 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts that the rectangle contained by the whole line and one of the parts may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...AB, BC, together with the square AC. Wherefore, if a straight line, &c. Q,. ED PROP. VIII. THEOR. f F 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 tip of the whole and that... | |
 | Peter Nicholson - Mathematics - 1825 - 1058 pages
...together with the square ot AC. Wherefore, if a straight line, &c. QED | żJ J'rojjosiiion VIII. Theorem. If a straight line be divided into any two parts,...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... | |
 | Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...solutions. For example, if it be required to divide a given straight line 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; this problem is determinate. If on the other hand,... | |
 | Euclides - 1826 - 226 pages
...THEOREM. I/* a rig A/ /ѓие iе аиу how ait into two parts, four times the rectangle, contained under the whole line, and one of the parts, together with the square of the other part, is equal to the square of the line, compounded of the whole line, and the first... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...the square of AC. Wherefore if a straight line, 8cc. QED G PROP. VIII. THEOR. If a straight line he 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... | |
 | John Playfair - Geometry - 1829 - 210 pages
...together equal to the square of the whole line. ..If a straight line be divided 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 foresaid part.... | |
 | John Playfair - Euclid's Elements - 1832 - 356 pages
...contained by the lines together with the " square of the difference of the lines. PROP. VIII. THEOR. If a straight line be divided into any two parts,...rectangle contained by the whole line, and one of I he parts? together with thesquare of the other part, is equal to the square of the straight line... | |
 | John Playfair - Euclid's Elements - 1833 - 348 pages
...contained by the lines together with the " square of the difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts,...line, and one of the parts, together with the square of the other part, is equalto the square of the straight line which is made up of the whole and the... | |
 | Euclid - 1835 - 540 pages
...with the square of AC. Wherefore, " if a straight line," &c. QED PROP. VIII. THEOR. JJ F E a 34. 1. If a straight line be divided into any two parts,...line, and one of the parts; together with the square of t/ie other part, is equal to the square of the straight line which is made up of the whole and 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... 
