| Euclides - 1862
...the square on AB. Conclusion. — Therefore, if a straight line, &c. QED PROPOSITION 3.— THEOREM. **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. (References— Prop. I.... | |
| Euclides - 1862
...straight line be divided into any two parts ; then the rectangle contained by the whole and one of Ihe **parts is equal to the rectangle contained by the two parts, together with the square of the** aforesaid part. (References— Prop. i. 31, 46.) Let the straight line AB be divided into any two parts... | |
| University of Oxford - 1863
...of its angles equal to a given rectilineal angle. 6. Describe a square on a given straight line. 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 bisected, and produced to any point, the rectangle... | |
| Euclides - 1864
...AB, BCis equal to the square on AB. If therefore a straight line, &c. 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... | |
| Euclides - 1864
...AB, BCis equal to the square on AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. **If a straight line be divided into any two parts,...rectangle contained by the whole and one of the parts,** it equal to the rectangle contained by the two parts, together with the square on the aforesaid part.... | |
| Euclides - 1865
...equal to the rectangles under the whole and each of the parts . . . . . II. 2. 2. The rectangle under **the whole and one of the parts, is equal to the rectangle** under the two parts, together with the square on the aforesaid part . . . . . . . n. 3. 3. The square... | |
| John Playfair - 1855 - 317 sider
...multiplying both members of this equality by a, we shall have a2=«A + a</ PE Q KLD PROP. III. THEOR. tf **a straight line be divided into any two parts, the...the parts, is equal to the rectangle contained by** the tttm parts, together with the square of the aforesaid part. Let the straight line AB be divided... | |
| 1867
...one another, and likewise those which are terminated at the other extremity equal to one another. 3. **If a straight line be divided into any two parts,...contained by the two parts, together with the square** on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. QED PROPOSITION 3. 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 at the point (7: the... | |
| Robert Potts - 1868 - 410 sider
...DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. **If a straight line be divided into any two parts, the rectangle contained** ky the whole and one of the parts, is equal to the rectangle contained by the twa parts, together with... | |
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