| Euclides, James Hamblin Smith - 1883
...the line, PROPOSITION III. THEOREM. // a straight line be divided into any two parts, the rectangk **contained by the whole and one of the parts is equal to the** netangle contained by the two parts together with the square on the aforesaid part. J) Let the st.... | |
| 1884
...whole дАЕО, Wherefore дАЕХ^дАСВ, and it has the iA which is common to both. — QEF 2. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** Prop. 3, Bk. II. 3. To divide a given straight line into two parts, so that the rectangle contained... | |
| Euclides - 1884
...CB. But DA and EB are each = AB ; NOTE. — The enunciation of this proposition usually given is : **If a straight line be divided into any two parts,...parts together with the square on the aforesaid part.** That is, in reference to the figure, an expression which can be easily derived from that in the text... | |
| University of Cambridge - 1884
...ABC are bisected in D, E respectively. Prove that the triangle DBG is double the triangle DEC. •i. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** 5. Describe a square that shall be equal to a given rectilineal figure. On the diagonal of a parallelogram... | |
| Stewart W. and co - 1884
...rectangle contained by AB, AC, together with the rectangle AB, BC, is equal to the square of AB. III. — **If a straight line be divided into any two parts,...contained by the two parts, together with the square** of the aforesaid part. Let AB be divided into any two parts in the point C; then the rectangle AB,... | |
| Oxford univ, local exams - 1885
...equal to three given straight lines, but any two whatever of these must be greater than the third. 5. **If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part.** 6. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle... | |
| Dalhousie University - 1885
...extremities of equal and parallel lines towards the same parts, are themselves equal and parallel. 10. **If a straight line be divided into any two parts,...by the whole and one of the parts is equal to the** square of that part together with the rectangle of the two paits. GEOMETRY. (EXHIBITIONS AND BURSARIES.)... | |
| GEORGE BRUCE HALSTED - 1885
...= a2. Cif Therefore 102 293. If c = a, then a(b + c) = a(b + a) = aa + a*. a*c Therefore If a sect **be divided into any two parts, the rectangle contained by the whole and one of the parts is** equivalent to the rectangle contained by the two parts, together with the square on the aforesaid part.... | |
| George Bruce Halsted - 1886 - 366 páginas
...a*. Therefore IO2 293. If c = a, then a(b + e) = a(6 + a) = ab + aa = ab + of. ac Therefore If a sect **be divided into any two parts, the rectangle contained by the whole and one of the parts is** equivalent to the rectangle contained by the two parts, together with the square on the aforesaid part.... | |
| Dalhousie University - 1888
...parallel. 3. If a straight line be diyided into any two parts, the rectangle contained by the whole line **and one of the parts, is equal to the rectangle contained by the two parts, together with the square** of the aforesaid part. 4. Prove, either by a diagram or in any other way, that if a straight line be... | |
| |