 | Sir John Leslie - 1809 - 522 σελίδες
...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 σελίδες
...between the points of section, is equal to the square of half the line. Prop. VI. Theor. If a straight line be bisected, and produced to any point; the rectangle...the part of it produced, together with the square of half the line bisected, is equal to the square of the «traight line which U made up of the half... | |
 | Euclides - 1816 - 588 σελίδες
...equal to the rectangle contained by their sum and difference. M ^5' PROP. VI. THEOR. IF a straight line be bisected, and produced to any point: the rectangle...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... | |
 | Daniel Cresswell - 1817 - 454 σελίδες
...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 σελίδες
...their sum and difference, or that AC3 — CD3 = (AC + CD) (AC-CD)." PROP. VI. THEOR. If a straight line be bisected, and produced to any point; the rectangle...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... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...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... | |
 | John Mason Good - 1819 - 800 σελίδες
...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. Prop. VII. Theor. If a straight line be divided into any two parts, the squares of the whole... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...Proposition VI. Theoretn. If a straight line be bisected, and produced .to any point : the recangle contained by the whole 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... | |
 | Robert Simson - 1827 - 546 σελίδες
...CD, is equal to the rectangle contained by their sum and difference. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the...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... | |
 | Hirsch - 1827 - 690 σελίδες
...construction is founded on Eue. VI. 13, 17. SECTION LXXIII. Рвов. То produce a given line, so that the rectangle contained by the whole line thus produced, and the part produced, may be equal to the square of a given line. SOLUT. Let the line AB be given (ßg. 86) : lengthen... | |
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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... 
