| Francis Cuthbertson - 1874 - 349 páginas
...CAQ. The Theorems in Proposition II. may be established independently as follows :— THEOREM (a). **If a straight line be divided into any two parts, the square** on the whole line is' equal to the squares on the parts together with twice the rectangle contained... | |
| Edward Atkins - 1874
...together with the rectangle AC, CB. Therefore, if a straight line, <fec. QED Proposition 4. — Theorem. **If a straight line be divided into any two parts, the square** on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle... | |
| Edward Atkins - 1874
...twice the rectangle contained by 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; PROPOSITIONS. CONSTRUCTION. — Upon AB describe the square ADEB (I. 46), and join BD.... | |
| Euclides - 1874
...on BC, together with the rectangle contained by AC and CB. QED PKOP. IV.— THEOREM. (Euc. II. 4.) **If a straight line be divided into any two parts, the square** on the whole line is equal to the squares on the two parts, together with twice the rectangle contained... | |
| Francis Cuthbertson (geometer.) - 1876
...= A PQR. Wherefore a rectangle has been described equal to the given triangle. QEF PROPOSITION III. **If a straight line be divided into any two parts, the square** on the whole line will be equal to the squares on the two parts, together with twice the rectangle... | |
| Education Department,London - 1876
...four right angled trianglc.-s of equal area can be drawn having the same hypotenuse. SECTION III. 1. **If a straight line be divided into any two parts, the square** on the whole line is equal to the squares on the two parts together with twice the rectangle contained... | |
| 1876
...to the squares described upon the sides which contain the right angle. 4. Proposition IV, Book II. **If a straight line be divided into any two parts, the square** on the whole line is equal to the squares on the two parts, together with twice the rectangle contained... | |
| Robert Potts - 1876 - 403 páginas
...straight line, which joins the middle points of two sides of a triangle, is parallel to the base. 9. **If a straight line be divided into any two parts, the square** on the whole line is equal to the squares on the two parts, together with twice the rectangle contained... | |
| Edward Atkins - 1876 - 119 páginas
...together with the rectangle AC, CB. Therefore, if a straight line, &c. QED Proposition 4.— Theorem. **If a straight line be divided into any two parts, the square** on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle... | |
| Richard Wormell - 1876
...rectangles contained by the first and second, first and third, and second and third parts respectively. 103. **If a straight line be divided into any two parts, the square** on the whole line and one of the parts is equivalent to twice the rectangle contained by the whole... | |
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