 | Euclides - 1848 - 52 pages
...IV. THEOREM. 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. COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...the trapezoid is equal to DE X KF. Hence the area of a trapezoid is equal to its altitude,multiplied by the line which joins the middle points of the sides...squares on AC, CB, together with twice the rectangle contained by AC, CB; that is, Upon AB describe the square ABDE; take AF equal to AC, through F draw... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...parts, the square of the whole line is equal to the squares of the two parts, together with tvtice the rectangle contained by the parts. Let the straight...AB be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB.... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...IV. THEOR. 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. Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. . Let the line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two -^ HC parts at the point E : then will the square described on AB be equivalent... | |
 | Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...Section 3. 1. If a straight line be divided into any two part» the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole... | |
 | 582 pages
...other part. 2. 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. In what sense is the area of a triangle said to be equal to half the product of tils base and altitude?... | |
 | 1852 - 316 pages
...SECTION II. 1. 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 paits. 2. If a straight line be divided into two equal and also into two unequal parts, the squares... | |
 | Euclides - 1852 - 152 pages
...rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C; the rectangle contained by AB, BC ; together with the rectangle* AB, AC, shall be equal... | |
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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. 
