Six Hundred Seventy Eight Thousand Millions, Six Hundred Fifty Four Thousand, 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 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, so 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 thefe 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 fand in that Place, and if their Sum be under Ten, jet 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 fa many Tens as the Sum of thofe Units amount to, you must carry to the place of Tens; Adding them and all the Figures that Atand 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 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 less 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 these Numbers, 3578+496+742+184+95. Thefe being placed, as before directed, will ftand as in the Margin. Then beginning (as before) at the place of Units, fay 5 and 4 is 9, and 2 is 11, 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: C 95 (as (as before) 2 I carry and 3 is 5, which being the laft, 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. 79489 86245 74 14 1915 From hence I prefume it will be eafy to conceive the truc 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 Reafon 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 Largenefs 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 must be taken to discover and correct the Error That any Number may be diminished, or made lefs, by taking another Rumber 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 alfo 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, must be greater than (or at leaft 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. must 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 - from the Figure that ftands over it, fetting down the Remainder or Difference underneath it's own place. If the Two Figures chance to be Equal, fet down a Cypher: But if the upper Figure be less than the lower Figure, then you must add 10 to the upper Figure, or mentally call it 10 more than it is, and from that Sum fubtract the lower Figure, fetting down the Remainder (as before directed). Now because the 10 thus added, was fuppofed to be borrowed from the next fuperior place (viz. of Tens) in the upper Figures, therefore you must either call the upper Figure in that place from whence the 10 was borrowed, one less than really it is, or elfe (which is all one, and moft ufual) you must call the lower Figure in that place one more than it really is, and then proceed to Subtraction in that place, as in the former; and fo gradually an from one Row of Figures to another until all be done. Let it be required to find the Difference between 6785, and 4572. That is, let 4572 be fubtracted from 6785. Thefe Numbers being placed down, as before directed, will ftand Thus 6785 { 4572 2213 Beginning at the place of Units, take 2 from 5 and there will remain 3 which must be fet down underneath it's own place, and then proceed to the place of Tens, taking 7 from 8, and there will remain I, to be fet down underneath it's own place; again, at the place of Hundreds, take 5 from 7, and there remains 2, which fet down, as before; laftly, take 4 from 6 and there will remain 2, which being fet down underneath it's own place, the Work is finished, and the Difference fo found will be 2213-6785-4572, as was required. EXAMPLE 2, 7496 5849 The Difference between 5849, and 7496 is required. Having placed the Numbers as in the Margin, begin at the place of Units (as before) and fay 9 from 6 cannot be, but 9 from 16 and there remains 7, to be fet down under it's own place; next proceed to the place of Tens, where you mult nów pay the 10 that was borrowed to make the 6, 16, by accounting the upper Figure 9 in that place one lefs than it is, faying 4 from 8 and there remains 4, or elfe (which is the most practifed) fay 1 I borrowed and 4 is 5 1647 from |