whole Cistern that is, 5. Which E-} quation, its FraЯtions being reduc'd to the fame Denomination will be 6. Wherefore, by Tranfpofiti on or equal Mul-304*204=600 | baxca=bc. tiplication, viz. by 600 or bc, by equal Divifi on, viz. by (30 +20=)50, or b+c bc That or 12 is the true Number fought, b+c may be prov'd by folving this following Quefti on, on, being the Inverse of the former, viz. both the Pipes A and B fill the Cistern in bor 12 Hours; and the Pipe A alone fills it in c or 20 Hours: In what Time therefore will the Pipe B alone fill it > Answer, In 30 Hours. For let the Time fought be a. Therefore, ab :: b: and c: 1 :: b: bc. But according to the b. b State of the Question,+1. Where bc C fore, by Reduction, a=cb=30. So the C Solution of both Questions agree one with the other, and confequently, both are truly folved. EXAMPLE VI. Three Companies of Soldiers paffing by, the First takes away from a Shepherd Half of his whole Flock, and Half of a fingle Sheep over, The Second takes away Half of the Remainder of the Flock, and alfo Half a Sheep over. The Third likewife takes away Half of the Flock yet remaining, and Half a Sheep All which was done without killing any Sheep, and there remain'd at laft b, or twenty Sheep to the Shepherd. How many Sheep therefore had he in his Flock at the First? Anf. 167. Namely, over. L4 1. Let 1. Let the Number of Sheep at the first be 2. Therefore, the Number of Sheep taken by the first Company, will be 3. And fo the first Remainder left to the Shepherd, will be 4. Then the Half of the first Remainder isa, to which adding (, or which is the fame) fingle Sheep, the Sum will be the Quantity taken by the fecond Company, viz. of a a+ 6. Accor 6. Accordingly, Half of the fecond Remainder will be a, to which adding (, or which is the fame) of a fingle Sheep, the Sum will be what was taken away by the third Company, viz. 7. Wherefore, the third Remainder left to the Shepherd, will be (a-, or which is the fame) za— lefsa+, that is, 8. But this third. Remainder is accor ding to the State of a-b=20. the Question, equal to b or 20, that is, 9. Wherefore, by}=b+7=20+% · Tranfpofition 10. Wherefore, by equally multiplying each Side of the Equation by 8, there will arise the Num ber fought, viz. a=8b+7=167. Accor Accordingly, the Half of 167 is 837, to which adding, the Sum is 84, the Number of Sheep taken by the first Company; and then the first Remainder was 83. Again, the Half of 83 is 41, to which adding, the Sum is 42, the Number of Sheep taken by the second Company; and fo the fecond Remainder was 41 Sheep. Lastly, the Half of 41 is 20, to which adding, the Sum is 21, the Number of Sheep taken by the third Company; and fo the third Remainder is 20 Sheep according to the State of the Question. I. Logarithms of great Ufe in Multi plication, Divifion, CHAP. XIV. Of the Use of Logarithms. T has been above observ'd, that the I'Multiplication and Division of larger Numbers, as alfo the Extraction of the Root of any Power, is render'd much more eafy by the Help of Logarithms. and the I have therefore referv'd this laft Chap Extraction ter to explain therein the Ufe of Loga of Roots. 2. Loga rithms, what. rithms. Logarithms are artificial Numbers, proceeding in Arithmetical Proportion, as the natural Numbers, to which they are applied, |