 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...another problem of the same nature; in which it is required to produce a straight line AB, such that the rectangle contained by the whole line thus produced and the part produced, shall be equivalent to the square of the line AB itself. Divide AB in C, so that the rectangle... | |
 | John Mason Good - 1813 - 714 pages
...equal to the square of half the line. Prop. VI. Theor. If a straight line be bisected, and produced to any point; the rectangle contained by the whole line...half the line bisected, is equal to the square of the «traight line which U made up of the half and the part produced. Prop. VII. Theor. If a straight line... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...<•! a + xx + aa=(aa + %ax+xx=) a+xf; that is, the rectangle contained by the line produced and part produced, together with the square of half the line bisected, is equal to the square of the line made up of the half, and part produced. QKD Cor. Hence, if three lines ,r, a 4 ,r, and 2rt + ,r... | |
 | Euclides - 1816 - 588 pages
...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 part. Let the straight line AB be divided into any two parts in the point C; four times... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...subtend equal angles, at the center of the circle. (LXVII.) To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. (LXVII i.) If, from the bisection of any given arch of a circle,... | |
 | John Playfair - 1819 - 354 pages
...AC3 — CD3 = (AC + CD) (AC-CD)." PROP. VI. THEOR. If a straight line be bisected, and produced to any point; the rectangle contained by the whole line...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 A B k)... | |
 | John Mason Good - 1819 - 800 pages
...bisected, and produned to any point; the rectangle contained hy the whole line thus produced, and Ihe part of it produced, together with the square of half...of the straight line which is made up of the half and. the part produced. Prop. VII. Theor. If a straight line be divided into any two parts, the squares... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...that AC2 - CD2 = (AC+ CD)(AC_CD)." PROP. VI. THEOR. if a straight line be bisected, and produced to any point ; the rectangle contained by the whole line...the part of it produced, together with the square nf half the. line bisected, is equal to the square of the straight line which is made up of the half... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...itself also touches the circle. PROP. LXXIII. 93. PROBLEM. To produce a given straight line, so that the rectangle contained by the whole line thus produced, and the part of it produced, shall be equal to a given square. Let AB be a given straight line, and L the side D EX of a given square... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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 tip of the whole and that part. j Let the straight line AB be divided into any two parts in the point... | |
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If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of... 
