 | 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,... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...proportional to the parts of them, between the given point and the convex circumference. PROP. L. 59. PROBLEM. To divide a given finite straight line into two parts, such, that another given straight line, not greater than the half of the former, shall be a mean proportional... | |
 | John Playfair - 1819 - 354 pages
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times the rectangle contained by the whole line, and one of the parts, together with the square of the other fart, is equal to the square of the straight line which is made... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...QED | ¿J J'rojjosiiion VIII. Theorem. 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 of the other part, is equal to the square of the straight line, which is made... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...reciprocally proportional to the parts of them between the given point and the convex circumference. L. PR. To divide a given finite straight line into two parts such that another given straight line, not greater than the half of the former, shall be a mean proportional... | |
 | Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...number of 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, it were... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...straight line, 8cc. QED G PROP. VIII. THEOR. If a straight line he 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... | |
 | 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.... | |
 | 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 part.... | |
 | Euclid - 1835 - 540 pages
...QED PROP. VIII. THEOR. JJ F E a 34. 1. 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 of t/ie other part, is equal to the square of the straight line which is made... | |
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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... 
