 | Allan Menzies - 1854 - 520 pages
...Euclid's general reasoning, and point out the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. A modification of what you have here proved constitutes the rule for the extraction of the square root.... | |
 | Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...required in the demonstrations of the 7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If a straight line be divided into any two parts,...the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ;... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...to each, to which the equal sides are opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF.... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...THEOREM. If a straight line (AB) be divided into any two parts (А С, С В) the square of the wlak line is equal to the squares of the two parts, together with twice the rectangle contained by the parts : that is, А В1 = А С* + С Вг + twice А ОС В. * 46 I. Upon А В describe the square AE... | |
 | Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...other demonstration than an explanation of exactly what is meant by the words of the text. THEOREM 33. If a straight line be divided into any two parts, the square of th« whole line is equal to the sum of the squares of the two parts, and twice the rectangle contained... | |
 | Euclides - 1855 - 270 pages
...one of the parts of the divided straight line, their rectangle becomes a square. PROP. IV. THEOREM. If a straight line be divided into any two parts,...the straig-ht line AB be divided into any two parts at С. square of AB is equal to the squares of A С and С B, together with twice the rectangle AС.СB.... | |
 | 1855 - 264 pages
...line drawn through the middle points of two sides of a triangle will be parallel to the third side' 5. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 6. In every triangle, the square of the side suhtending either of the acute angles is less than the... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Section 2. 1. If a straight line be divided into any two parts,...together with twice the rectangle contained by the two parts. 2. If a straight line be divided into two equal and also into two unequal parts ; the squares... | |
 | 1855 - 424 pages
...than in ordinary language. The proposition, (Euclid 4, 2,) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by squaring a binomial. Let the side of a square be represented... | |
 | John Playfair - Geometry - 1855 - 334 pages
...therefore, multiplying both members of this equality by c, we shall have oc^ic+c 2 . PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line ts equal to the squares of the two parts, together with twicetke rectangle contained by tin- parts.... | |
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IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
