| Moffatt and Paige - 1879
...AC is equal to the square on A B. Therefore, if a straight line, etc. QED Proposition III. Theorem. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** Let the straight line AB be divided into any two parts in the point C. Then the rectangle AB, BC shall... | |
| W J. Dickinson - 1879 - 36 páginas
...Deduce from this that a square on a straight line is equal to four times the square on half the line. 3. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part** 1G Same proposition. Divide a given line so that the rectangle contained by the whole line and one... | |
| Euclides - 1879
...this formula in terms corresponding to the enunciation of the proposition.] PROPOSITION III. THEOREM. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** Let AB be divided into any two parts at C. Then rect. AB, BC == rect. AC, BC, together with sq. on... | |
| Edward Harri Mathews - 1879
...sides is a right angle. Find a square equal to the difference of two given squares. Section III. 1. **If a straight line be divided into any two parts,...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... | |
| University of Oxford - 1879
...the line, and the two interior angles on the same side of it together equal to two right angles. 3. **If a straight line be divided into any two parts,...contained by the two parts, together with the square** of the aforesaid part. 4. From a given point, either without or in the circumference of a circle, draw... | |
| Isaac Sharpless - 1879 - 266 páginas
...AF+CE=AE; AF=AD.AC=AB.AC, CE=CF.CB = AB. CB, AE-AB * ; AB.AC+AB.CB=AB\ Proposition 3. Theorem.—If **a straight line be divided into any two parts, the...contained by the two parts, together with the square** of the aforesaid part. Let the straight line AB be divided in two parts in the point C, then AB.BC=AC.CB+BC\... | |
| Euclid, F. B. Harvey - 1880 - 119 páginas
...rectangles contained by MN and MO, and by MN and NO, together = the square on MN. PBOP. III. THEOREM. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** Let AB be a straight line divided into any two parts in C. Then it is to be proved that The rectangle}... | |
| Isaac Todhunter - 1880 - 400 páginas
...line lie divided into any ttco parts, the rectangle contained by tlie whole and one of the parts, u **equal to the rectangle contained by the two parts, together with the square on the aforesaid part.** Let the straight line AB be divided into any two parts at the point C: the rectangle AB, BC shall be... | |
| Euclides - 1881
...when the two straight lines mentioned in Us enunciation are equal, their rectangle is a square. FK **If a straight line be divided into any two parts,...contained by the two parts, together with the square** of the foresaid part. Let the straight line AB be divided into any two parts at the point C. The rectangle... | |
| Marianne Nops - 1882
...AC, and AB, CB = sq. on AB. Wherefore if a straight line, &c. — QED *2 PROPOSITION III., THEOREM 3. **If a straight line be divided into any two parts the...parts, together with the square on the aforesaid part.** Let the straight line AB be divided into any two parts at C. The rect. AB, BC = the rect. AC, CB, and... | |
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