| 1867
...sum of the squares of two lines cannot be less than twice their rectangle. 3. If a straight line be **divided into any two parts, four times the rectangle...line and one of the parts, together with the square** of the other part, is equal to the square of the straight liue which is made up of the whole and that... | |
| Euclides - 1852
...Proposition are equal to the two squares AE and kc added together.] PROP. VIII. THEOR. If a straight line be **divided into any two parts, four times the rectangle...line and one of the parts, together with the square** of the other part, is equal to the square of the straight line, which is made up of the whole and that... | |
| Euclides - 1853 - 147 sider
...of a С. Wherefore, if a straight line, &c. QED PROPOSITION VIII. — THEOREM. If a straight line be **divided into any two parts, four times the rectangle...line, and one of the parts, together with the square** of the other part, is equal to the square of the straight line which is made up of the whole and that... | |
| Euclides - 1853
...the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOREM. If a straight line be **divided into any two parts, four times the rectangle...line, and one of the parts, together with the square** of the other part, is equal to the square of the straight line which is made up of the whole and that... | |
| Royal Military Academy, Woolwich - 1853
...square of AC. Wherefore, if a straight line, etc. QED PROPOSITION VIII. THEOR. If a straight line be **divided into any two parts, four times the rectangle...line, and one of the parts, together with the square** of the other part, is equal to the square of the straight line, which is made of the whole and that... | |
| Euclid - 1853 - 136 sider
...and the produced part, to• gether with the square on <• half the line bisected, is equal in area **to the square on the straight line which is made up of the** half and the produced part. 11.10.. . II. 11, cor. II. 4, cor. 2.. . II. 1. . II. l.cor. II. 5, schol.... | |
| Euclides - 1853
...other part. Let AB be the given straight line. It is required to divide it into two such parts, that **the rectangle contained by the whole line and one of the parts** shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing... | |
| Royal Military Academy, Woolwich - 1853
...question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that **the rectangle contained by the whole line and one of the parts** shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less... | |
| William Walton, Charles Frederick Mackenzie - 1854 - 225 sider
...parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that **the rectangle contained by the whole line and one of the parts** shall be equal to the square of the other part. Produce a given straight line to a point such that... | |
| Cambridge univ, exam. papers - 1854
...parallelograms GF, EH is equal to twice the triangle KBD. 2. Divide a given straight line into two parts so that **the rectangle contained by the whole line and one of the parts** shall be equal to the square of the other part. Produce a given straight line to a point such that... | |
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