| Richard Wormell - 1876
...its parts are together equal to the square on the whole line. . . - . . . . . . . . . . . . 145 3. **If a straight line be divided into any two parts,...by the whole and one of the parts, is equal to the** square on that part, together with the rectangle contained by the two parts. .. .. 145 6. If a straight... | |
| Robert Potts - 1876 - 403 sider
...square on AB. If therefore a straight line, &c. QE ji. PROPOS1TION III. THEOREM. iJ a itraiyht line Tie **divided into any two parts, the rectangle contained by the whole and one of the** parti, is equal to the rectangle contained by the tun parti, together with the square. on the aforesaid... | |
| Francis Cuthbertson (geometer.) - 1876
...squares on the whole and on the other part by twice the rectangle contained by tlie whole and that other **part. Let the straight line AB be divided into any two parts in** C. Then shall the square on AC be less than the squares on AB and BC by twice the rectangle AB, BC.... | |
| Euclides, James Hamblin Smith - 1878 - 349 sider
...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... | |
| Āryabhaṭa - 1878
...divided Mo any two parts, the rectangle contained by the whole line and one of its parti is equal to th* **rectangle contained by the two parts, together with the square of the** for esaid part. And conversely, if there be a rectangle and the square of one of its sides, the rectangle... | |
| Isaac Sharpless - 1879 - 266 sider
...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...aforesaid part. Let the straight line AB be divided** in two parts in the point C, then AB.BC=AC.CB+BC\ Upon BC describe (I. 41) the square CE; produce ED... | |
| 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,...parts, together with the square of the aforesaid part.** 4. From a given point, either without or in the circumference of a circle, draw a straight line which... | |
| 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,...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... | |
| 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,...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 - 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,...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,... | |
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