123 PART XI. Of Numerical Questions. СНАР. І. Questions producing Simple Equations. Section 1. Question 1. s (200) Pounds are to be Divided between two Men, that the one may have d (73) Pounds more than the other. What is the Share of each Man? A Gentleman finding feveral Beggars at his Door, gave each of them b (3) Pence, and had c (6) Pence remaining; but he wou'd have given them d (4) Pence each, but that he wanted f (2) Pence for to do fo. How many Beggars were there? Suppofe a the Number of Beggars =? 3 c+f 4÷d-b5 642 d a (= = 8 Beggars). 4-3 Question 4. One being ask'd. how old he was, anfwer'd, if — (a) the b Number of Years I liv'd were Multiplyed by that Num ber, the Product wou'd be my Age. I demand his Age? Question 5. A Man with his Wife did ufually drink out a Veffel of Beer in b (12) Days; and they found, by often Experience, that, the Wife being abfent, the Man drank it out ine (20) Days. The Queftion is in how many Days wou'd the Wife alone drink it out at that Rate? 1. Suppofe fhe wou'd drink it out in a Days. 2. Now, in order to find what Quantity he would drink out in a Days, fay a 3. Therefore the Quantity (or Number of Vessels) which he and the together would drink out in a Days is + c+a Veffels. 4. But he and fhe together did alfo (by the Question) drink out I Vessel in b Days; therefore to find what Quantity they both together did drink out in a Days at this Rate, fay b Days .. 1 Vessel :: a Days .. I a Ъ Veffels. 3=45 C b Question 6. A Hare, being (50) Paces, or Leaps of her own, before a Grey-hound, makes r (4) Leaps to the Grey-hound's s (3) Leaps But m (2) Leaps of the Grey-hound's are as much as 2 (3) Leaps of the Hare's. How many Leaps must the Grayhound take to catch the Hare? 1. For the Number of the Gray-hound's Leaps fought put a. Gray-hound's Leaps is to thofe of the Hare's in any time, fo are all the Gray-hound's Leaps to all the Hare's Leaps after he began to course her.) Number of the Gray-hound's Leaps is to the whole Number of the Hare's Leaps.) Or, having proceeded as far as the 3d Step, it is evident rat sb that a Leaps of the Gray-hound's must be equal to S Leaps of the Hare's: And, by the latter Part of the Question, m Leaps of the Gray-hound's are Leaps of the Hare's therefore ma Leaps of the Gray-hound's arena Leaps of the Hare's; confequently (by dividing each Part by m) a Leaps of the Gray-hound's are = a Leaps of the Hare's, which are (by what has been here faid) rasb: And, by Multiplying each Part by m, you get the Equation in the 5th Step foregoing. n m = * Vitruvius (in Lib. 9. Cap. 3.) reporteth that King Hiero having given Commandment for the making a Crown of pure Gold, was inform'd, that the Workman had detained part of the Gold, and mixt the reft with as much Silver as he had ftoln of Gold. The King being much difpleas'd at the Deceit, recommended commended the Examination of the Bufinefs to the famous Archimedes of Syracufe, who, without defacing the Crown, difcover'd the Cheat in this Manner, viz. Experience telling him that a Quantity of Gold wou'd poffefs lefs Room or Space than a Quantity of Silver of the fame Weight, and confequently that a mixt Mafs of Gold and Silver of the fame Weight wou'd take up fome mean Space between the two former, He made a Mafs of pure Gold of the fame Weight with the Crown, likewife another Mafs of Silver of the fame Weight with the Crown; then having put the Crown, as also the other two Maffes feverally into a Veffel filled up to the Brim with Water, he diligently referv'd the Water flowing over into another Vef fel; and from those three Quantities of Water fo expell'd, he found out the Quantity of Gold and Silver in the Crown. But, fince Vitruvius delivers not the Practical Operation, I shall here thew the fame after the manner of others. Question 7. Suppofe the Weight of the Crown, as alfo of the two Maffes to have been each b(10) ; alfo that by putting the Mafs of Gold into the Veffel, c(.52)b of Water was thereby expell'd, by putting in the Mafs of Silver, d (.92) t; and by putting in the Crown, f(.64) tt. The Queftion is to know how much Gold and how much Silver the Crown was compos'd of? Suppofe of att of Gold, and therefore of bat of Silver then, If bt of Gold expel ct of Water, at of Gold will expel of Water. ca ; Again, if of Silver expel dt of Water, bath of Silver will expel db da Ъ fb of Water. And therefore the Quantity of Gold and Silver in the Crown will expel ca+db b da b of Water, which must be f# of Water, by the Question. And by Multiplying each Part by b, we have cada+ By Tranfpofition cada db = tf. By Division a= bf-bd = bf-bd. = £b (= 3 of Silver.) Queftion |