1929 a sourcebook in mathemathics - david eugene smith
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SOURCE BOOKS IN THE HISTORY OF THE SCIENCESGregory D. Walcott General
A SOURCE BOOK
HISTORY OF THE SCIENCESGregory D. Walcott General
7^0 w ready
A SOURCE BOOKHarlow Shapley
Dnector, Harvard Observatory
A SOURCE BOOK
David Eugene Smith Columbia
OTHER volumes TO BE
Endorted bj the American Philoiophicjl Aisocuition, tht
Auoc\Atum for Ac AdvancementSociety.
the Htsicny of Science
Ameucan Anihropological Association, th Maihc
Assoaatum of America, the American Miiihanerceive not.
your great Clerk-Iinesse by the I will let that passe now, because it toucheth not the matter that I intend, and I will shew you how Arithmetick doth profit in all these somewhat grosly, according to your small understanding, omitting other reasons moreperceive
ordering of your Sciences: but
you reckon them) Musick hath not onely great help is made, and hath his perfectnesse of it: for all Musick standeth by number and proportion: And in Physick, beside the calculation of critical! dayes, with other things, which I omit, how can any man judge the pulse rightly, that is ignorant of the proportion of numbers? And so for the Law, it is plain, that the man that is ignorant of Arithmetick, is neither meet to be a Judge, neither an Advocate, nor yet a Proctor. For how can hee well understand anotherFirst (as
of Arithmetick, but
cause, appertaining to distribution of goods, or other debts,
he be ignorant of Arithmetick?
oftentimes causeth right to bee hindered, when the Judge either delighteth not to hear of a matter that hee perceiveth not, or cannot judge for lack of understanding: this commeth by ignoranceof Arithmetick.
Grammer, me thinketh you would not doubt in what it needeth number, sith you have learned that Nouns of all sorts. Pronouns, Verbs, and Participles are distinct diversly by numbers: besides the variety of Nouns of Numbers, and Adverbs. And if you take away number from Grammer, then is all the quantity of Syllables lost. And many other ways doth number help Grammer. Whereby were all kindes of Meeters found and made? was it not by number? But how needfull Arithmetick is to all parts of Philosophy, they
that do read either Aristotle, Plato, or any other For all their examples almost, and their Philosophers writings. It is the saying of Aristotle, probations, depend of Arithmetick.
that hee that
ignorant of Arithmetick,
RECORDSAndPlato his Master wrote alittle
sentence over his Schoolhouseis
door, Let none enter in hither (quoth he) that
Geometry. Seeing hee would have all his Scholars expert in Geometry, much rather he would the same in Arithmetick, without which Geometry cannot stand.
And how needfull Arithmetick is to Divinity, it appeareth, seeing many Doctors gather so great mysteries out of number, and so much do write of it. And if I should go about to write all theso
commodities of Arithmetick in civill acts, as in governance of Common-weales in time of peace, and in due provision & order of Armies, in time of war, for numbering of the Host, summing of their wages, provision of victuals, viewing of Artillery, with other
Armour; beside the cunningest point of all, for casting of ground, for encamping of men, with such other like: And how many wayesalso Arithmetickis
private Weales, of Lordsail
Possessioners, of Merchants,all
other occupiers, and
estates of men,
besides Auditors, Treasurers,
Receivers, Stewards, Bailiffes, and such like, whose Offices without Arithmetick are nothing: If I should (I say) particularly repeat all such commodities of the noble Science of Arithmetick, it were enough to make a very great book. No, no sir, you shall not need: For I doubt not, but Scholar. you have said, were enough to perswade any man to this, that
think this Art to be right excellent and good, and so necessary for
think now) so
lacketh of his sense and wit.
What, are you so
these few commodities in generall:
you would be farre changed if you knew all the particular Commodities. Scholar. I beseech you Sir, reserve those Commodities that rest yet behinde unto their place more convenient: and if yee will bee so good as to utter at this time this excellent treasure, so thatlikelihoodI
be somewhat inriched thereby,I
requite your pain.
sith that to learn it
very glad of your request, and you bee so ready.I
to your authorityit
wit do subdue; whatso-
ever you say,
That is too much; and meet for no man to bee beleeved without shewing of reason. Though I might of my Scholar some credence require, yet except I shew reason, I do itMaster.in all things,
SOURCE BOOK IN MATHEMATICSBut nowit is
you are so earnestly set this Art to some other passion coole heat, and then you leave off before you see the end. this great Scholar. Though many there bee so unconstant of mind, that flitter and turn with every winde, which often begin, and never come to the end, I am none of this sort, as I trust you partly know. For by my good will what I once begin, till I have it fully ended, I would never blin. Master. So have I found you hitherto indeed, and I trust younot desire.sith
to omit no time, lest
were never to the mid way: But I trust 30U will assay, then to shrink and briefly: What call you the Science not do so; therefore tell mee that you desire so greatly. Why sir, you know. Scholar. Master. That maketh no matter, I would hear whether you know, and therefore I ask you. For great rebuke it were to have studied a Science, and yet cannot tell how it is named. Some call it Arsemetrick, and some Augrime. Scholar. Master. And what do these names betoken? That, if it please you, of you would I learn. Scholar. Master. Both names are corruptly written: Arsemetrick for Arithmetick, as the Greeks call it, and Augrime for Algorisme, as the Arabians found it: which both betoken the Science of Numbring: for Arithmos in Greek is called Number: and of it commeth Arithmetick, the Art of Numbring. So that Arithmetick is a Science or Art teaching the manner and use of Numbring: This Art may be wrought diversly, with Pen or with Counters. But I will first shew you the working with the Pen, and then thewill increase rather
then go back.flie in
other in order.Scholar.
But how many things are
to bee learned to attain this Art fully?
There are reckoned commonly seven parts or works of it. Numeration, Addition, Subtraction, MultipHcation, Division, Progression, and Extraction of roots: to these some men addeMaster.
Duphcation, Triplation, and Mediation. But as for these three they are contained under the other seven. For Duplication, and Triplation are contained under Multiplication; as it shall appear in their place: And Mediation is contained under Division,last
will declare in his place also.
Yet then there remain the
So there doth: Howbeit if I shall speak exactly of the Numbrlng, I must make but five of them: for Progression is a compound operation of Addition, Multiplication and Division. And so is the Extractions of roots. But it is no harme to name them as kindes severall, seeing they appear to have some several! working. For it forceth not so much to contend for the number of them, as for the due knowledge and practising of them. Scholar. Then you will that I shall name them as seven kindes distinct. But now I desire you to instruct mee in the use of eachparts of of them.
not learn the last so soon as thethat order, as
must be done in order: for you may first, but you must learn them in did rehearse them, if you will learn them speedily,will,
as you please. Then to begin; Numeration is what shall I do with it? First, you must know what the thing is, and then after
learn the use of the same.
(Translated from the French by Professor Vera Sanford, Western
Reserve University, Qeveland, Ohio.)invention of the decimal fraction cannot be assigned to any single Pellos (1492) used a