(28) A. is 13 years younger than B. and 17 years older than C. who in the year 1747 was known to be 24 years of age. How old was each of these persons in

17847

(29) A public edifice was finished towards the close of the 10th of King John, who began his reign 134 years after the conquest in 1066; and it stood till within 76 years of the peace of Utrecht, in 1713. Of what duration was it?

(30) A grant was made by the crown, anno 1239, which was forfeited 137 years before the revolution in 1688. How long did the same subsist?

(31) Moses was born anno Mundi 2433; Homer 832 years. after him; Julius Cæsar lived 40 years before our Saviour, and Alexander 312 years before Cæsar; now, as Christ was incarnate 4000 years after the creation, the sum of the intervals between Homer and the three great personages last mentioned is required.

(32) The semidiameter of the earth's orbit, or annual path round the sun, in the centre of the system, is about 81,000,000 of miles, that of Venus 59,000,000: when they are both on the same side the sun, they are in Perigao; when on different sides, in Apogæo. What is the difference of their distances in both these circumstances?

(33) B. was born 14 years after C. who came into the world 19 years before A. who was 23 years of age eight years ago. What then is the age of D. who is within 22 years of being as old as those three together?

(34) Arphaxad was born to Shem two years after the Deluge, and 500 before his father's death; but at 35 years of age he had Selah, who at 30 was father to Eber; who at 34 had Peleg, and he lived 430 years after that. The question is, whether Shem or Eber died the first? and, at nine score and fourteen years after the death of the longest liver, what interval might be wanting to complete the term of 1000 years after the Flood?

(35) K. is 19 years older than L. who was 27 years of age in the South-Sea year, 1720. How old was M. in 1740, who, in the year 1738, was within 24 years of being as old as both of them together?

(36) A. born A. D. 318, lived 207 years before B. who lived 104 years after C. who was successor to D. 84 years. E. was also 112 years after D. but predecessor to F. by 47 years. In what year did each of these gentlemen flourish ?

(37) Sam was born 28 years before Toby, who died at 12, and lived 19 years after him. Rachel came to light when Sam was 16, and died 11 years before him. Joshua, when Rachel was 7 years, being himself then 14, went abroad, where he continued 9 years, and returning, survived Rachel 4 years. How old was each of these, and what is the sum of their ages?

(38) B. born anno 1108 lived 48 years before C. who was 113 years senior to D., and X. was 114 years before Y., who was 74 years after Z., born anno 1527. In what years were these men severally born?

(39) You were born 34 years after me.

How old shall I be when you are 17? And how old will you be when I am 70 years of age?

(40) Five notable discoveries were made in 215 years' time, viz. 1. The invention of the Compass. 2. Gun-powder. 3. Printing. 4. The discovery of America, 5. Truth, in the Reformation. The last was brought about anno 1517; the third 77 years before; the second 42 years after the first, and the fourth 148 years after the second. The question is, in what year of Christ did each of these happen to be found? (41) Three and thirty years before the Restoration in 1660, the crown granted demesnes to certain uses for 210 years then to come. The proprietor, in 1715, procured a reversionary grant for 99 years, to commence after the expiration of the first. In what year of Christ will the second term end?

(42) A. was born when B. was 18 years of age. How old will A. be when B. is 41 ? And what will be the age of B. when A. is 72?

(43) The building of Solomon's temple was in the year of the world 3000; Troy was by computation built 443 years before the temple, and 260 years before London. Now Carthage was built 113 years before Rome, founded 744 years before Christ, born anno Mundi 4000. Is London or Carthage the most ancient city, and how much?

(44) If the mean distance between the earth and sun be 81 millions of miles, and between the earth and moon 240 thousand, how far are those two luminaries asunder in an eclipse of the sun, when the moon is lineally between the earth and sun? and in another of the moon, when the earth is in a line between her and him?

(45) From the Creation to the Flood was 1656 years; thence to the building of Solomon's temple 1336 years; thence to Mahomet, who lived 622 years after Christ, 1630 years. In what year of the world was Christ then

born?

(46) Seth was born when Adam was 130 years of age, and 800 years before Adam's death: Seth at the age of 105 years had Enos: he, at 90, was father to Cainan, who at 70 had Mahalaleel. This man at 65 begat Jared, who, at the age of 162 years, was father to Enoch: this patriarch at 65 years of age had Methuselah; and by the time he was 187 years of age, his son Lamech came into the world, who at 182 years old was father to Noah; and when Noah was 600 years old, the Flood swept away the bulk of mankind. In what year of the world did this happen, and how long after the death of Adam?

(47) Miss Kitty told her sister Charlotte, whose father had before left them twelve thousand twelve hundred pounds a piece, that their grandmother by will had raised her fortune to fifteen thousand pounds, and had made her own twenty thousand. What did the old lady leave between them?

(48) The powder-plot was discovered 88 years after the Reformation in 1517: The murder of King Charles the First was committed 43 years after that discovery: The accession of the Brunswick family to the crown was in 1714, just 54 years after the return of King Charles the Second, who had lived in exile ever since the death of his father Charles the First. How long was that?

(49) B., born 161 years ago, died when C. was 47 years of age, who it seems came into the world 180 years since, and out-lived B. 43 years. The sum of their ages is required. (50) If Samson were born 17 years after Timothy, and Timothy 26 years before Jacob, who 28 years hence

will be just 50, in what year of Christ were they severally born; the question being proposed anno 1806?

(51) A. born 445 years before the year 1733, died anno 1362; B. born 37 years ago, will die 18 years hence; C. born 256 years ago, died 197 years since; D. born anno 1578, lived till within 75 years of the said 1733. The length of these people's lives is severally required.

(52) A. born anno 1441, lived till B. was seven years of age, which was 23 years before the Reformation in 1517: B. survived this remarkable æra just 49 years; C. born 9 years after the death of A. lived but till B. was 36 years of age. The sum of the ages of these three persons is required.

(53) A. born anno 1438, died at 48 years of age: B. died anno 1502, aged threescore and seventeen; C. in the year 1577, was 22 years of age, and survived that time 54 years; D., anno 1616, had lived just half his time, and died in 1648; E. was 13 years old at the death of D. and 14 years after that was father to F. who was 31 when his son G. was born, who at his grandsire's death was 7 years of age. The years

of Christ, wherein these men were born, and the years wherein the first five of them died, are severally réquired. (54) A. born 17 years after C. and 13 before B. died 42 years before King George the Second's inauguration in 1727, aged 47 years: C. died anno 1712, and B. exactly 6 years before him; D. born 23 years before C. died at 64; E. born 11 years after B.'s death, died 12 years after the year 1733; and F. born just in the midway of the interval between the births of A. and D. did not reach the time of E.'s death by 14 years. What is the sum of all their ages, and which of them lived longest?

Case 1. When the Multiplier consists of the same Figures in all the places, (i. é.) all 9's or all 7's, &c. then, for each Figure in the Multiplier, annex a cipher to the Multiplicand, and, from the line thus produced, subtract the Multiplicand; and if the repeating Figure is 9, the Remainder will be the Product required; but if any other figure, multiply it into the ninth part of the Remainder; or, for the figure 3, take the third part of the Remainder; and for six, multiply the third part by 2, which will give the required number.

In many cases the work may be performed with more ease, likewise more concisely, than is usually practised.

IX. COMPOUND MULTIPLICATION

TEACHETH to multiply, by one common Multiplier, any sum or number consisting of different denominations.

Case 1. When the given quantity doth not exceed 12.

RULE.

1. Write the Multiplier, or given quantity, under the lowest denomination of the Multiplicand.

2. Multiply the number of the lowest denomination by the Multiplier, and divide that Product by as many of that as make one of the next higher denomination, the same