Let AB and CD (Fig. 285) be two given lines; make EH equal to A B, and HG equal to CD; then E G equals the sum of the two lines.
Make FG equal to A B, which is equal to EH.
Bisect E G in J; then, also, J bisects HF; for -
EJ=JG, and -
Subtract the latter from the former; then -
EJ- EH= JG-FG;
JG-FG = JF;
therefore - .
Now, E J is half the sum of the two lines, and HJ is half the difference; and -
Or: Half the sum of two quantities, minus half their difference, equals the smaller of the two quantities.
a =a+b/2 - b-a/2 (128.)
We also have E J + JF= EF = CD; or, half the sum of two quantities, plus half their difference, equals the larger quantity,