 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
 | Charles Hutton - Mathematics - 1812 - 620 pages
...made up of the four figures, viz, the two squares AF,FD, and the two equal rectangles EF, FB. That is, the square of AB is equal to the squares of AC, CB, together with twice the rectangle of AC, CB. QED Corol. Htnct, if a line be divided into two equal... | |
 | Euclides - 1816 - 588 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, and join BD, and through... | |
 | John Playfair - Circle-squaring - 1819 - 350 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= ACa + CB3 + 2AC.CB. Upon AB describe (46.... | |
 | John Playfair - 1819 - 354 pages
...rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; Uie square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB== AC3 + CB3 + 2AC.CB. Upon AB describe (46.... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 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...of a square are likewise squares. PROP. V. THEOR. IP a straight line be divided into two equal parts, and also into two unequal parts; the rectangle... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...up of the four figures, viz. the two squares AF, FD, and the two equal rectangles EF, FB. That is, the square of AB is equal to the squares of AC, CB, together with twice the rectangle of AC, CB. ft. ED Corol. Hence, if a line be divided into two equal... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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...rectangle AC, CB. Wherefore, if a straight line, &c. Gt. ED Cor. From the demonstration, it is manifest, that the parallelograms about the diameter of a... | |
 | Euclid - 1826 - 234 pages
...CK, AG, GE, are equal to the squares of AC, св, and to twice the rectangle AC, св. But HF, CK, AG, GE, make up the whole figure ADEB, which is the...Therefore the square of AB is equal to the squares of AC, св, together with twice the rectangle contained under AC, св. Wherefore if a right line, &c. QE... | |
 | Euclides - 1826 - 226 pages
...ск, AG, GE, are equal to the squares of AC, св, and to twice the rectangle AC, св. But HF, ск, AG, GE, make up the whole figure ADEB, which is the...Therefore the square of AB is equal to the squares of AC, св, together with twice the rectangle contained under AC, св. Wherefore if a right line, Scc. QE... | |
 | George Lees - 1826 - 276 pages
...AE = AB2 ; therefore, AB2 = AC2+CB2+2AC.CB. Wherefore, if a straight line, &c. QED Cor. 1. From this demonstration, it is manifest that the parallelograms...about the diameter of a square are likewise squares. Cor. 9,. The square of any line is equivalent to four times the square of half the line. Cor. 3. If... | |
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