 | 1867 - 336 σελίδες
...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 - 152 σελίδες
...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 - 176 σελίδες
...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 - 146 σελίδες
...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 - 400 σελίδες
...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 - 176 σελίδες
...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 - 334 σελίδες
...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 - 476 σελίδες
...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 - 266 σελίδες
...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 - 284 σελίδες
...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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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... 
