Chap. VI. tiplied into the Divifor, and the Product wrote under the Dividend, and fubftracted out of it. Thus, 3 is in 8 twice, and there remains a Which Remainder is wont 3. particular vifion. over. 3)8(2 6 2 to be placed by the Quotient gure If the left-hand Figure of the DiviThe first dend be greater than the left-hand FiRule rela- of the Divifor, then there must be ting to Di- taken at one Time no more Figures (how many foever they be) of the Dividend, than are equal to the Number of Figures in the Divifor. And if one Operation being perform'd, what remains of the Dividend, be equal to, or greater than the Divifor, then a fecond Operation is to be perform'd; and fo as many Operations, as there is Occafion. Thus in the adjoining Example, because 8 is bigger than 3, therefore only 8 of the Dividend is to be taken the firft Time. Which being divided by 3, gives 2 for the Quotient, and leaves 2 over; which, with the other Figure 7 of the Dividend (plac'd by the Remainder 2) ma there- 3)87(29 27 27 nothing of the 3) 879 (293 king a Number greater than the Divifor, Chap. VI. is therefore to be divided anew by the Divifor; upon which Divifion, there will arife 9 for the Quotient; for 9×3=27, and fo there will remain Dividend given. And confequently 3 is in 87, just 29 Times. In like manner, 3 dividing 879, will give for the Quotient 293, as in the Example adjoining. 6 27 27 09 cond par And here it is to be observed, that fo 4. many Figures of the Dividend given as The feare taken at one Divifion, are diftin- ticular guifh'd by the Name of a Dividual or Rule. Partial Dividend. And it is ufual and convenient to distinguish the several Dividuals of any Dividend, by putting a Point under each Dividual, if of one Figure; or under the last Figure thereof towards the Right-hand, if of more. Thus in the last Example, the Dividend 879 is distinguish'd into three Dividuals of one Figure each, as appears by the Points. And Note, that as many Dividuals or Points as there be in the Dividend, fo many Figures must be in the Quotient. If, when one or more Operations have 5. been perform'd, the remaining Figure (or The third Figures) of the Dividend, together with Rule. particular the Chap. VI. the Remainder (if any there be) of the Operations perform'd, be lefs than the Divifor, then a Cypher is to be added to the Quotient, and all that remains is to be plac'd by the Quotient, as afore in 1. 2. Namely, because in 6. Rule. the adjoyning Exam- 15) 314 (20 30 14 tient, and leaves over; which Remainder 1, together with the remaining Figure 4 of the Dividend, is less than the Divifor; therefore a Cypher is to be added to the first Quotient 2, and after 20 is to be placed. If, when the Divifor confifts of two The fourth or more Figures, the faid Divifor be particular compounded, or the Product of feveral Digits multiplied together, then the Divifion may be perform'd by the faid Digits fingly, inftead of the Divifor given. Namely, the Dividend given being divided by any one of the fingle Digits or Divisors first, the Quotient thence arifing is to be divided by any other of the faid fingle Digits; and fo the Work is to be repeated, fo often as there are single Digits. The Quotient arifing by the last Operation, is the Quotient fought. Thus 12048 divided by 48; or firft fingly by 8, and then by 6; (or first by 6, and then then by 8: For 6×8=48,) the Quoti- Chap. VI. ent will be found the fame, viz. 251, as in the following Examples. 48) 12048 (251 or thus, 6) 12048 (2008 And the fame will hold good, when the Divisors do not exactly divide the Dividend, but there is fome Remainder left: As in the following Examples. 48) Chap. VI. 48) 12056 (25148, or thus, 8) 12056 (1507 96 245 .... 8 If the Divifor confifts of many Figures, then the Divifion may with greater Quickness be perform'd by the Help of Naper's Bones. Namely, the Divifor being tabulated, by Infpection of the faid Bones may easily be perceiv'd, how often the Divifor may be taken out of its refpective Dividual. Thus in the following Example, 754 being the Divisor, and 2635 the first Dividual, it appears by infpecting the Rods or Bones, that the faid Divifor (multiplied by 3, makes 2262, and multiplied by 4, makes 3016, and consequently) is contain'd in its re spective |