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The third Place is Hundreds, the fourth Place Thousands, &c. That is, each Place towards the Left-hand is Ten Times the Value of that next it, towards the Right.
For Instance, suppose 759 were proposed to be read or proEsunced according to the Value of each Figure as they now fand. The first Figure in this Sum is 9, because it stands in the Place of Units, and therefore signifies but it's own simple Value, to wit, 9 Units, or 9. The second Figure 5 stands in the Place of Tens, and therefore signifies Five Tens or Fifty. The Figure 7 ftands in the third Place, or Place of Hundreds, and therefore it signifies Seven Hundred; and the whole Sum is to be read or pronounced thus, Seven Hundred Fifty Nine.
Note, Although the Figure 7 stands in the third Place (according to the Order of Numbering) yet when the whole Sum comes to be read, it is first pronunced; the reading of Numbers being performed like that of Letters or Words, always beginning with the outmost Figure towards the Left-hand, and so many Figures as are placed together without any Point, Comma, Line, or other Note of Distinction between them, are all but one Sum, and muft be read as such.
For Example, 763596 is but one entire Sum or Number, notwithstanding it consists of fix Places of Figures, and is thus read; Seven Hundred Sixty Three Thousand, Five Hundred Ninety Six.
The like is to be observed in reading or expressing the true Value of any Sum or Rank of Numbers consisting of Seven, Eight, Nine, or more Places of Figures, each Figure being to be valued according to it's Distance from the Place of Unity: As in the foregoing 'Table.
Now such Values may as well arise by Cyphers, as by other Figures; for instance, 6 standing by itself, represents but Six Units: But if a Cypber be annext to it thus, 60, then it becomes Sixty; for the Cypher possessing the Place of Units, hath hereby removed the 6 into the Place of Tens; and another Cypher more would make ic 600, Six Hundred, &c.
Whence it may be noted, that although a Cypher of itself fignify nothing (as hath been said before) yet being placed on the Right-hand of any Figure, it augments the Value of that Figure by advancing it into a higher Place than otherwise it would have been, had not the Cypher been there.
Take one Example more in Numeration (if you please, that in the Table) viz. 678987654321, which is, according as is there fignified,
Six Hundred Seventy Eight Thousand Millions,
Three Hundred Twenty One Units. Of any proposed Species or Quantities whatsoever.
And here it may be observed, that every third Figure from the Place of Units, bears the Name of Hundreds; which shews that if any great Sum be parted, or rather distinguished into Periods, of Three Figures in each Period (as in the foregoing Table) it will be of good Use to help the young Learner in the easier valuing and expressing that Sum.
Sect. 2. Of godition.
Poftulate or Petition. That any given pumber may be increased or made more, by putting
another Pumber to it. addition is that Rule by which several Numbers are collected and put together, that so their Sum or Total Amount may be known.
. . In this Rule Two Things being carefully observed, the Work will be easily performed.
1. The first is the true placing of the Numbers, so as that each Figure may stand directly underneath those Figures of the same Value, viz. place Units under Units, Tens under Tens, and Hundreds under Hundreds, &c. . Then underneath the lowest Rank (always) draw a Line to separate the given Numbers from their Sum when it is found.
Example. If these Numbers 54327, and 2651, were given to be added together, they must be placed
Thus, § 54327
each Freire, vous entendreds, Beli Rank calling
2. The second thing to be observed is the due Collecting or Adding together each Row of Figures that stand over one another of the same Value: And that is thus peformed:
RULE. Always begin your Addition at the Place of Units, and Add together all the Figures that fland in that Place, and if their Sum be under Ten, set it down below the Line underneath it's own Place; but if their Sum be more than Ten, you must set down only the overplus, or odd Figure above the Ten (or Tens) and to many Tens as the Sum of those Units amount to, you must carry to tbe place of Tens; Adding them and all the Figures that ftand in the place of Tens together, in the same manner as those of tbe Units were added; then proceed in the same order to the pe of Hundreds, and so on to each place until all is done.
The Sum arising from those Additions will be the Total Amount required,
É X A MPLE I.
Let it be required to find the Sum of the aforesaid Numbers
56978 the Sum required. Beginning at the place of Units, I say I and 7 is 8, which being less than 10, I set it down (according to the Rule) underDeath it's own place of Units; and then proceed to the place of Tens, saying 5 and 2 is 7, which being less than 10, I set it down underneatb it's own place of Tens, and proceed to do the like at the place of Hundreds, and then at Thousands, setting each of their Sums underneath their own respective places: Lastly, because there is not any Figure in the lower Rank to be added to the Figure 5, which stands in the place of Ten Thousands, in the upper Rank, I therefore bring down the faid 5 to the rest, placing it underneath it's own place, and then I find that 54327+2651356978, the true Sum required.
Suppose it were required to find the Sum of these Number 3578 +496+742+184+95. These being placed, as before the rected, will stand as in the Margin. Then herinning (as before) at the place of Units, say 5 and 4 is 9, and 21 A, and 6 is 17, and 8 is 25; let down the 5 Units underneath it's 3578 own place of Units, and carry the 20, or two Tens, to the 496 place of Tens (at which place they are only 2) saying, 2 742 and 9 is 11, and 8 is 19, and 4 is 23, and 9 is 32, and 7 184 is 39; set down the 9 underneath it's own place of Tens, 95 and carry the 30, or three Tenis (which indeed is 300) -to the place of Hundreds, at which place they are but 3, 5095 saying, 3 I carry and 1 is 4, and 7 is 11, and 4 is 15, and 5 is 20 ; here because there is no Figure overplus (as before) I set down a Cypber underneath the place of Hundreds, and carry the 2 Tins (or rather the 2000) to the place of Thousands, saying
The Sum of the Row of Units, is
기 The three Thousand brought down 13lololo
The Sum or Total Amount as before, is 5095
From hence I presume it will be easy to conceive the true Reason of carrying the aforesaid Tens; and also that Cyphers do not augment or increase the Sum in Addition. (See Page 4.)
I might have here inserted a Lineal Demonftration of this Rule of Addition; but I thought it would rather puzzle than improve a young Learner, especially in this place; besides the Reason of it is sufficiently evident from that Natural Truth ofi the Whole being Equal to all it's Parts taken together. Euclid 1. Axiom 19.
That is, the Numbers which are proposed to be added together, are by that Axiom understood to be the several Parts, and their Sum or Total Amount found by Addition is understood to be the Whole.
And from thence is deduced the Method of proving the ? Truth of any Operation in Addition, viz. By parting or separating
the given Numbers into Two Parcels (or more, according to the Largeness of it) and then adding up each Parcel by it self: For if those particular Sums fo found, be added into one Sum, and that Sum prove Equal, or the same with the Total Sum first
found, then all is right; if not, care must be taken to discover and correct the Error.
Sect. 3. Of Subtraction.
Poftulate or Petition. That any Rumber may be diminished, or made less, by taking
another pumber from it.
Subtraction is that Rule by which one Number is deducted or taken out of another, that so the Remainder, Difference, or Excess may be known.
As 6 taken out of 9, their remains 3. This 3 is also the Difference betwixt 6 and 9, or it is the Excess of 9 above 6.
Therefore the Number (or Sum) out of which Subtraction is required to be made, muft be greater than (or at least equal to) the Subtrahend or Number to be fubtracted.
Note, This Rule is the Converse or Direct contrary to Addition.
And here the same Caution that was given in Addition, of placing Figures directly under those of the same Value, viz. Units under Units, Tens under Tens, and Hundreds under Hundreds, &c. must be carefully observed ; also underneath the lowest Rank there must be drawn a Line (as before in Addition) to separate the given Numbers from their Difference when it is found.
Then having placed the leffer Number under the greater, the Operation may be thus performed.
RUL E. Begin at the Right Hand Figure or place of Units (as in Addition) and take ar fubtract the lower Figure in that place