 | Robert Potts - Geometry - 1876 - 446 pages
...opposite angle, and acute angle. (Take the case where the perpendicular falls within the triangle.) 5. If a straight line be divided into any two parts, the squares on the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and... | |
 | Henry Major - 1876 - 784 pages
...the triangle CNK equal to the triangle ARC, and the triangle BMF equal to the triangle ARB, &c.) 2. If a straight line be divided into any two parts, the squares ou the whole line and one of the parts are equal to twice the rectangle contained by the whole and... | |
 | Edward Atkins - 1876 - 130 pages
...on EC, 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... | |
 | Alfonzo Gardiner - 1878 - 146 pages
...x, 5a;= ~- + 7. 6. The product of two numbers is 15, and their difference is 2. Find the numbers. 7. 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 contained by the whole and... | |
 | Euclides - 1879 - 146 pages
...interpret this formula in terms corresponding to the enunciation of the proposition.] PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the. rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two... | |
 | University of Oxford - Greek language - 1879 - 414 pages
...equal sides be produced the angles on the other side of the base shall be equal to one 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 contained by the whole and... | |
 | Edward Harri Mathews - 1879 - 94 pages
...equal to the rectangle contained by the two parts together with the square on the aforesaid part. 2. 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 contained by the whole and... | |
 | Moffatt and Paige - 1879 - 506 pages
...rectangle AC, CB together with the square on B C. Therefore, if a straight line, etc. QED Proposition IV. Theorem. 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... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...but also, and AE-AD+CE; AE = AB.BE=AB.BC; AD-AC.CD = AC.CB, CE= CB\ AB.BC-AC.CB+CB\ Proposition 4. Theorem. — If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...rectangle AC, CB, together with the square on BC. Wherefore, if a straight line &c. QED PKOPOSITION 4. THEOREM. 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... | |
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IF a straight line be 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. 
