 | Peter Nicholson - Mathematics - 1825 - 1046 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 poin С ; four times... | |
 | Robert Simson - Trigonometry - 1827 - 546 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... | |
 | Meyer Hirsch - Geometry - 1827 - 288 pages
...construction is founded on Eue. VI. 13, 17. SECTION LXXIII. PROB. To 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... | |
 | Hirsch - Algebra - 1827 - 690 pages
...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... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...contained by the whole line, and one of the 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. Let the straight line AB be divided into any two parts in the... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...equivalent ta the difference of their squares, B ID PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by...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... | |
 | Euclid - 1835 - 540 pages
...rectangle contained by their sum AD and difference DB. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by...thus produced, and the part of it produced, together ivith the square of half the line bisected, is equal to the square of the straight line which is made... | |
 | Robert Mudie - Mathematics - 1836 - 542 pages
...RECTANGLE. 473 Geometrically, this last truth is usually enunciated : " If a straight line be bisected, and produced to any point ; the rectangle contained by...of the straight line, which is made up of the half of the part produced." 10. Some very useful problems may be performed by means of the principles which... | |
 | Robert Mudie - Mathematics - 1836 - 524 pages
...stated. Geometrically, this last truth is usually enunciated : " If a straight line be bisected, and produced to any point ; the rectangle contained by...of the straight line, which is made up of the half of the part produced." 10. Some very useful problems may be performed by means of the principles which... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...CD)(AC— CD)." a 46. 1. b 31. 1. c 36. 1. d 43. 1. PROP. VI. THEOR. If a straight line be bisected, and produced to any point ; the rectangle contained by...square of the straight line which is made up of the hay' and the part produced. Let the straight line AB be bisected in C, and produced to the point D;... | |
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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 on half the line bisected, is equal to the square on the straight line which is made... 
