A ‘Treatise os Algebra. 177

Note) and we (hall thence have 37,30,23, 16, 9 and 2,for the successive Values of x t and 4, 9,14,19,24. and 29,for the corresponding Values of y. Which are all thepossible Answers in whole Numbers, when z= I.

Let z be now taken = 2, then x = 3 2 and y = 6 jlet the former of these Values be increased or decreasedby the Multiples of 7, and the latter by those of 5, as faras possible, till they become negative; and then we shallhave 39,32,2;, 18, n and 4 for the successive Values of*, in this Cafe, and I, 6, 11, id, 21 and ad, for therespective Values of y. Which are all the Answers whenz is =: 2.

Again, let z be taken — 3 ; then, by proceeding asabove, the corresponding Values of x and y will be foundequal to 34, 27, 20, 13, 6 and 3, 8, 13, 18, 23 respec-tively. And so of the rest. Whence we have the fol*lowing Answers, being 60 in number.

z

y

X

I

4. 9.14.19.24.29.

37 -30-23.16. 9.2

2

1. 6.1,. 16.21.r6.

39.32.25.18.11.4

3

3. 8.13.18.23.

34.27.20.13. 6.

4

5.to.15.20.2;.

29.22.15. 8. 1.

5

2. 7.12.17.22.

zi.24.17.10. 3.

6

4. 9.14.19,

26. 19.12. 5 .

7

I. 6.11.16.

28.21.14. 7.

<

3. 8.13.18.

23.16. 9. 2.

9

;.10.15.

18.11. 4.

10

2. 7.1a.

20.13. 6.

11

4. 9.14.

r;. 8. I.

12

r. 6.11.

17-10. z.

I?

3 . 8.

12. 5.

14

;. 10.

I+- 7.

-5

2. 7.

9 - 2.

16

4 *

4 -

17

6 .

i8|3.

I .

N

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