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 Inftance, fuppofe 759 were proposed to be read or pronounced according to the Value of each Figure as they now ftand. The first Figure in this Sum is 9, because it stands in the Place of Units, and therefore fignifies but it's own fimple Value, to wit, 9 Units, or 9. The fecond Figure 5 ftands in the Place of Tens, and therefore fignifies Five Tens or Fifty. The Figure 7 ftands in the third Place, or Place of Hundreds, and therefore it fignifies Seven Hundred; and the whole Sum is to be read or pronounced thus, Seven Hundred Fifty Nine. Note, Although the Figure 7 ftands in the third Place (according to the Order of Numbering) yet when the whole Sum comes to be read, it is firft pronunced; the reading of Numbers being performed like that of Letters or Words, always beginning with the outmost Figure towards the Left-hand, and fo many Figures as are placed together without any Point, Comma, Line, or other Note of Diftinction between them, are all but one Sum, and must be read as fuch. For Example, 763596 is but one entire Sum or Number, notwithstanding it confifts 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 expreffing the true Value of any Sum or Rank of Numbers confifting of Seven, Eight, Nine, or more Places of Figures, each Figure being to be valued according to it's Diftance from the Place of Unity: As in the foregoing Table. Now fuch Values may as well arife by Cyphers, as by other Figures; for inftance, 6 ftanding by itself, represents but Six Units: But if a Cypher be annext to it thus, 60, then it becomes Sixty; for the Cypher poffeffing the Place of Units, hath hereby removed the 6 into the Place of Tens; and another Cypher more would make it 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 Six Hundred Seventy Eight Thousand Millions, Six Hundred Fifty Four Thousand, Three Hundred Twenty One Units. Of any propofed Species or Quantities whatsoever. And here it may be obferved, that every third Figure from the Place of Units, bears the Name of Hundreds; which fhews that if any great Sum be parted, or rather diftinguished into Periods, of Three Figures in each Period (as in the foregoing Table) it will be of good Ufe to help the young Learner in the easier valuing and expreffing that Sum. Sect. 2. Of Addition. That any given Number may be increased or made more, by putting another Number to it. Addition is that Rule by which feveral Numbers are collected and put together, that fo their Sum or Total Amount may be known. In this Rule Two Things being carefully obferved, the Work will be eafily performed. 1. The first is the true placing of the Numbers, fo as that each Figure may ftand directly underneath thofe Figures of the fame 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 2. The fecond thing to be obferved is the due Collecting or Adding together each Row of Figures that ftand over one another of the fame 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, fet it down below the Line underneath it's own Place; but if their Sum be more than Ten, you must fet down only the overplus, or odd Figure above the Ten (or Tens) and fo many Tens as the Sum of thofe Units amount to, you must carry to to the place of Tens; Adding them and all the Figures that ftand in the place of Tens together, in the fame manner as thofe of the Units were added; then proceed in the fame order to the place of Hundreds, and fo on to each place until all is done. The Sum arifing from thofe Additions will be the Total Amount required. EXAMPLE I. Let it be required to find the Sum of the aforefaid Numbers 54327 2651 viz. { 56978 the Sum required. Beginning at the place of Units, I fay 1 and is 8, which being less than 10, I fet it down (according to the Rule) underneath it's own place of Units; and then proceed to the place of Tens, faying 5 and 2 is 7, which being lefs than 10, I fet it down underneath it's own place of Tens, and proceed to do the like at the place of Hundreds, and then at Thousands, fetting each of their Sums underneath their own refpective places: Laftly, because there is not any Figure in the lower Rank to be added to the Figure 5, which ftands in the place of Ten Thousands, in the upper Rank, I therefore bring down the faid 5 to the reft, placing it underneath it's own place, and then I find that 54327+265156978, the true Sum required. EXAMPLE 2. 496 742 184 Suppose it were required to find the Sum of thefe Numbers 3578+496+742+184+95. Thefe being placed, as before d rected, will ftand as in the Margin. Then beginning (as before) at the place of Units, fay 5 and 4 is 9, and 2 is, and 6 is 17, and 8 is 25; fet down the 5 Units underneath it's 3578 own place of Units, and carry the 20, or two Tens, to the place of Tens (at which place they are only 2) faying, 2 and 9 is 11, and 8 is 19, and 4 is 23, and 9 is 32, and 7 is 39; fet down the 9 underneath it's own place of Tens, and carry the 30, or three Tens (which indeed is 300) to the place of Hundreds, at which place they are but 3, 5095 faying, 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 fet down a Cypher underneath the place of Hundreds, and carry the 2 Tens (or rather the 2000) to the place of Thousands, faying 95 (as before) 2 I carry and 3 is 5, which being the last, I fet it down underneath it's own place, and all is finished. And find the Sum or Total Amount to be 5095=3578+496+742+184+95. If this Example be well confidered, it will be fufficient to fhew the ufual Method of Addition in whole Numbers; but to make all plain and clear, I fhall fhew the young Learner the Reason of carrying the Tens from on Degree or Row of Figures, to the next Superior Degree, which is done purely to fave Trouble, and prevent the ufing of more Figures than are really neceflary, as will appear by the following Method of adding together the fame Numbers of the last Example. Thus, add together each fingle Row of Figures by it felf; as if there were no more but that one Row, fetting down the Sum underneath it's own place. The Sum of the Row of Units, is The three Thousand brought down The Sum or Total Amount as before, is 3 496 742 184 1915 From hence I prefume it will be eafy to conceive the true Reason of carrying the aforefaid Tens; and alfo that Cyphers do not augment or increase the Sum in Addition. (See Page 4.) I might have here inferted a Lineal Demonftration of this Rule of Addition; but I thought it would rather puzzle than improve a young Learner, efpecially in this place; befides the Reason of it is fufficiently evident from that Natural Truth of the Whole being Equal to all it's Parts taken together. Euclid 1. Axiom 19. That is, the Numbers which are propofed to be added together, are by that Axiom understood to be the feveral 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 feparating the given Numbers into Two Parcels (or more, according to the Largeness of it) and then adding up each Parcel by it felf: For if thofe particular Sums fo found, be added into one Sum, and that Sum prove Equal, or the fame with the Total Sum firft found, found, then all is right; if not, care muft be taken to discover and correct the Error. EXAMPLE. Add 3289 The Sum of thefe Parts is, 12952 4016 ! That any Number may be diminished, or made lefs, by taking another Number from it. Subtraction is that Rule by which one Number is deducted or taken out of another, that fo the Remainder, Difference, or Excefs 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 Excefs 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 Converfe or Direct contrary to Addition. And here the fame Caution that was given in Addition, of placing Figures directly under thofe of the fame Value, viz. Units under Units, Tens under Tens, and Hundreds under Hundreds, &c. muft be carefully obferved; alfo underneath the lowest Rank there must be drawn a Line (as before in Addition) to feparate 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. RULE. Begin at the Right Hand Figure or place of Units (as in Addition) and take or fubtract the lower Figure in that place C 2 from |