Cockers arithmetick being a plain and familiar method suitable to the meanest capacity for the full understanding of that incomparable art as it is now taught by the ablest school-masters in city and countrey / composed by Edward Cocker ... ; perused and published by John Hawkins ...

CHAP. XIV. The Rule of three Com∣posed of 5 Numbers. (Book 14)

1. THE Rule of three Composed, is when questions (wherein there are 5 Numbers given to find a 6 in Propor∣tion thereunto) are Resolved by one single

Rule of 3 Composed of the 5 given Num∣bers.

2. When questions may be performed by the double Rule of 3 Direct, and it re∣quired to resolve them by the Rule of 3 Composed, (first Order or Rank your Num∣bers according to the 7 Rule of the 12th. Chapter, then)

The Rule is

Multiply the terms (or numbers) that stand one over the other in the first place, the one by the other, and make their Pro∣duct the first term in the Rule of 3 Direct, then Multiply the terms that stand one over the other in the third place, and place their product for the third term in the Rule of 3 Direct, and put the middle term of the 3 uppermost for a second term, then having found a fourth Proportional, direct to these 3, then this 4th. Proportional so found, shall be the Answer Required.

So the first question of the 12 Chap. (viz. If 100 l. in 12 Months gain 6 l. Interest, what will 75 l. gain in 9 Months? the numbers being Ranked (or placed) as is there Directed and done.

Then I multiply the 2 first terms 100 and 12, the one by the other, and their Pro∣duct is 1200 (for the first term) then I multiply the two last terms 75 and 9 toge∣ther,

and their Product is 675 for the 3d. term. Then I say, As 1200 is to 6, so is 675 to the Answer, which by the Rule of 3 Direct will be found to be 3 l. 7 s. 6 d. as before.

3. But if the Question be to be Answer∣ed by the double Rule of 3 Inverse, then (having placed the 5 given terms as before) multiply the lowermost term of the first place, by the uppermost term of the third place, and put the Product for the first term; then multiply the uppermost term of the first place, by the lowermost term of the third place, and put the Product for the third term, and put the second term of the 3 highest numbers for the middle term to those two, then if the Inverse Proporti∣on is found in the uppermost 3 numbers, the 4th. Proportional direct to these 3 shall be the Answer; so the first question of the 13th. Chapt. being stated, viz. If 100 l. Principal in 12 Months gain 6 l. Interest, what Principal will gain 3 l. 7 s. 6 d. in 9 Months? State the numbers as is there Directed in the first order, viz.

M.	l.	M.
12	100	9
l.		l.	s.	d.
6		3	7	-6

then Reduce the 6 l. and 3 l. 7 s. 6 d. in∣to pence, the 6 l. is 1440 d. and 3 l. 7 s. 6 d. is 810 d. then multiply 1440 by 9, the product is 12960 for the first term in the Rule of 3 Direct, and multiply 810 by 12, the product is 9720 for the third term, then I say, As 12960 is to 100 l. so is 9720 to the Answer, viz. 75 l. as before. But if the terms had been placed after the second order, viz.

l.	l.	l.	s.	d.
6	100	3	-7	-6
M.		M.
12		9

then the Inverse Proportion is found in the lowest numbers, and having composed the numbers for a single Rule of 3 as in the se∣cond Rule foregoing, then the Answer must be found by a single Rule of 3 In∣verse, for here it falls out to multiply 810 by 12 for the first number, and 1440 by 9 for the third number, and then must say, As 9720 is to 100 l. so is 12960 to the Answer, which by Inverse Proportion will be found to be 75 l. as before.

The questions in the 12 and 13 Chap∣ters may serve for thy further experience?