 | Allan Menzies - 1854 - 520 pages
...the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts, the square of the whole line is equal to the...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.... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...GEOMETRY. PEOPOSITION IV.— THEOREM. If a straight line (AB) be divided into any two part» (А С, С В) the square of the whole line is equal to the squares...together with twice the rectangle contained by the parts : that is, AB1 = AC" + CB2 + twice AC'C B. * 46 I. t 31 I. • 29 I. ts l. «61. Upon AB describe the... | |
 | Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. 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 their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ;... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...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. A rectangle is said to be contained by any two of its adjacent sides^."] * A rectangle has been... | |
 | Euclides - 1855 - 270 pages
...line, their rectangle becomes a square. PROP. IV. THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the...the straight line AB be divided into any two parts at C. The square of AB is equal to the squares of AC and CB, together with twice the rectangle A C.CB.... | |
 | 1855 - 264 pages
...sides of a triangle will be parallel to the third side' 5. If a straight line be divided into any two parts, the square of the whole line is equal to the...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 - 1855 - 978 pages
...angles equal to a given rectilineal angle. Section 2. 1. If a straight line be divided into any two parts, the square of the whole line is equal to the...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
...ordinary language. The proposition, (Euclid 4, 2,J that when a straight line is divided into two paru, the square of the whole line is equal to the 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... | |
 | Euclides - 1856 - 168 pages
...square of the first mentioned part. XLIX.—EUCLID II. 4. If a straight line be divided into any two parts the square of the whole line is equal to the...rectangle contained by the parts. Let the straight line AB (Fig. 39) be divided into any two parts in C. The square of AB is equal to the squares of AC, CB and... | |
 | W F. Richards - Elementary school teaching - 1856 - 198 pages
...every triangle are together equal to two right angles. 5. If a straight line be divided into any two parts, the square of the whole line is equal to the...together with twice the rectangle contained by the parts. 6. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite... | |
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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. 
