| Euclides - 1862 - 140 pages
...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 - 172 pages
...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 - Education, Higher - 1863 - 328 pages
...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 - 262 pages
...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 - 448 pages
...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.... | |
| Robert Potts - 1865 - 528 pages
...BC is equal to the square on AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. lf a straight line be divided into any two parts, the...contained by the two parts, together with the square on the aforemid part. Let the straight line AB\>& divided into any two parts in the point C. Then the... | |
| Euclides - 1865 - 402 pages
...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 - Geometry - 1855 - 360 pages
...multiplying both members of this equality by a, we shall have a2=ŤA + 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 - 224 pages
...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 - Euclid's Elements - 1867 - 424 pages
...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... | |
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