Of Changes in Bells; in Mufical Inftruments, &c. I I. Of Changes in Bells. T. is often difputed among common Ringers, what Number of Changes may be made in 5, 6, 7, 8, or any other Number of Bells. This and fuch like Questions may be easily refolved; for it is but multiplying every number from the Unite fucceffively into each others Product, unto the number of Unites affigned; according to which the following Table is made, as is eafy to perceive: And fo the Number standing against VI in the Table,is 720, and fo many Changes may be made upon Six Bel's; 5040 upon Seven, &c. II. Of Voices. If it were required to know how many Conforts Ten Voices will make, each man keeping his own Note, but altering his Place; against the Number X in the Table you find this number 3628800; which is Three millions, fix hundred twenty eight thousand, and eight hundred; and so many Conforts may be made of Ten Voices. It it also the fame in Stringed Instruments; and the Gamauth may be varied. according to this, anfwerable to the Number standing against XXII, namely, 1124000727777607680000 Notes. III. Of Changes of Places. Into how many feveral Pofitions may the Twelve Figures about the Dial-Plate of a Watch or Clock-Dial be placed? The work is cafily done, for the Number standing against XII in the Table will refolve you, viz. 479001600, which is, Four hundred feventy nine millions, one thousand and fix hundred times. And according to this way there was a pretty Bargain made between a Young Scholar and a Countrey Gentleman; which is this: A Young Scholar being come to a Countrey Town where he intended to refide fome time, lit into a Gentleman's Houfe, where there were in Family the Mafter, Miftrefs, and Four Children, which with himself made Seven. At dinner they difcourfed concerning the Scholar's Board there for a Year, for which the Gentleman demanded a certain Sum of Money; which the Scholar thinking too much, made this Overture; That he would give him fo much for a Year as he did demand, provided, That for that fame Money he should have his Board fo long time as he could daily place thofe Seven Perfons that were then at the Table, in a feveral and diftinct Order, fo that they Should never all of them fit in the fame Places as then they did: The Gentleman condefcends: The Question is, How many days may the Scholar Sojourn with the Gentlemán, before all thefe Changes of Places come about? Look in the Table for the Number ftanding against VII, and you fhall find it to be 5040, fo that the Scholar (according to this Agreement) must fojourn with him Five thousand and forty days, which is Fourteen years wanting 70 days; and that at Three-Pence a day will amount unto Threefcore and three Pounds Sterling. IV. Of the Letters of the Alphabet. From hence it is no marvel, that from the mutability of Transmutations, out of the 24 Letters of the Alphabet, there ariseth and is made fuch Variety of Languages as are in the world, and fuch infinite number of Words in each Language, feeing the diverfity of Syllables produceth that effect; and alfo by the interchanging and placing of Confonants among the Vowels, and amongst themselves; fince this Alphabet of XXIV Letters may be varied fo many times as the Number against XXIV amounteth to; viz. 620448401733239439360000. Six hundred and twenty thousand, four hundred forty eight myriads, four hundred and one thousand feven hundred thirty three thousand two hundred thirty nine millions of millions, four hundred thirty nine thousand millions, three hundred and fixty thousand. Now if from hence we fhould allow that a man may read or speak One hundred thousand Words in an hour, which are as many as are contained in all the Gofpels of the Four Evangelifts, and in the Acts of the Apofiles Apoftles alfo, (a Task too great for a man to do in fo fhort a time) and if there were Four thousand fix hundred and fifty thousand millions of men, they could not speak all the Words that the 24 Letters are capable to make (according to the hourly proportion aforefaid in 70000 ThreeScore and ten thousand years; which number of Words if they fhould be written in Books, each Book being 15 inches long, 12 broad, and 6 thick, the Books made of the aforefaid Tranfmutation of the 24 Letters, would be 38778037089928788. And if a Library of a Mile Square every way, of 50 foot high, and in which were 250 Galleries of 20 Foot broad apiece, it would contain but Four hundred millions of the faid Books: So that there must be to contain the reft no less than 96945092, Ninety fix millions, nine hundred forty five thousand, ninety two, fuch Libraries: And if the Books were extended over the fuperficial furface of the whole Earth, it would be a Decupal Covering to the fame, And it is from hence that Tacquet in the 8th. Chapter of his 5th. Book of Arithmetick affirms, That the Permutation of 24 Letters are so numerous, that a Thousand millions of able Clerks, in a Thousand millions of years (not fparing Dominicals nor Festivals) were not able to transcribe them. And Galdinus afferts, That the Books which might be compiled of the variety of 23 Letters only (accounting 1000 Pages to each Volume, and 100 Lines to each Page, and 60 Letters to each Line, and not any two Words in any of thofe Volumes the fame) would do more than twice cover the whole Superficies of the Earth and Sea: Nay farther, he seems to be of opinion, that the Paper of those Volumes laid fingly Sheet by Sheet, would cover the very Firmament. And as in the Tranfpofition of Letters, fo alfo in the Tranfpofition of the Nine Digit Figures, which with the Nul. or Cypher makes Ten, are capable of 3628800, that is, of Three millions, fix hundred twenty eight thousand, and eight hundred Changes. And in Mr. Henry Briggs his Logarithms to 100000, confifting of Sixty nine Sheets, in each Sheet Four Pages, and in each Page Four hundred and fifty numbers, in all 124200; i. e. One hundred twenty four thousand and two hundred Numbers. And in the Canon of Sines Tangents and Secants of the fame Book, confifting of 22 Sheets and a half, in which are Forty Pages, and in each Page Three hundred and fixty numbers; in all 16200; i. e. Sixteen thousand and two hundred Numbers, which with those of the Logarithms, make together 140400, i. e. One hundred and forty thousand and four hundred numbers, and not two Numbers exactly the fame in both the Books: Yet notwithstanding this vaft Number, it is defs than the Number against X in the Table by 3488400: Nay, it is very little above the Twenty fixth part thereof: So that if Twenty fix fuch Books, all of Numbers, and each Book to contain One hundred and forty thousand four hundred numbers, and not any two numbers the fame in all the Books, they would but contain the number of the Number that the Table exhibits against X in the Table. CHAP. CHAP. VIII. СНАР. Of Arithmetical Versifying. Shewing an Artificial way, How from any Six or Five of the Nine Digit Numbers (promiscuously taken, or fet down at all adventures), to make both Hexameter and Pentameter Latin Verfes, which shall be Good Latin, and Good Sense; altho the Party which writes the Verse from the Six or Five Figures fo fet down, doth not understand any thing of the Latin Tongue. The Fundamental SCHEME. How to make Hexameter Verfes by the Scheme. Let Six Figures be written by any person, as these 8, 6, 4, 3, 9, 5, or any other. 6 4 3. 9 5 Triftia Vota Scio, Prædicunt Tempora Tantum. And from any Five Figures collected by the bottom of the Scheme (as thefe 1,9,7,2, 6,) may be made this or any other Pentameter Verfe. Example, 1, 9, 7, 2,6. 2 6 Fœdera Concedunt Afpera Jura Malis. СНАР. If 136 Pound be to be divided between two perfons, fo that one must have 18 Rom the given Sum (136) fubftract (18) the overplus that one perfon must have above the other, and the Remainder will be (118) the half whereof is (59); and fo much muft the one perfon have: And if you add (18) to (59) the Sum will be (77); and so much muft the other perfon have; for these two numbers (77 and 59) added together, do meke up the whole Sum of (136 Pound). PROB L. II. If 136 Pound be to be divided between two perfons, in fuch fort, that the Leffer Share fhall have fuch Proportion to the Greater Share, as 2 bath to 5; What must each perfon have? FOR OR the Working of this or the like Queftion, this is the RULE, or Analogy. As the Sum of the two Proportional terms 2 and 5, (viz. 7.) So is (2) the Leffer of the Proportional Terms given, To(38) the Leffer Share: And fo is (5) the Greater Pro- So if you multiply the given Number (136) by (2) the PROB L. III. There is a certain number of Pounds to be diftributed among Six perfons, in ET the Six perfons be reprefented by these Six Letters, ABCD E must 33 |