 If a straight line be divided into any two parts, four times the rectangle contained by the whole 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...  Euclid - Page 130by Euclid, Rupert Deakin - 1903 - 164 pagesFull view - About this book
 | 1867 - 336 pages
...geometrically that the 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...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 - 152 pages
...other in this 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...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 - Mathematics - 1853 - 400 pages
...together 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...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... | |
 | Euclides - 1853 - 146 pages
...BC, 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...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 - Geometry - 1853 - 176 pages
...together with the 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...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 - 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 - 476 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 - 284 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 - Education - 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 - 334 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...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 vp of the whole and thefirst-mentioned... | |
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