 If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided...  The Elements of Euclid - Pagina 34door Euclid - 1838 - 416 pagina’sVolledige weergave - Over dit boek
 | Euclid, John Playfair - 1826 - 326 pagina’s
...a straight line, &e. Q. E, D. PROP. ViI. THfiOR. Jf a straight line be divided into any two partsj the squares of the whole line, and of one of the parts, are equal to twiee the reetangle eontained by the whole and that part> together with the square of the other part.... | |
 | George Lees - 1826 - 276 pagina’s
...the square of half the line. Cor. 3. If a straight line AB, be divided into any ^yo parts, AC, CB, the squares of the whole line, and of one of the parts, are equivalent to twice the rectangle contained by the whole, and that part, together with the square of... | |
 | John Playfair - 1829 - 210 pagina’s
....BC. Therefore, the square &c. QED COR. 1. If a straight line AB be divided into any two parts AC, CB, the squares of the whole line and of one of the parts are together equal to twice the rectangle contained by the whole line and that part together with the square... | |
 | John Playfair - 1832 - 358 pagina’s
...«= CD% therefore AD.DB+ CB3 EGF =CD". Therefore, if a straight line, &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts, the...whole and that part, together with the square of the oilier part. Let the straight line AB be divided into any two parts in the point C; the squares of... | |
 | 1836 - 488 pagina’s
...equal to the square of the straight line which is made up of the half and the part produced. VII. If a straight line be divided into any two parts, the...part, together with the square of the other part. Сон. Hence the sum of the squares of any two lines is equal to twice the rectangle contained by... | |
 | John Playfair - 1837 - 332 pagina’s
...to each member of the equality, we shall have, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one....part, together with the square of the other part. L et the straight line AB be divided into any J^ CB two parts in the point C ; the squares of AB, BC,... | |
 | Euclides - 1837 - 112 pagina’s
...= AL + CM + LG, which = AM + LG, and that these last = AD X DB + CB*. PROPOSITION VII. Theorem. If a straight line be divided into any two parts, the...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. i> K Proved by showing that AB* + uc*... | |
 | Euclides - 1840 - 82 pagina’s
...equal to the square of the line made up of the half and the produced part. DA PROP. VII. THEOR. If a straight line be divided into any two parts, the...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line... | |
 | Euclides - 1840 - 192 pagina’s
...the produced part. PROP. VII. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the squares of the whole line and of one of the parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. Upon AB construct the square ACDB ;... | |
 | Euclides - 1841 - 378 pagina’s
...to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts, the...whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB,... | |
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