 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...line be divided into any two parts, four times the reetangle eontained by the whole line, arid ohtt of the parts, together with the square of the other part> iS H equal to the square of the straight line whieh is made up of the whole and the first-mentioned part.... | |
 | 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,... | |
 | 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 - 358 pages
...twice the rectangle contained by the lines together with the " square of the difference of the lines. PROP. VIII. THEOR. If a straight line be divided into...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 - 346 pages
...twice the rectangle contained by the lines together with the " square of the difference of the lines." PROP. VIII. THEOR. If a straight line be divided into...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.... | |
 | 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,...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... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...the rectangle contained by the " lines together with the square of the difference of the " lines." PROP. VIII. THEOR. If a straight line be divided into...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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...KF, and that 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,...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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...of two lines, is equal to the square of their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into...parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight... | |
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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 on the other part, is equal to the square on the straight line which is made up of the whole and that... 
