55. Example 1. Find the Value of 15s. 6d in the Decimal of a £, to three Places of Decimals. First, 15 Shillings, with an o on its right Hand, is 150, Half of which call.75. And 6d4=25 Farthings, which being above 24, we add one, calling it 26 Farthings, or .026; and .75 + .026.776 for the Decimal required. 56. Example 2. Put 10s. 11d. into the Decimal of a L. Here, 10s, with an o on the Right, becomes 100, Half of which is 50, which is 10s .50 of a £. And 11d being 44 Farthings, and 44 + 1 (because above 24 is) = 45, which is 11d= .045 of a £, and confequently 10s 11d.50 +.045.=.545 of a, true to three Places of Decimals. The Reader, by comparing these Examples with the Examples in Cafe 7, will eafily fee the Reason of thefe Operations, this Cafe being only the Reverse of that. 57. Having now given the most useful Cafes of Reduction, fuch Readers as are well acquainted with them, will find very little, if any Difficulty, in applying Decimals to any Rule of Arithmetic. However, for Example Sake, we fhall proceed to apply Decimals to a few of the most useful Rules. CHA P. VII. Of the APPLICATION of DECIMALS to the RULE of THREE DIRECT. 58. A Few Examples will plainly fhew the Method of applying Decimals to this Rule, without the Help of any formal Precepts. Example 1. What comes 6C. 1 Qr. 14 to, at 2£ 16s per C? Solu Solution. By Reduction of Decimals 1 Qr. 14tb, in the Decimal of a C, is .375 of a C. very near, and fo 6 C. 1 Qr. 14tb 6.375 C; and 16 s, in the Decimal of a,.8, snd. 2 16s2.8: Hence £ the Stating will be, C. £ C. If 12.8:6.375 2.8 51.000 12750 Anfwer £17.8500 (by Reduction, Cafe 3, or 6 or 7) 17£ 175. See this worked by common Arithmetic, Article 191. of the first Effay. 59. Example 2. What come 7 Yards of Linnen to, at 2s id per Ell? 2 Yd Yard An Ellis, which in Decimals is 1.25; and 2 s id, in the Decimal of a £, is = .106249, whence the Stating is, If 1.25 Yds: 0.106249::7 Yds Anfwer, .5949 of a £ = (by Reduction of Decimals) 10s 10d 3. See this folved by common Arithmetic in Art. 192. in the first Effay. 66. Example * 3. A May-pole there was, whofe Height I would know; The Sun fhining clear ftraight to work I did go : The Length of the Shadow, upon level Ground, Juft fixty-five Feet, when meafur'd, I found: A *This Queftion I believe was firft propofed in one of the Monthly Entertainments for the Year 1711. A Staff I had there, juft five Feet in Length; The Length of its Shadow was four Feet one Tenth: How high was the May-pole, I gladly would know ? And it is the Thing you're defir'd to fhew. Solution. It is evident, that if there are two Poles standing upright on the Ground, and their Heights be as 2 to 1, their Shadows muft alfo be as 2 to 1; for a Pole, being twice as high as another, must certainly caft a Shadow twice as long: And, if the Ratio of their Heights be as 3 to 1, that of their Shadows will be as 3 to 1, or in the fame Ratio with their Heights, for the above Reafon, &c. Confequently, as the Length of the Shadow of any Thing is to its Height, fo is the Length of the Shadow of any other Thing to its Height. Hence the above Queftion may be stated thus : 61. F CHAP. VIII. FELLOWSHIP. ELLOWSHIP fhews how to divide a Number into any Number of Parts proportional to other given Numbers. In Vulgar Arithmetic, we gave a Definition not fo general as this. 62. As the first and fecond Terms continue the fame in all the Statings, it will be many Times the fhorteft Method of Solution to divide the fecond Term by the firft, and referve the Quotient as a common Number which, being feparately multiplied by the third Number of each Stating, will give the Anfwers for each refpective Stating*. 63. Example. Suppofe 4 Men, A, B, C, and D, trade in Company; A put in 50; B, 16£; G, 25£; and D, 18. 10s; they gained 20. 155: What was each Man's Part? Solution. First 50+16+25+18.5=109.5=the whole Stock put in; hence the Statings would stand thus: 109.520.75: 25: C's Share. 109.5 20.75 18.5: D's Share. Now, 20.75109.5.189497 = "the common Number, Hence, .189497 x 50 = 9.47485 3. *The Reason of this will eafily appear, for, if four Quantities, a, b, c, d, are proportional, that is, as a: b :: c ; d, bc b bc -- b x c = ‡ d. a £. £. s. d. 3.031952=307 B's Share; and 189497 x 18.5 £. s. d. =3.5056945 = 3 10 1 nearly D's Share; and l. s. d. 1... .189497 x 254.737425 4 14 8C's Share. And, for Proof, 9.474850 +3.031952 +4.737425 +3.5056945 20.749921, which is very nearly. 20.75 the whole Gain. 64.T CHA P. IX. SIMPLE INTEREST. O find the Intereft. Multiply the Principle by the Time, and that again by the Rate; the last Product will be the Intereft required. A Year being the Integer for the Time, and one Pound. the Integer for the Money*. 65. By the Rate, in the last Article, we would be understood to mean a hundredth Part of the Rate per Cent. per Annum; or, which is the fame Thing, the Intereft of 1 per Annum. Thus, if the Intereft of 100 for 1 Year be 5, that of 1 for the fame Time is .05 of a Year; and, if the Rate per Cent. per Annum be 61, that of 1 for a Year is .06, &c. for I as * The Reason of this Rule will plainly appear thus: Letr the Intereft of 100 for 1 Year; t the Time in Years, p = the Principal; then by five Numbers (in common Arithmetic) the Numbers will stand thus : "} Here the Blank falls under 100£ 1 Year |