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151 to have laid 152 in his way. 153 Upon the whole, 154 I would endeavour 155 to establish 156 this maxim, 157 that the practice 158 of virtue 159 is the most 160 proper 161 method 162 to give 163 a man 164 a becoming assurance 165 in his words 166 and actions. 107 Guilt 163 always 169 seems 170 to shelter 171 itself 172 in one 173 of the extremes, 174 and is 175 sometimes 176 attended 177 with both.
9 a resolution
45 of all
46 those checks 147 and restraints 148 bis temper 249 and complexion
ARITHMETIC is the most necellary of all the sciences From hence we may account for the perfection to which this part of literature is brought, atove any other branch of mathematical science.
Notation, ftri&tly speaking, is that part of arithmetic which teaches how to write any number by its proper chara&ters, or figures, and consequently in their due places; also to read, or discover, the true value of such number, when written,
All numbers, and the various combinations of them, are noted by these ten characters, I one, 2 two, 3 three, 4 four, s five, 6 fix, 7 feven, 8 eight, 9 nine, o cypher or nothing.
Each of these characters, when used alone, stands for no inore than its own intrinsic value : thus, i stands only for one in number, 2 for only 2, &c. But when any of them are joined to other figures, they together stand for more than their own real separate value: thus, 1 and 2, joined together thuis, 12, stands for twelve; 6 and 5, joined together, stands for 65, Gxty-five, &c.
In order to discover the value of any compounded num ber it mutt be observed, that a number placed in the first place towards the right hand, hands for no more than its seal intrinsic value, but increases in value in a tenfold proportion by every remove wowards the left hand : thus, in the number 1799, the first figure g stauds for 9 only; the second figure being in the second place towards the left hand, its value is increased tenfold; thus it represents ninety, or ten tia pes nine ;, which, with the foregoing, stands for ninetyni ne. Again, the figure 7, which stands in the third place towards the left band, is increased to ten times as much as it
ould be if it stood in the next inferior place, viz. where the la ft-mentioned 9 ftands: thus it represents feven hundred ;
bich, with the two fore-mentioned figures, stand for feven bundred and ninety-nine. The figure 1, which stands in the fourth place, towards the left hand, is also increased ten times Jo value to what it would be if it ftood in the next inferior place, where the 7 is placed ; in which case it would represent one hundred; whereas, in the present instance, it stands for one thousand; and with the other figures represents one thousand, seven hundred, and ninety.niixe.
This description of the four foregoing figures may ferve to give the uninformed an idea of the value of figures, according to the different places they occupy in a compounded number. For every remove of a figure towards the left hand increases its value to ten times as much as before; as will more fully appear by the following table, called the Numeration Table;
Home Hundreds of millions of millions.
is Tens of millions of millions.
o Thousands of millions.
1 2 3, 4 5 6, 7 8 9,0 99, 7 6 5
1 2 3, 4 5 6
In order to read any number with facility and ease, it is necessary that the learner have all the names of the numbers at the head of the table perfectly in his memory, that he may apply them to any other number he may have occasion for ; calling the first figure, on the right hand, units; the second, tens; the third, hundreds; the fourth, thousands; &c. as in the table..
Thus, the bottom figure in the table, ftanding under the place of units, is itself an unit, or a fingle one. The next
higher nu mber in the table consists of two figures, i and o; the first w hereof, standing in the place of tens, stands for ten, being only a figure one: the other figure, being a cypher, and in the place of units, stands for nothing, or na units : these two figures, therefore, express only ten. The next number consists of the figures 432; the four being in the place of hundreds, signifies so many hundreds ; the three, as many tens; and the two, as many units; and is thus ex. pressed : four hundred and thirty-two. The fourth number in the table consists of four figures, the first whereof stands in the place of thousands;, this number, therefore, is thus expressed : eight thousand, seven hundred, and fixty-five, The fifth number has its highest figure in the place of tens of thousands, and is thus expressed : seventy-eight thousand, nine hundred, and nine; it having a cypher in the place of tens, which stands for nothing. The fixth number confifts of hundreds of thousands, and is thus expressed ; one bun. dred and twenty-three thousand, four hundred, and fifty-six. The highest place of the seventh number is that of millions ; it is expressed thus : fix million, five hundred and forty-three thousand, two hundred, and ten. The eighth number con. fifts of tens of millions, and is thus expressed: fixty-seven million, eight hundred and pinety thousand, nine hundred, and eighty-seven. The ninth number has its highest figure in hundreds of milions; it is expressed thus : three hundred and twenty-one million, twelve thousand, three hundred, and forty-five.
The six other numbers are expressed as follows:- The tenth number : seven thousand, eight hundred and ninety millions, nine hundred and eighty-seven thousand, fix hundred, and fifty-four. The eleventh number: forty-three thousand, two hundred and ten million, one hundred and twenty-three thousand, four hundred, and fifty-fix. The twelfth oumber : four hundred and fifty-fix thousand, seven hundred and eighty-nine million, ninety-eight thousand, seven hundred, and, fixty-five. The thirteenth number: