| 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 - 372 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 - 326 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 - 513 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 - 186 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 - 333 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 - 333 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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