Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/457

 R I T H M E T I C K. 375' IV. How many folid feet in a polifhed Hone, VI. Superficial feet into lineal inches produce paral- thatExamp. is 8 feet 9 inches ^ lines long, 7 feet 3 inches broad, lelepipeds, whofe bafe is 1 fquare foot, and their height 1 inch; which divided by 12 quote folid feet; and the and 3 feet 5 lines thick i remainder, multi-plied by 144, produces folid inches. 7X9 = 63 VII. Superficial feet into lineal lines produce paral8X3=24 lelepipeds, whofe bafe is 1 fquare foot, and their height , by Rule II. 1 line ; which divided by 144 quote folid feet; and the 12)87(7^. '7 remainder multiplied by 12 produces foiid inches. 12X3=36 in. VIII. Superficial inches into lineal lines produce pa7 X 5 = 3 5 /'«. by Rule III. rallelepipeds, whofe bafe is 1 fquare inch, and their 3X5 = 15 ^ height r line; which divided by 12 quote folia inches ; 12)15(1 »'». v by Rule IV. and the remainder multiplied by 12 produces folid inches. Bbjfup. 12X3 = 36//.j IX. Lineal feet into fuperfietal inches produce parallin. lelepipeds, whole bafe is one- fquare inch, and their 189 8o5 63X5=315, and 144)3x5(2 height 1 foot; which divided by 144 quote felid feet; 12X27=324 /«. F. byR.VIi: and the remainder multiplied by 12 produces folid lines. 3X99=297, and j 44)297(2F. ?byR.IX. X. Lineal feet into fuperfieiat lines produce parallele12X9=108 in. pipeds, whofe bafe is 1 fquare line, and their height 1 3X36=108, and 12)108(9 in. by Rule X. foot; which divided by 12 quote folid inches; and the 5X99=495, and i2)495(4i/>z. 57 l ^ n VTTT remainder multiplied by 144 produces folid lines. 144X 3=432//«<?/. XL Lineal inches into fuperficial lines produce paral- The482I612 lelopipeds, whofe bafe is 1 fquare line, and their height c n operation may be facilitated by previoufly redu1 inch; which divided by 144 quote folid inches; and- and to two denominations, inches lines,,threeas fadtors was done in Example II. onviz. fuperficial the remainder multiplied by t2yproduces folid lines. Examp. III. In apiece of timber, whofe length is 18 meafure. Or the three fadlors may be reduced to the loweft defeet 16 inches, breadth 2 feet 4 inches, and thieknefs 2. nomination, viz, lines, which being multiplied contifeet 3 inches, how many foKd feet? nually, will produce folid lines, which divided by 1728, F.j /$, will quote folid inches, the remainder being folid lines ; 1.8) 6) 2X6=12 and the folid inches divided by 1728 will quote folid 8X4=72 feet, the remainder being folid inches; and the folid feet. divided by 27 will quote folid yards, the remainder be24 12)84(7 F.^ ing folid feet; and the folid yards divided by 216 will quote fblid roods; the remainder being folid yards. We fhall only further obferve, that as the rules for fuperficial working queflions by crofs multiplication are numerous,, lineal 2X24=48 ? bvR. and the operation tedious, it is eafier to convert the parts 12X48=5x6//?. 3 IX. into a decimal fradlion of their integer, and then work as taught in the multiplication of decimals. III. The Proof of Multiplication. 97I 216 folid Multiplication may be proved feveral ways; viz. Here firfl: multiply r8 feet 6 inches into 2 feet 4 inches, by multiplication, by divifion, and by caflingout the 9’s, as formerly, and'..the produdb is 43 feet 24,inches fuper- 1. By multiplication: Change the places of the facficial ; which next multiply into 2 feet 3 inches li- tors, and make that the multiplier which before was the neal, thus, 43 fuperfieial feet into 2: lineal feet produce multiplicand; and if the york be right, you will have 86 folid feet, and 24 foperficial incites into 3 lineal inches- the fame produft; as before; but this method is tedious. produce 72 folid inches, by Rule V.; then a 3 fuperfi- 2. By divifion : When the work is right, the prod eft cial feet into 3 lineal inches produce 1.29 parallelepipeds, divided by the multiplier quotes the multiplicand; or, whofe bafe is 1 fquare, foot, and their height 1 inch; divided by the multiplicand, quotes the multiplier. But which divided by 12 quotes. 10 folid.feet.; and tl>e re- this fuppofes thfr learner acquainted with divifion. mainder 9 multiplied into 144 produces-1296 folid inches,, 3. The moft ufual method therefore of proving multiby Rule VI. Again, 2 lineal feet into 24 fuperficial. plication is by calling out the 9’s; which is done, thus: inches produce 48; which, being kfs than 144, you e- Call the 9’s out of the multiplicand and multiplier, and fteem a remainder, and multiplying it into 12. you have a. place the excelfes on the right and left fides of a crofsproduft of 576 folid inches, by Rule IX. multiply thefe two figures into one another, calling the Becaufe the fum of the inches exceeds 1728, carry 9’s out of their produft, if need be, and place the excefs 1 Qwn from thence to the feet, and the overplus 216 fet at the top of the crofs; then calling the 9’s alfo out of^ ‘ the produA of your multiplication, place its excefs at the : bottom 5.
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