 | 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,... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D... | |
 | 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
...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, four...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
...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, four...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.... | |
 | Euclides - 1834 - 518 pages
...with the square of AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. • THEOR.. — If a straight line be divided into any two parts, four...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 - 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, four...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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...produced, and the part of it produced, together with the square of half the line bisected, is equ2l to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D... | |
 | 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... | |
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Iff 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... 
