| 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
...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, 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 - Euclid's Elements - 1833 - 333 pages
...lines 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...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 jir si-mentioned part.... | |
| John Playfair - Euclid's Elements - 1835 - 316 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line which is made up of the whole and the first-mentioned part. Let the straight line AB... | |
| Euclid - 1835 - 540 pages
...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, four times the...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... | |
| Mathematics - 1835 - 684 pages
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, **the rectangle contained by the whole line and one of the parts,** shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid... | |
| Mathematics - 1836 - 472 pages
...contained by the lines together with the square of the difference of the lines. VIII. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line which is made up of the whole and the first mentioned part. Сок. 1. Hence, four times... | |
| John Playfair - Euclid's Elements - 1836 - 488 pages
...lines 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...contained by the whole line, and one of the parts,** togetiier with the square of the other part, is equal to the square of the straight line which is made... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...twice the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line which is made up of the whole and the first mentioned part. Let the straight line AB... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...these = 2 AH + KF ; ;and that these = 2 AB x BC + AC*. CBD PROPOSITION VIII. Theorem. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** line made up of the whole and that part. R In the construction of the figure it is necessary to show... | |
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