...hases, in the same straight line and on the same side of it, are between the same parallels. 6. If a straight line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole and that part, together with...

...decreasing. 14. If a straight 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...that part together with the square of the other part. Enunciate any subsequent proposition of Euclid in which this result is employed. 16. If four straight...

...another. 3. If a straight 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...by the whole and that part together with the square on the other part. 4. When are circles said to touch one another ? One circle cannot touch another...

...-THEOREM. If a straight line be divided into any two parts, the squares on the wlutle line) and on one of the parts, are equal to twice the rectangle...the whole and that part, together with the square on the other part. (References— Prop. I. 31, 34, 43, 46; II. 4, cor.) Hypothesis. — Lst the straight...

...straight line, &c. QED PROP. VII.— THEOREM. If a straight line be divided into any two parts ; tlien the squares of the whole line and of one of the parts, are equal to twice tjie rectangle contained by the whole and that part, together wM the square of the other part. (References...

...9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It a straight line be divided into any two parts the squares of the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and that part, together with...

...equal to the squares of the two parts, together with twice the rectangle contained by the parts. 8. If a straight line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole and that part, together with...

...whole line (AB), and of one of the parts (BC) are equal to twice the rectangle (AB, BC) contained bg the whole and that part, together with the square of the other part (AC). Upon AB describe the square AE (I. 46) and join BD. Through through G draw HGK parallel to AB...

...n letters a, b, c, and their powers. Find the number of terms in the expansion of (a+b+c+d)\ 9. If a straight line be divided into any two parts, the...twice the rectangle contained by the whole and that pan, together with the square of the other part. Prove that the area of any right-angled triangle is...

...VII. THEOREM. If a straight 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...the whole and that part, together with the square on the other part. Let the straight line AB be divided into any two parts in the point C. Then the...