Hence it is evident, that if either of the Roots be found, the other may be easily had without Divifions.

If the Contents of this Section be well underftood, it will be eafy to give a Numerical Solution to any Quadratick Equation, that happens to arife in refolving of Queftions, &c. And as for giving a Geometrical Conftruction of them, I think it not proper in this Place; becaufe I here fuppofe the Learner wholly igno rant of the first Principles of Geometry, therefore I fhall refer that Work to the next Part.

CHAP. IX.

Of Analysis, or the Method of refolving Problems exemplified by Variety of Numerical Dueftions.

N.B. HERE I advise the Learner to make Use always of the fame Letters, to represent the fame Data in all Questions."

aaeez the Sum of their Squares. Laax the Difference of their Squares.

Any two of the fix (s, d, p, q, z, x) being given, thence to find the reft; which admits of fifteen Variations, or Questions.

Question 1. Suppose s and d were given, and it were required by them to find a

Let {

p.g.

ate=s

z. and x.

240

and suppose {
d=192} Then

32a=s+d=432

std

216, here a is found.

2.

I252e=s-d=48.

9-1012aaee=sd=x=46080, * found.

Question 2. Let s and p be given, to find the reft.

That is 1\a+e=s. = 240 } Quære a. e. d. q.z.x. is{ 2ae=p=5184

IG

3aa+2ae+ee = ss=

57600
20736

3-45aa2ae+ee=ss=4p=36864

5 w2 6a-e=√ss=4p=d=192 1+6 72a=5+ √ss= - 4P

12 13 14 aa+ee=ss-2p==47232

13 15 aa—ce=s√ss=4p=x=46080.

4P

-

2

5155-0 4P

2

Question 3. Suppose s and q are given, to find the reft.

Question 4. Let s and z be given, to find the reft.

1|a+e=s. = 240 } Quære a.e.d. p. q.x.

2aa+ee=2.47232.

3aa+2αetee=ss

412ae=ss-Z

4

2ae+ce=2x-ss

6a—e=√2% — s s = d

The reft are found juft as in the 2d Question; the 8 and 10 Steps here being the very fame with the 8 and 10 Steps there.

Question 5. When s and x are given, to find the reft.

Question 6. Suppofe d and p are given, to find the reft.

Viz. {

1|a-e=d=192 Quære a.c.$.9. % . * . 2ae=p= 5184

1 2 3 4α-20e+ce=dd

IG

2 x 4 4

4a0=4p

3+4 5a+zac+ee=dd + 4 p
5 ww2 6a+e=√dd+4p=s

ພ

12 13 14 4 a + c e = d d +2p=z

12-131500-ee = d√dd+4p=x

Question 7. Let d and q be given, to find the reft.

9