 | 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,...contained by the two 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,... | |
 | 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,...contained by the two 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... | |
 | 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,...contained by the two parts, together with the square on the aforesaid part 1G Same proposition. Divide a given line so that the rectangle contained by the... | |
 | 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,...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... | |
 | 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,...contained by the two 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... | |
 | 1880 - 160 pages
...described upon the other two sides of it ; the angle contained by these two sides is a right angle. 7. If -a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. 8. If a straight line be divided into any two parts, the squares on the whole... | |
 | 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... | |
 | 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,...foresaid part. Let the straight line AB be divided into any two parts at the point C. The rectangle AB.BC is equal to the rectangle AC.CB, together with the... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...but and and AF+CE=AE; AF=AD.AC=AB.AC, CE=CF. CB =AB. CB, AB.AC+AB.CB = Proposition 3. Theorem. — If a straight line be divided into any two parts,...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\... | |
 | Education, Higher - 1882 - 498 pages
...subtending the right angle is equal to the squares described on the sides which contain the right angle. 14. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. 15. Find the centre of a circle. 16. If in a circle two straight lines cut one... | |
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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. 
