 | Euclid, Robert Simson - Geometry - 1829 - 548 pages
...rentangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IF a straight line be divided into any two parts, the...the rectangle contained by AC, CB. Upon AB describe (46. 1.) the square ADEB, and join BD, and through C draw (31. 1.) CGF paralleMo AD or BE, and through... | |
 | John Playfair - Geometry - 1829 - 210 pages
...equal to the rectangle contained by the two parts together with the square of the foresaid part. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the two parts. Or, in other words, the square of the sum of two lines is greater than the sum of their... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...= BC'; therefore AB.BC= AC.CB + BCJ. Therefore, if a straight line, &c. QED D E PROP. IV. THEOR. If a straight line be divided into any two parts, the...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, ABa= AC8+CBa+ 2 AC.CB. Upon AB describe... | |
 | Education - 1833 - 412 pages
...equal to the rectangle contained by the two parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts, the...together, with twice the rectangle contained by the parts. a. Find the value of x in x1 — a x-\-b*^0. b. Divide a*— 3x*+x* + J x'-l'2x + 6 by ^-3. Find the... | |
 | Euclides - 1834 - 518 pages
...together with the square of BC. If, therefore, a straight line, &c. o. ED PROPOSITION IV. THEOR. — If a straight line be divided into any two parts, the...divided into any two parts in C : the square of AB shall be equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB. Upon AB, describe... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...AC, CB together with the square of BC. " If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the...CB, and to twice the rectangle contained by AC, CB. a 46. 1. b31. 1. c 29. I. a .j. I. e6. I. Upon AB describe a the square ADEB, and join BD, and Book... | |
 | Euclid - 1835 - 540 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... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...and CE=BC2; therefore AB.BC=AC.CB, +BC2. Therefore, if a straight line, SEc. QE DPROP. IV. THEOR. If a straight line be divided into any two parts, the...AC, CB, and to twice the rectangle contained by AC, CD, that is AB2=AC2+CB2+2AC.CB. a *6. 1. Upon AB describe a the square ADEB, and join BD, b31. 1. and... | |
 | John Playfair - Geometry - 1836 - 148 pages
...diagonal of any parallelogram, are equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any two parts, the...rectangle contained by the parts. Let the straight line AB he divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice... | |
 | Mathematics - 1836 - 488 pages
...to the rectangle contained by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms about the diameter of a square... | |
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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. 
