SCHOLIUM. Thus we have shown, that if four quantities be proportionals by the common algebraic definition, they will also be proportionals according to Euclid's definition; and conversely, that if four quantities be proportionals by Euclid's definition, they will also be proportionals by the common algebraic definition; and by a similar method of reasoning we may easily show, that when four quantities are not proportionals by one of these two definitions, they cannot be proportionals by the other definition.

Thus it appears, that the two definitions are altogether equivalent; each comprehending, or excluding, whatever is comprehended, or excluded, by the other.

THE END.

ERRATA.

Page 6, line 21, for letter, read letters.

1

p. 19, 1. 1, 3, for 8xy and 552, read 3xy and 55x2.

p. 33, 1. 12, for to, read to the addition of.

p. 44, 1. 20, for 5a, read 5a3.

p. 83, 1. 22, 23, for (m-n) and (m+n), read (m

n)c and (m±n)c.

do. 1. 26, for members, read numbers.

p. 88, 1. 34, for continued, read contained.

p. 96, 1. 15, for ac2, read a3c2.

p. 104, l. 11, 12, for +b3 and -b2, read +62 and

p. 107, 1. 4, for-x read -x2.

p. 116, 1. 12, for 3x, read 3ax.

p. 125, 1. 3, dele 2,.

1

p. 132, 1. 2, 9, for 4x2 and +2ab, read 6x2 and

+26x.

p. 138, 1. 22, for law that, read law, that is to say,

at the general formula, that.

p. 156, 1. 7, for plynomials, read polynomials.

p. 159, l. 16, for (a+x2), read (a+x)2.

p. 161, 1. 12, for unknown, read known.

p. 168, 1. 7, for conditions, read condition.

p. 173, 1. 4, for x=2, read x=4.

p. 176, 1. 14, for 30, read 20.

p. 179, 1. 7, for 198, read 199.

p. 180, 1. 8, for quantities, read quantities, values.

do. 1. 29, for formulæ, read formula.

p. 181, 1. 5, 16, for formulæ, read formula.

do. 1. 21, dele 199.

p. 188, 1. 17, for 9, read 13.

p. 192, 1, 5, 11, for 2x and +6a, read 3x and -6.x.

p. 195, 1. 21, for quantities, read equations.

p. 200, 1. 15, for are, read are the.

p. 201, 1. 13, for furnish, read furnishes.

p. 215, 1. 5, for Analysts employ, read Analysis

employs.

p. 216, 1. 2, for formulæ, read formula.

p. 224, 1. 2, for depend, read depends.

p. 248, 1. 15, 18, for y= and y=3, read y=3 and

p. 257, 1. 23, for other, read others.

p. 279, 1. 7, for form, read from.

p. 284, 1. 12, 27, for plus and 720, read minus and

752.

p. 289, 1. 13, for 4, read 5.

p. 301, 1. 11, for 3s. and 2s. read 2s. and 3s.

p. 313, 1. 23, for devoted, read denoted.

p. 314, 1. 5, 9, for a"-3b and is, read an-ss and

dele is.

p. 317, 1. 14, for-27x3a=x3, &c., read
27x3a = (Art. 293) -27×2x2xa°=-3×
XxX a2- За2 х.

p. 323, 1. 8, for 16x2y and by, read 15x2y and
6xy5.

p. 325, 1. 25, 26, for square of be and root c2, read
square root of ba and root of c2.

do. 1. 31, for +20x3-15x2+5x-1, read

20x3+15x2-5x+1.

do. 1. 33, 34, for a

and for 4ax+3, read 4ax3+.
p. 329, 1. 3, for square of,

-

4a3x, read a2-4a3x,

read square root of.

p. 349, 1. 5, 6, for a and a3+a α, read a and a

4

do. 1. 18, 30, for 6243 and 109, read243
and 2/9.

p. 350, 1. 10, 31, for a and a2, read a2 and a-2.

1.3

1-3

2

p. 351, 1. 24, for (2ax)2 +, read (2ax) =.

p. 356, 1. 3, for where, read when.

p. 360, 1. 11, for 2/9, read 3/9.

p. 365, 1. 14, for to observed, read to be observed.

p. 370, 1. 17, for increased, read concerned.

p. 371, 1. 6, for having, read have.

p. 374, 1. 7, 22, for(19-4) and 2, read (9

-4) and 2.

p. 376, 1.

and =3x2.

2, 30, for x-y2 and -3x2, read x2-y

p. 377, 1. 16, After Ex. 1. read the following: Cubing both sides, x2=a+b; x=±√(a+b). Ex. 2. Given lues of x.

(x2-8)=√(x-3), to find the va

p. 377, 1. 16, 18, 24, for value and quantity, read values and equation...

p. 380, 1. 1, 25, for 3abx and x, read 2abx and a.

p. 381, 1. 29, for x y, read x-у.

do. 1. 33, for y=4, read y=3.

p. 382, 1. 17, for y3, read+y3.

p. 383 1. 4, for a given ratio, read given ratios. p. 337. 1. 3. for 16, read 6.

p. 386, 1. 16, Jar to the sum of their cubes as 20. to 7, read to the difference of their squares as 52 to 1. p. 388, 1. 37, after were, read persons relieved ; and each woman received twice as many shillings as there were women more than men.

p. 390, 1. 3, for x=-n, read x=-n. p. 394, 1. 18, for x2 read x.

p. 400, 1. 12, for =5, read =1.
p. 402, 1. 12, for -61, read -21.

p..404, 1. 18, for±√-7, read-7.

p. 406, 1. 9, for 6, read -6.