N. B. The Term, which moves the Queftion, hath generally fome of those Words before it; viz. that will? How many? How long? How far? or How much? &c. Then (carefully obferve this; viz.) the firft Term in the Suppofition must always be of the fame Kind and Denomination with that Term which moves the Question. And the Term fought will always be of the fame Kind and Denomination with the fecond Term in the Suppofition. Thus, { yds fbil. yds fail. 3:9::6: Then All Questions in direct Proportion may be anfwered by three feveral Theorems. Multiply the fecond and third Terms together, and divide their Product by the firft Term; the Quotient will be the Answer required. Theorem 2. 6 3) 54 (18 Shillings, { S because the second Term was Shillings. Divide the fecond Term by the firft, then multiply the Quotient into the third Term, and their Product will be the Anfwer required. yds. fhil. yds. fhil. 396: 18. Thus 3) 9 (3. Then 3 x 618, as before. Theorem 3. Divide third Term by the first, then multiply the Quotient into the fecond Term, and their Product will be the Anfwer. yds. fhil. yds. fhill. 396: 18. Thus 3) 6 (2. And 9 x 2 = 18, as before. Here you fee that all the three Theorems are equally true; but the first is most general, and ufually practifed. Yet the two laft may be readily performed, when either the fecond or third Term can be divided by the firft; and will be found of fingular Ufe in the Rules of Fellowship, &c. as will appear further on. Quest. Queft. 2. If 8 Pounds of Tobacco coft 14 Shillings; what will half a hundred Weight (viz. 56 Pounds) coft at the fame Rate? Thus 8 lb 145.:: 56 lb: 41. 18s. The Answer. 14 224 8) 784 (98 s. 41. 18s. Or thus 8) 56 (=7 Then 14 x 798 s. as before. Queft. 3. If 14 Shillings will buy 8 Pounds of Tobacco; how much will 47. 18 s. buy after the fame Rate? Stated thus, 14 8 lb 4l. 18 s. = 98 s. : 784. And 14) 784 (56 lb. The Answer. Queft. 4. If half a hundred Weight of Tobacco be worth 41. 18 s. How much may I buy for 14 Shillings at that Rate? Stated thus, 41. 186. =98 s. : 56 lb :: 14s. : Then 56 x 14784. And 98) 784 (8 lb. The Answer. Queft. 5. Suppofe 4 1. 18 s. will buy 56 Pounds of Tobacco; what will 3 Pounds of the fame Tobacco coft? This Question is thus ftated, 56 lb: 41. 18 s.98 s. 8 lbThen 98 x 8784. And 56) 784 (145. The Answer. Note, The three laft Questions are only the fecond varied, being propofed purely to give an Inftance how any Queftion in this Rule of Three may be varied, according to page 86. Queft. 6. What will three quarters of a Yard of Velvet coft, when the Price of 21 Yards and a half is worth 227. 10s. 6 d. This Question truly ftated will stand Thus, 21 yds. : 22 l. 10s. 6 d. :: To the Answer. Which may be found three feveral Ways; viz. by Reduction; by Vulgar Fractions; and by Decimals. 1. By Reduction. Bring the first and third Terms into one Denomination; viz. into Quarters, and reduce the fecond Term into it's leaft Denomination, per Sect. 4. page 42. Thus 2186 Quarters. And 22 l. 10 s. 6 d. 5406 Pence. Then 86 5406 :: 3: 155, 838 d. For 5406 x 316218. And And 86) 162 18 (1888 d. Then 188 Pence 15 s. 8 d. 24 Farthings; the Anfwer required. 901 2. The fame Queftion stated in Vulgar Fractions will stand Thus 213 : 22 48 = 203 ::: (See Sect. 3. page 50.) Then 20x270. And 2) 723 (=1486 page 55, 56. 40 160. 160 These Parts of a Pound are brought into Shillings by Multiplying the Numerator with 20, and dividing the Product by it's Denominator, &c. Thus 5406 x 20=108120. And 6880) 108120 (15 5. 0,75 3. The fame wrought by Decimal Fractions will be thus ; 16,89375 And 21,5) 16,89375 (0,78571 to the Anfwer. 272 15 s. 8 d. 2 far. 150 Quest. 7. If 2 C. 3 qrs. 21 lb. of Sugar coft 61. 1 s. 8 d. What will 12 C. 2 grs. coft at the fame Rate? That is, 2 C. 3 qrs. 21lb: 61. 15. 8d.:: 12C. 2qrs. To what? Viz. 308+21=329lb:1460 d. :: 1406 lb: Then 1460x1400=2044000. And 329) 2044000 (62 1 2 1 d. 25. 175. 84 d. the Anfwer required. The fame Queftion ftated in Decimals will ftand Thus 2,9375: 6,0833 :: 12,5: To the Antwer. Then 6,0833 x 12,5 = 76,04125, which being divided by 2,9375 will give 25,8863, &c. the Anfwer in Decimals, which brought into Coin, will be 25 l. 175. 84d. as before. Note, When the firft Term is an Unit or 1, the Question is anfwered by Multiplication only. Example. Suppose I give 5 Shillings 4 Pence for one Ounce of Silver, What must I pay for 32 Ounces at the fame Rate? That is Ounce: 5 s. 4 d.:: 32 Ounces: To, &c. Which is beft ftated thus 1:64 d. 32,5: :: N Then Then 32,5×642080d.=8l. 13s. 4 d. the Answer required. For neither multiplies nor divides. When the fecond or third Term is an Unit or 1, then the Question is answered by Divifion only. As in this Example. If a Silver Tankard weighing 21 Ounces, coft 5 l. 19 s. What is that an Ounce? Thus 1 oz. 57. 119 s. 3= 19 s. :: 1 : 5 s. 8 d. the Answer. 5 s. 8 d. The Proof of all Queftions in the Rule of Three Direct, may be eafily conceived from what hath been already faid; viz. That the Product of the first and fourth Terms, must always be be equal to the Product of the fecond and third Terms. Or otherwife, by varying the Queftion, as in the fecond, third, fourth, and fifth Questions. I fhall conclude this Section with inferting a few Questions and their Answers; leaving their Work for the Learner's Practice. Quest. 1. What will the Carriage of 17 C. 3 qrs. 11 lb. come to, at the Rate of 7 s. the Hundred? Anfwer 61. 4 s. 11 d. Queft. 2. If 61. 4 s. 114 d. be paid for the Carriage of 17 C. 3 qrs. 11 lb; What was paid for the Carriage of 1 lb? Anfwer 3 Farthings. Quest. 3. A Grocer bought 3 C. 1 gr. 14 lb Weight of Cloves, at the Rate of 2 s. 4 d. per Pound, and fold them for 527. 14 s. Whether did he gain or lofe by the Bargain, and how much? Anfwer, he gained 87. 12 s. Quest. 4. A Draper bought of a Merchant eight Packs of Cloth; every Pack had four Parcels in it; and each Parcel contained ten Pieces; every Piece was Twenty-fix Yards; he gave after the Rate of four Pounds fixteen Shillings for 6 Yards. What came the eight Packs to, and what were they worth per Yard? Anfw. They came to 66561. And were worth 16 s. per Yard. Queft. 5. A Merchant bought 436 Yards of Broad Cloth for 8s. 6d. per Yard; and fold it again for 10 s. 4 d. per Yard. What did he gain by the 436 Yards? Anfw. he gained 397. 195. 4 d. Quest Queft. 6. A Goldsmith bought a Wedge of Gold, which weighed 14 lb. 3 oz. 8 pw. for 5141. 4s. What did he pay per Ounce? Anfw. 3. per Ounce. Queft. 7. What will 48 oz. 17 pw. 20 Grains of Silver Plate come to, at the Rate of 5 s. 6 d. per Ounce? Anfw. 137. 15. 10 d. Queft. 8. If in four Weeks one spend 13 s. 4 d. How long will 53. 6s. laft at that Rate? Anfw. 6 Years, 47 Days, 2 Hours, 24. Queft. 9. What will the one eighth Part of a Ship be worth when the half is valued at 1015 l. 105. Anfw. 253. 17 s. 6d. Queft. 10. The Sun is faid to perform one entire Revolution, (or 360 Degrees) in the Space of 365 Days, 5 Hours, 48 Minutes, and 57 Seconds of Time, called a Tropical or Solar Year; How much doth it move in one Day? Anfw. 59 8 19 &c. Queft. 11. If of a Yard of Velvet coft of a Pound Sterling, What will of a Yard cost of the fame Velvet at that Rate? Anfw. s. 4 d. 245 Queft. 12. Suppofe 2 1. and of of a Pound Sterling will buy 3 Yards and of of a Yard of Cloth, How much will of a Yard coft at that Rate? Anfw, 22 of a Pound 9 s. 41⁄2 d. 4896 Sect. 2. Of Reciprocal Propoztion; ufually called The Rule of Three Inverse. REciprocal Proportion is, when of four Numbers the third (viz. that which moves the Question) beareth the fame Ratio to the firft: As the fecond does to the fourth. Therefore, the lefs the third Term is, in refpect to the first; the greater will the fourth Term, be in refpect to the second. EXAMPLE i. If fixteen Men can do a Piece of Work in fix Days; How many Days muft eight Men require to do the fame Work, at the fame Rate of working? Here it is plain that eight Men muft needs have more Time than 16 Men to do the fame Work. Confequently the greater N 2 the |