I John Smyth, Writing-Master Johnson Thompson, Writing-Mafter James Thurston, Ditto To the RECOMMENDERS. GENTLEMEN, Return you hearty thanks for the honour you have done me, by the favour of your names to this little Treatife let me crave your further affistance in noting down thofe errors that you may occafionally find, and you will ftill further oblige, April 10, 1765. GENTLEMEN, Your very humble Servant, Daniel Fenning. N. B. Gentlemen are taught Algébra, and the Use of the Globes, at their own houses, by the Author. THE THE INTRODUCTION. CHAP I. DIALOGUE I. Between PHILO, a Tutor, or Mafter, and TYRO, a young Scholar; concerning the Rudiments of Arithmetic. Tyro. 136 Tyro vifits Philo. EAR Sir, I am your humble fervant -You will pardon me, I hope I hear you have done inftructing Tyrumculus, and I am come to lay claim to a former promife, of your giving me a better notion of common Arithmetic. Philo. You pleafe me very much, young Tyro, I affure you, to fee you fo willing to learn; but I hear you understand the first four Rules already. Tyro. Tyro. When I was at school I had fome knowledge of them, as I thought; but it was not well-grounded; and when I left fchool, instead of practifing at home, and making myself mafter of what I learnt there, I bent my mind to play and idleness, like other naughty boys; and were it not for your kind offer, I should know the want of it too late, I choose therefore, Sir, to begin at the very loweft branch, that I may fee the reafon of what I am doing, and not learn by rote as too many school-boys do, to the great difcredit of their master, grief of their parents, and their own fu-ture ruin. Philo. You fay very right; for in beginning againyou will be confirmed in what you know already; for I fhall proceed with you the fame as if you never had began, that others may be the better informed; therefore, for their fakes, do not you be angry, if I should dwell upon fome things longer than you may think there is occafion for, fince I tell you the reafon before hand. Tyro. Far be it from me, Sir, to take it amifs, for though I do know fomething of the first four Rules, I am fenfible there are many thousands who know nothing of the matter, and you do well to confider them alfo. Philo. I am glad, Tyro, to see you fo confiderate; it gives me great hopes of your being mafter of what I am about to instruct you in. TO DIALOGUE II. SECTION I of NUMERATION, ADDITION of Whole Numbers, Money, Weights, and Measures, &c. Tyro.WHAT is Numeration and what does it teach Philo. Numeration is the true diftinction and pronun ciation of Number; that is, it teaches us to write down, read, and exprefs any number or numbers whatsoever: for the better understanding of which, obferve the following Table. N. B. The letter C ftands for an hundred, and X for ten. to hundreds of millions. row are units; thofe in left hand, are under the All the figures under the first the fecond row towards the place of tens; all the third are called hundreds; thofe in the fourth row thousands, &c, row Now, in order to know the value of, or how to exprefs any number in the Table, I begin at the top figure towards the right hand, and fay units; (1) then units, tens, (twenty-one, 21;) then units, tens, hundreds, (three hundred and twenty one, 321;) thus I go on and find the fourth figure (viz. 4) under the place or name of thousands, and accordingly, I call it four thousand, which, joined to the other three figures, will be four thousand three hundred, and twenty-one, 4,321. The fifth figure being in the place of tens of thousands, is thus read: fifty-four thousand, three hundred, and twenty-one, 54,321. Thus proceed till you come to the laft figure of all, towards the left hand, (which ftands in the place of hundreds of millions) and you will eafily perceive that thofe nine figures are thus expreffed: nine hundred, eighty feven millions, fix hundred, fifty-four thousand, three hundred, and twenty one, 9,87,654,321. Read this once more, and obferve the comma's, or- ftops, that are put to the figures: for they answer to, or correfpond with, the ftops in the words that are written out at length. NOTE 2. You are further to obferve, Tyro, that the Numeration Table is not always fet with these figures just in the form they here ftand: for had they been any other nine figures, they are numbered and expreffed after the fame manner; for inftance, fuppofe they were 1,2,3,4,5,6,7,8,9 this is expreffed after the fame manner, only instead of 987 million, it is now 123 million; inftead of 654 thousand, it is here 456 thouand inftead of 321, it is now 789. So alfo, fand; 999,999,999 |