612. It is required to find three Terms in whofe Sum is s and their Product equal to the Sum of their Squares. From the last Step it appears that for s can be affumed no Number 2 whofe Square is less than 54, because thus 5-353-54ss will be impoffible, as fuppofing the Square Root of a defective Quantity. If so, then is the Term, the fecond 2, and the third Term a whofe Product and Sum of their Square is 110. PROBLEM LVI. 613. To find four Terms in, whofe Sum is s, and Sum of their Squares z. Effection. Put a for the firft Term, and the common Difference. Then. 362-9ss Ex. gr. If s=28, and z=216, then a 2. Confequently the other three Terms are 6, 8, 10. PROBLEM LVII. 614. To find five Terms in, viz. a, ate, atze, atze, at-4e, whereof the firft Term is in Proportion to the laft as b to d, and the Sum of all the Terms is equal to the Square of the Middle or third Term. 249 · --Ex.-gr. If b=3,-and-d=5, then will the five Terms required be 2, 102, 222, 222, 24 or 4, 4, 40, 42, 20. 120 8 PROBLEM LVIII. 615. To find three Numbers in 4, e, y, whofe Sum is s, and Sum of their Squares z. Effection. jayee (In. 191.) 1X2 22ay=2ee 3afety's by the Question. 3-e 4a+y=s—e 4025a2+2ayyy-ss25eee. 6-\-ee 7 a2+e2+y2=ss—25e+ee=z by the Queftion. Ex. gr. If s=228, z=19152, e=72, y=108, a=48. PROBLEM LIX. Theo. III. 616. To find three Quantities in Geometrical Progreffion b, e, y from the first given equal b, and the Sum of the Squares of the other ee+y=z. Ex. gr. If b=48, and z=16848, then y=108, and e=72. PROBLEM LX. 617. To find three Quantities in÷a, e, y, whofe Sum is s, and the Sum of the Squares of the Extreams z. Effection. 1lay=ee (In. 191.) 1X2 22ay=2ee 3afety s by the Question. 3-e 4a+y=se |