...line is divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and...that part together with the square of the other part : where is this proposition employed ? 8. Derive Prop. 8 from Props. 4 and 7. 9. Shew that the second...

...line be divided into any two parts, the square on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. (LooMis AND LEGENDRE.) 1. If a straight line, meeting two other straight lines,...

...parts, the squares of the whole line and one of the parts are together equal to twice the rectangle of the whole and that part, together with the square of the other part. Shew also that {a — t)2 — a" 4- *2 — 2 <*& i® the algebraic eqivalent of the proposition. 2....

...line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Enunciate any other proposition of the second book in which this theorem is used....

...zab + b2 = 2a(a + &) + &*. By the commutative law, 2a(a + K) + <52 = 2(0 + £)a + &*, Therefore 105 rectangle contained by the whole and that part, together with the square on the other part. a> 300. By the commutative and distributive laws, and 294, 4(a + b)a -fb* = 4#2...

...the commutative law, 2a(a + 6) + P = a(a + b)a + P, .-. (a + i>Y + a* = 2(0 + 6)a + 6*. Therefore 105 rectangle contained by the whole and that part, together with the square on the other part. 300. By the commutative and distributive laws, and 294, 4(a + t)a + 6* = 4** + yib...

...straight line be divided into two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. 5. Hence give a Geometrical proof of the algebraic proposition, a2 + 'r>2ai, a and...

...BC = sq. on AC + 2 sq. on BC + 2 rect. AC, CB = sq.on AC + 2 rect. AB,BC (by III.). PROP. VIII. — Let the straight line AB be divided into any two parts in C, and produced to D, so that BD=BC : then shall the square on AD be equal to four times the rectangle...

...line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. If AB be divided in C so that the square on AC is double the square on CB, the sum...

...divided into any two parts, prove that the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Prove that the rectangle contained by the diagonals of the squares on the whole...