The Jackson standard. [volume] (Jackson C.H., Ohio) 1847-1888, 1879-06-26

numbers given, to find the numbers.
Rule. From the square of their sum take four
times their pl oduct, and the square root of the
remainder will be the difference ofthe numbers.
the sum of their squares given, to find the num-
bers.
Rule. From the square of the sum take the
sum of the sum of the squares and half the
remainder will be the product. Then proceed
CASE 5. Prop. Given the sum of two num-
bers and the difference of their squares, to find
Rule. Divide the difference of their squares.
by their sum, and you will have the difference
| CASE g. Prop. The sum of the squares and
| the difference OF the squares of two numbers
| given, to find the numbers.
| Rule From the sum take the difference, and
| half the remainder is the square of the less,
| which taken from the sum of the squares will,
| of course give the square of the greater. Then
| extract for the numbers
| CAsE7 Prop. Given the difference of two
| numbers and their product to find the num-
| T1ze To the square of the difference add four
| times product, and the square root of the sum
will be the sum of the numbers. Then proceed
| by Case lst.
CASE 8. Prop. The difference of two num-
bers, and their quotient given, to find the num-
bers.
less one, for the smaller number, and add it to
the difference for the larger.
| CASE g. Prop. Given the difference OF two
numbers and the sum of their squares, to find
the numbers.
| take the square of the difference, the square
root of the remainder will he the sum of the
CASE 10. Prop. The difference of two num-
bers, and the difference of their squares given,
Rule. Divide the difference of the squares by
the difference of the numbers, the quotient will
be the sum OF the numbers. Then proceed by
Case 1st.
CASE IL. Prop The product of two numbers
and the sum of the squares given to find the
Rule. Add twice the product to the sum of
the squares; the square root of the sum will be
the sum of the numbers. Then proceed by
Case Sd.
CASE IL. Prop. Given the product of two
numbers. and the difference OF their squares, to
find the numbers.
Rule. Add one-fourth of the square OF the
difference of squares to the squares of the pro-
duct; take the square root of the sum from
this root take half the difference of squares,
and the square root of the remainder Will be
the less number.
and their quotient given, to find the numbers.
Rule. Divide the product by the quotient
and, the square root of the result will be
CASE IA. Prop. Given the product of two
numbers, and the square of the difference, to
find the numbers.
Rule. Add four times the product to the
the sum will be the sum of the numbers. Then
having the sum and product, proceed by Case
CASE 15. Prop. The quo ent of two numbers
and the sum of their squares given, TO find the
numbers.
Rule. Divide he sum of the squares by the
square of the quotient, plus one; and the square
root of the result will be the less number.
CASE l6. Prop. Given the QuOtient OF two
numbers, and the difference of their squares, tt
find the numbers.
Rule Divide the difference of squares by the
square of the quotient less one; the square root
of the resulting quotient will be the less mum
ber.
CASE II. Prop. The quotient of two mum
; bers, and the square of their sum given, TO hnt
the umberS
Rule Divide the square of the sum by thu
square of the quotienG plus one; the square roo
of the resulting quotient will be the less mum
Der.
CASE IS. Prop. The quotient of two mum
bers, and the square of their difference given
to find the numbers.
Rule Divide the square oftheir difference bJ
the square of the quOtient less one the square
root of the resulting quotient will be the less
number.
CASE 10. Prop. Given the square of the sum
and the sum of the squares of two numbers, tt
find the numbers.
Rule. From the square of the sum, take the
sum of the squares, and twice the product o
the numbers will remain. Then subtract foul
times the product from the square of the sum
and the remainder will be the square of the
difference. Then having the square of the sun
and difference, extract the roots and proceed by
Case lSt. ST. WHITE.