| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...with the 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...square of the other part, is equal to the square of the** straight line, which is made of the whole and that part. Let the straight line AB be divided into any... | |
| Euclides - Geometry - 1853 - 176 pages
...square 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...square of the other part, is equal to the square of the** straight line which is made up of the whole and that part, LET the straight line ab be divided into... | |
| Euclides - 1853 - 146 pages
...together with 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...square of the other part, is equal to the square of the** straight line which is made up of the whole and that part. Let the straight line AB be divided into... | |
| Euclides - Geometry - 1853 - 334 pages
...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 - Mathematics - 1853 - 472 pages
...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... | |
| Cambridge univ, exam. papers - 1854 - 282 pages
...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... | |
| William Walton, Charles Frederick Mackenzie - Mathematics - 1854 - 266 pages
...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... | |
| John Playfair - Geometry - 1855 - 336 pages
...derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line lie **divided into any two parts, four times the rectangle...square of the other part, is equal to the square of the** straight line which is made vp of the whole and thefirst-mentioned part. Let the straight line AB be... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...into any two parts, the squares of the whole line and of one of the parts are together equal to twice **the rectangle contained by the whole line and one...parts, together with the square of the other part.** 5. To construct a square equal to a given rectangle. 6. If a straight line passing through the centre... | |
| Euclides - 1855 - 262 pages
...divided into any two parts, four times the rectangle con'ained by the whole line, and one of the parís, **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 thai part. Let the straight line AB be divided into... | |
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