 | Euclid - 1835 - 540 σελίδες
...CD. Wherefore, " if a straigtd line" &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in Book i i- the point C ; the squares of AB,... | |
 | John Playfair - 1836 - 148 σελίδες
...the square of AH. Which was to be done. E PROP. XXV. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal... | |
 | 1836 - 488 σελίδες
...line which is made up of 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...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... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal... | |
 | Euclides - 1837 - 112 σελίδες
...and that these last = AD 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...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*... | |
 | Andrew Bell - 1837 - 290 σελίδες
...the diiferencc between the squares of half the line and the mean distance. PROPOSITION TIL THEOREM. to twice the rectangle contained by the whole and...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BO, are... | |
 | Euclides - 1838 - 264 σελίδες
...Wherefore, if a straight line, Ac. «,in D. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one...part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C : the squares of AB, BC shall... | |
 | Euclides - 1840 - 82 σελίδες
...made up of the half and 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...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 σελίδες
...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 σελίδες
...straight line, &c. QED 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...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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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... 
