 | Euclides - 1878 - 398 pages
...square on a straight line is equal to four times the square on half the line, PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...the rectangle contained by the two parts together mth the square on the aforesaid part. J> Let the st. line AB be divided into any two parts in C. Then... | |
 | Moffatt and Paige - 1879 - 506 pages
...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 - Geometry - 1879 - 44 pages
...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 - 146 pages
...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 - 94 pages
...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 - Greek language - 1879 - 414 pages
...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 - Geometry - 1879 - 282 pages
...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\... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...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 - Euclid's Elements - 1880 - 426 pages
...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 - Euclid's Elements - 1881 - 236 pages
...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... | |
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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 parts, together with the square of the aforesaid part. 
