| Allan Menzies - 1854
...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
...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 - 192 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
...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 - 335 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
...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
...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
...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
...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 - 318 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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