Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/456

 H M R I TICK, 3”4 3. If your multiplier confifts of integers and parts, the 23X9=207 operation is performed by a crofs multiplication of the 38X8=304 f$veral parts of the multiplier into all the parts of the multiplicand. 12)511(42 The contents of mafon and joiners work are frequent48 3*j ByRuleH. ly call up by this kind of multiplication ; for underftanding of which obferve, that B-i The fupierficial content of any redtangle is found by 24 multiplying the length into the breadth ; and the content 9x998 of a right-angled triangle is found by multiplying the bafe into half the perpendicular or height. 38X6=228 The dimenfions are ufually taken in lineal feet, inches, 23X6=138 and lines; and the operation is performed by the following rules. 144)366(2 By Rule III. ByRulelV. 288 I. Any lineal meafure multiplied into the fame lineal meafure produces fquares of that name. Thus, 78 12X6=72. lineal feet multiplied into lineal feet produce fquare feet; lineal inches into lineal inches produce fquare Becaufe the fum of the inches exceeds 144, carry 1 from them to the column of feet, and fet down theoinches, i^r. viz. 98. II. Lineal feet into lineal inches produce redangles verplus, The operation may be rendered eafier and flxorter by 1 foot long and 1 inch broad, which divided by 12 quote previcufly reducing the fadors to two denominations, fquare feet: and the remainder multiplied by 12, proviz. inches and lines. Thus the former example may be duces fquare inches.. and wrought as follows. III. Lineal feet into lineal lines produce redangles 1 prop.ofed an area or floor, in length 465 inches 6 lines, and foot long and 1 line broad, which divided by 144 quote in Inbreadth fquare feet; and the remainders are redangles equal to and feet ? 284 inches 6 fines, how many fquare inches fquare inches. IV. Lineal inches into lineal lines produce fmall red465X6=2790 angles 1 inch long and x line broad, 4hich divided by 284X6=1704 12 quote fquare inches; and the remainder, multiplied by 12', produces fquare lines. By Rule IV. Examp. I. In an area, pavement, or piece of plaifter-work, in length 24 feet 7 inches, and in breadth 18 feet 5 inches, how many fquare feet ? 18X7=126 The anfwer here is 1324314 fquare inches, and xo8 24X5=120 fquare lines; and if the inches be divided by 144, you will fquare feet and a remainder of 98 fquare 12)246(20 by Rule II. inches,haveas910 before. Or the fadors may be reduced to the lowed denomi24 nation, viz. lines, and then the produd will be fquare 12X6=72 452 fines, which, divided by 144, will quote fquare inches, the remainder will be fquare lines; and the fquare Here multiply 18 lineal feet into 24 lineal feet, and and divided by 144, will quote fquare feet, and the the produd is 432 fquare feet; then multiply 5 lineal inches, remainder will be fquare inches. Again, the fquare inches into 7 lineal inches, and the produd is 35 fquare feet, divided 9, will quote fquare yards, and the reinches, by Rule I.; then multiply 18 lineal feet into 7 mainder will beby fquare and the fquare yards, divilineal inches, and the produd is 126; and again multi- ded by 36, will quote feet; ply 04 lineal feet into 5 lineal inches, and the produd is will be fquare yards. fquare roods, and the remainder J20; which added to the former produd, gives 246 If this crofs multiplication be extended to the menfiiTedangles, each being 1 foot.in length and one inch in ration the content of which is found by multibreadth; thefe divided by 12 quote 20 fquare feet; and plying ofthefolids, fuperficial content of the bafe into the height, the remainder 6 multiplied by 12, produces 72 fquare depth, length, or thicknefs, the operation muft be coninches, according to Rule H. ; thefc add to the former ducted by the following rules. fquare feet and inches, and you’ll find the anfwer or total V. Any fuperficial meafure multiplied into the fame produd to be 452 fquare feet, and 107 fquare inches. lineal meafure produces a folid of the fame name. Thus Examp. II. In an area or floor, in length 38 feet 9 fuperficial feet multiplied into lineal feet produce folicf foches 6 lines, and in breadth 23 feet 8 inches 6 lines, feet; fuperficial inches multiplied ixita lineal.inches prohow. many fquare feeti duce folid. inches, <&c.