man and therefore like as manye do esteme greatly other Bookes so I doubt not but some wil like this my Booke aboue any other English Arithmetike hitherto wrtiten and namely such as shall lacke instructers for whose sake I haue so plainely set foorthe the examples as no Booke that I haue seene hath done hitherto whyche thing shall bee greate ease to the rude readers Therefore gentle reader though this booke can bee small aide to the learned sorte yet vnto the simple ignorant which needeth most help it may be a good furtherance and meane vnto knowledge And though vnto the King his Maiestie priuatelye I doe it dedicate yet I doubt not suche is his clemencie but that hee can bee content yea and much desirous that all his louing subiects shal take the vse of it and employ the same to their most profit Which thing if I perceiue that they thankefullie do and receiue with as good will as it was written then wil I shortly with no lesse kindnesse set forth suche introductions in to Geometry and Cosmography as I haue at other times promised and as hitherto in English hath not bene enterprised wherwith I dare say al honest heartes wil be pleased and all studious wittes greatlye delighted I wil say no more but let euerie man iudge as he shal see cause And thus for this time I will staye my penne committing you all to that true fountaine of perfect number which wrought the whole world by number and measure he is Trinitie in Vnitie and Vnitie in Trinitie To whom be all praise honor and glorie AMEN Here folovveth a Table of al the Contents of this Booke The Contents of the firste Dialogue containeth the Declaration of the profite of Arithmetike Numeration with an easie large Table Addition Subtraction Multiplicatiō Diuision with diuers Exāples

The Proofes An other Example SVBTRACTION Scholer THen haue I learned the two first kindes of Arithmetike nowe as I remember doeth folowe Subtraction whose name me thinketh doth sounde contrarie to Addition Maister So is it in déede for as Addition encreaseth one grosse summe by bringing manye into one so contrarie waies Subtraction diminisheth a grosse summe by withdrawing of other from it so that Subtraction or Rebating is nothing else but an art to withdrawe and abate one summe from an other that the Remainer may appeare Scholer What do you call the Remainer Maister That you maye perceyue by the name Scholer So me thinketh but yet it is good to aske the trouth of all such things leaste in trusting to myne owne coniecture I bée deceyued Maister So is it the surest waye And as I sée cause I wyll still declare thyngs vnto you so plainelie that you shall not neede to doubte Howbeit if I doe ouerpasse it sometimes as the manner of men is to forget the small knowledge of them to whome they speake then do you putte me in remembraunce your selfe and that way is surest And as for this worde that you laste asked me take you this description Remainer The Remainer is a summe lefte after due Subtraction made which declareth the excesse or differēce of the two other numbers as if I woulde abate or subtract 14 out of 18 there should remaine 4 which is called the remayner and is the difference betwéen those two numbers 14 18. Scholer I perceiue then what Subtraction is Nowe resteth to knowe the order to worke it Maister That shall you doe by this meanes Firste you muste consider ☜ that if you should go about to rebate you must haue two sundrie summes proposed the firste which is your grosse summe or summe totall and it must be set highest and then the rebatement or summe to be withdrawen which must be set vnder the firste whether it bée in one parcel or in many and that in suche sort that the firste figures be one iuste ouer an other and so the seconde and thirde and all other folowing as you did in Addition then shal you drawe vnder them a line and so are your summes duelie set to beginne youre working Then beginne you at the righte hande as you did in Addition and withdrawe the nether number out of the higher and if there remaine anye thing write that righte vnder them beneth the line and if ther remaine nothing by reason that the 2 figures were equal then write vnder them a ciphar of noughte And so doe you with all the other figures euermore abating the lower out of the higher and write vnder them the Remainer still til you come to the ende And so will there appeare vnder the line what remayneth of youre grosse summe after you haue deducted the other summe from it as in this example I receiued of your father 48 s of whiche I haue layde out for you 36 s nowe woulde I knowe what doeth remaine and therefore I set my numbers thus in order First I write the greatest summe and vnder him the lesser so that the figures at the right side be euen one vnder another and so the other thus Then do I rebate 6 out of 8 and there resteth two which I write vnder them right beneath the line thus Then I go to the second figures and do rebate 3 out of 4 where there remaineth 1 which I write vnder them righte and then the whole summe and operation appeareth thus Whereby it appeareth that if I withdraw 36 out of 48 there remaineth 2. Scholer Nowe will I proue in a greater summe And I wil Subtract 2367924 out of 3468946. Those summes I set in order thus Then doe I beginne at the righte side and deducte 4 out of 6 and there resteth 2 whiche I write vnder them Then goe I to the seconde figures and withdrawe 2 out of 4 and there remaine two whiche I set vnder thē also then I take 9 out of 9 and there resteth 0 which I write vnder them for you say that if the figures be equall so that nothing remain I must write this ciphar 0 vnder them Maister It was well remembred nowe go foorth Scholer Then I come to the fourth place and draw 7 out of 8 and there remayneth 1 which I write vnder them also Then in the fifte place I take 6 from 6 and there resteth nought for it I write vnder them a ciphar 0 Then in the sixt place 3 rebated from 4 there remayneth 1 which I write vnder them and likewise in the vij last place 2 taken from 3 there is lefte 1 whiche I write vnder them so haue I done my whole working and my summes appeare thus Whereby I sée that if I rebate 2367924 out of 3468946 there remayneth 1101022. Maister Thys is well done And that you maye be sure to perceiue fullye the Art of Subtractiō let me see how can you subtract 52984732 out of 8250003456. Scholer Firste I sette downe the greatest summe and after that I write vnder if the lesser number beginning at the righte syde and then my figures will stand thus Then take I 2 from 6 and the reste is 4 whiche I write vnder them then doe I withdrawe 3 from 5 and there remayne 2 which I write vnder them Then take I 7 out of 4 but that I cannot what shal I now doe Mayster Marke well what I shall tell you now Note how you shall doe in this case and in all other like If any figure of the nether summe be greater than the figure of the summe that is ouer him so that it cannot be taken out of the figure ouer him then muste you put 10 to the ouer figure and then consider how muche it is and out of that whole summe withdrawe the nether figure and write the rest vnder them Can you remember this Scholer Yes that I trust I shall Now then in mine example where I shoulde haue taken 7 out of 4 and coulde not I put 10 to that 4 which maketh 14 from it I take awaye 7 and there resteth 7 also whiche I write vnder them Mayster So haue you done well but nowe muste you marke another thing also that whensoeuer you doe so put 10 to any figure of the ouer number you must adde one stil to the figure or place that followeth next in the nether line as in this example there followeth 4 to which you must put 1 and make him 5 then go on as I haue taught you Schol. Then shall I say 4 and 1 which I must put to him for the 10 that I added to 4 before make ● which I should take out of 3 but that cannot be therefore must I put to it also 10 then it will be 13 from whiche I take 5 and there resteth 8 to be written vnder them and because of that 10 added to the 3 I must ad 1 to 8 that followeth in the nether line