PROBL. XIV. There is a Cistern which hath Four Cocks of feveral Sifes, which Cistern holds 8 Barrels of Water? If the first or leaft Cock be opened, the Water will be 6 hours in running out: If the fecond Cock be only opened, the Water will iffue out in 4 hours: If the third be only opened, it will run out in 3 hours; and if the fourth and biggest be only opened, it will run out in 2 hours: In what time will it run out, if all the four Cocks be fet running together? F the leaft Cock will vent 8 Barrels (that is, all the Water) in 6 hours, the second would vent 12 Barrels in that time, the third 16, and the fourth 24 Barrels, in all 60 Barrels. Here is now a Proportion between 60 Barrels and 8 Barrels, and between 6 hours and the time that all the Water will be vented in, if all the Cocks were opened: Wherefore fay, If 60 Barrels will run out in 6 hours; In what time will 8 Barrels run out? Multiply 6 by 8, the Product is 48, which fhould be divided by 60, but being it is lefs, the Quotient will be parts of an hour, or 48 Minutes, and in fuch time will all the Water run out, if all the four Cocks be fet open. PROBL. XV. A Man dies, and leaves his Wife big of her first Child; and by Will bequeaths his Estate in manner following: That if the Child his Wife then went withall fhould prove a Daughter, then his Wife should have two Thirds, and the Daughter one Third of his Eftate: If it should be a Son, then the Son was to have two Thirds, and the Mother one Third of his Eftate, which Eftate was 2600 Pound.- After the deceafe of the Father, the Mother was delivered of two Sons and one Daughter. How muft the Eftate be divided amongst them, according to the Will of the Father? Y the Teftators Will it is evident that for one Third that the B Daughter had, the Mother was to have two Thirds; and the Son was to have double to the Mother. Then This 11 Pound fhould be equivalent to 2600 Pound, wherefore divide 2600 by 11, and the Quotient will be 236l. 75. 3 d. 1q. for the Daughters fhare: And then will The If there be 160 Pound (or 38400 Pence) to be distributed among an equal number of Poor Prifoners, Lame Men, Widows and Children, fo that every Prifoner shall have a Shilling, every Lame Man Six Pence, every Woman Four Pence, and every Child Three Pence: How many of fuch People will this Money relieve? TH 'HE Sum of Pence in 160 Pound being 38400, fet that down for a Dividend; then add 12 d, 6 d, 4 d, 3 d together, and they make 25, by which divide 384co, and the Quotient will be 1536; and fo many Perfons muft there be of each kind: For fo And now if you multiply 1536 by 4, the Product will be 6144, and many will be the whole number of Perfons to be relieved. PROBL. XVII. What Number is that, which if you divide it by 9 there shall remain 8, divide it by 8 there fball remain 7, divide it by 7 there shall remain 6, and so by 6, 5, 4, 3 and 2, and being divided by 2 there fhall remain One? I O 23 3 II Here are several fuch Numbers to be found, and to find the leaft TH that is thus qualified, do thus, Set down all the nine Digits orderly one under another, and against fet a Cypher; then under 1 fet 2, and add 2 and 1 together, they make 3, which fet against 2; then fay 3 times 3 is 9, and 2 over 3 is 11, fet 11 against 3, and fay 4 times II is 44, and 3 over 4 is 47, fet 47 against 4, and thus continuing you fhall find 725759 to stand against 9, and that is the leaft number that is capable to be divided as abovesaid, for the remainder fhall be always a Unite less than the number you divided by. 4 47 6 1439 Ι F CHAP. X. Of Numbers thought upon. any Number be doubled, and that doubled be multiplied by 5, the Product of that Multiplication fhall be the fame with the Number firft doubled, cutting off the Cypher which will always be on the Right hand: So 472 being doubled, makes 944, which multiplied by 5, produceth 4720, from which the Cypher being cut off there will remain the first Number 472.- And from hence it is ufual to bid one think any Number, then bid him double his number thought, and then multiply that double by 5, and give you the Product, which will be the very number he thought, with a Cypher before it; which omitted, you tell him what number he thought: But this way is fo plain and obvious, that any one will difcover it: I fhall therefore fhew fome other ways not fo liable to discovery. ID him which thinketh double his number thought, unto that double add 4, and multiply that Sum by 5, and unto that Product bid him add 12; then bid him tell you this laft Product, unto which do you privately add a Cypher, and from the Sum fubftract 320, the remainder (two Cyphers being cut off) will be the number thought. This laft Product 3682 being given you, add unto it a Cypher, and it makes 36820, from which substract (always) 320, and the remainder will be 36500, from which the two Cyphers being taken, there will be left 365, the Number thought. Bh The Second Way. ID the Party that thinketh, break his number into any two parts; then bid him multiply each of those parts by themselves, and alfo the parts one by the other twice; then bid him add all those four Products together, and give you the Sum of them; from which Sum do you Extract the Square Root, and that Root fhall be the number thought. Example. Let the Number thought upon be 365; which let be broken into these two parts 221 and 144, which together make 365. The Sum of the four Products 133225 The Square Root whereof is 365, the Number first thought upon. L A Third Way. ET any Person think (and fet down) what Number he pleaseth; then bid him multiply that Number, and their Products fucceffively by all the nine Digits; then bid him give you the last Product; which Product, if you divide it by 362880, the Quotient shall be the Number thought. So if the Number thought (or fet down) were 321, that Number multiplied by One (1) produceth only 321: Now if you divide this laft Product 116484480 (in any cafe) by 362880, the Quotient will be 321, equal to the Number thought. any A Fourth Way. Letiply Perfon think (or fet down) any Number, then let him multiply that Number by all the nine Digits; then let him add all the Products together, and give you the Sum of all the Products fo added together; which Sum, if you divide (in any case) by 45, the Quotient will be the number thought. So Which Sum 1170 being divied by 45 (the Sum of the nine Digits) the Quotient will be 26, the Number thought. B A Fifth Way. ID a Perfon think (or fet down) any Number, then bid him multiply the fame Number by any other Number, what he pleases, (telling you what Number he multiplies by.) Then let him multiply that Product by what other Number he pleases (telling you what he multiplies by, as before.) And fo continue multiplying three, four, or as many times as he pleases: In the mean time do you fet down the Number by which he firft multiplied, and multiply that Number by the fecond Number that he multiplied by, and that Product by what he multiplied by the third time, and as many times as he multiplies; and when he hath done, bid him give you his laft Product, which if you divide by your laft Product, the Quotient will be the Number which he thought upon. Example. Suppofe the Number thought upon be 36, which he firft Multiplies by 7, and the Product is 252, which he again will multiply by 3, and the Product is 756; which again he will multiply by 9, and the Product will be 6804; which laft Product when he hath given you, then privately fet down 7 (the Number that he first multiplied by) and multiply it by 3 (the second Number he multiplied by) and the Product will be 21, which multiply by 9 (the third and laft Number he multiplied by) and the Product will be 189, by which, if you divide his laft Product 6804, the Quotient will be 36, the Number thought upon. F 2 Other |