| Miles Bland - 1819 - 377 sider
...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,... | |
| Peter Nicholson - 1825 - 372 sider
...AC. Wherefore, if a straight line, &c. QED | ¿J J'rojjosiiion 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... | |
| Henry Parr Hamilton - 1826 - 326 sider
...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
...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 - 1827 - 513 sider
...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 - 1829 - 186 sider
...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 - 1832 - 333 sider
...together with the " square of the difference of the lines. PROP. VIII. THEOR. If a straight line be **divided into any two parts, four times the 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 - 1833 - 333 sider
...together with the " square of the difference of the lines." 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 equalto the square of the straight line which is made up of the whole and the... | |
| Euclides - 1834
...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 part.** BOOK II. PROP. VIII. Let the straight Iine AB be divided into any two parts in the point C : four times... | |
| Euclid - 1835 - 513 sider
...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, four times the rectangle...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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