 CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC,...  Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 47by Euclides - 1842Full view - About this book
 | Mathematics - 1836 - 488 pages
...to the squares of the two parts, 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 are likewise squares. V. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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 the rectangle contained by AC, CB. Upon AB describe (16. 2.) the square ADEB, and join BD,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...therefore, HF, CK, AG, GE are equal to the squares of AC, CB, and twice the rectangle AC.CB. But HF, CK, AG, GE make up the whole figure ADEB, which is the...to the squares of AC, CB, and twice the rectangle AC.CB. * Wherefore, &c. Cor. 1.' From the demonstration, it is manifest that the parallelograms about... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...HF+CK+AG + GE=AC2+CB2+2AC.CB. But HF+CK+AG + GE=the figure AE, or AB2; therefore AB2= AC2+CB2+2AC.CB. COR. From the demonstration, it is manifest that the...about the diameter of a square are likewise squares. SCHOLIUM. This property is derived from the square of a binomial. For, let the two parts into which... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the rectangle contained by the parts. Let the straight line 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. Upon AB describe the square ADEB (I. 46), and join BD, and... | |
 | Euclid - Geometry - 1838 - 470 pages
...figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB, but HF, CK, AG, GE make up the whole figure ADEB, which is the...about the diameter of a square are likewise squares. two unequal parts: the rectangle contained by the unequal parts, together with the square of the line... | |
 | Euclides - 1838 - 264 pages
...figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC'CB : but HF, CK, AG, GE make up the whole figure ADEB. which is the square of AB : therefore the square of AB is n Al equalf to the squares of AC, CB, and twice the rectangle AC'CB. Wherefore if a straight line,... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...the rectangle contained by the parts. Let the straight line 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. Upon AB describe (46. 1.) the square ADEB, and join BD,... | |
 | Euclides - Geometry - 1841 - 378 pages
...the rectangle contained by the parts. Let the straight line 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. * 46. 1. Upon AB describe* the square ADEB, and join BD,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...the rectangle contained by the parts. Let the straight line 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. Upon AB describe (Prop. 46.... | |
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