 | Mathematics - 1836 - 488 pages
...the half and the part produced. VII. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal...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 - Euclid's Elements - 1837 - 332 pages
...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. of the parts, are equal...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 - Euclid's Elements - 1837 - 112 pages
...X DB + CB*. PROPOSITION VII. Theorem. 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 line and that part, together with the square of the other part. i> K Proved by showing that AB* + uc*... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...other part, is equal to the square of the straight line which is made up of the whole and the former part. Let the straight line AB be divided into any two parts in C ; * Otherwise — Because (II. 4.) AB» == AC» + BC» + 2AC.BC, add BC8 to both; then AB8 + BC»=... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...is equal to the squares of the two parts, together with twice 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.... | |
 | Euclides - 1838 - 264 pages
...is equal in the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be 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 AC'CB. Upon... | |
 | Euclides - 1840 - 82 pages
...the produced part. DA PROP. VII. THEOR. 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 line and that part, together with the square of the other part. PROP. VIII. THEOR. If a straight line... | |
 | Euclides - 1840 - 192 pages
...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, are 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 - Geometry - 1841 - 378 pages
...PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal...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,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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 of the parts, are equal...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,... | |
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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... 
