 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 Geometry, Symbolically Arranged - Page 63by Great Britain. Admiralty - 1846Full view - About this book
 | George Lees - 1826 - 276 pages
...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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...of CB, is equal to the square of CD. Wherefore, if a straight line, &c. Q. £. JO. PROP. VII. THEOR. If a straight line be divided into any two parts,...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 be equal... | |
 | John Playfair - Geometry - 1829 - 210 pages
....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 - Euclid's Elements - 1832 - 358 pages
...CF «= 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,...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... | |
 | Euclid - 1835 - 540 pages
...square of CB, is equal to the square of CD. Wherefore, " if a straigtd line" &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts,...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, BC are... | |
 | John Playfair - Geometry - 1836 - 148 pages
...so that the rectangle AB, BH is equal to the square of AH. Which was to be done. E PROP. XXV. THEOR. If a straight line be divided into any two parts,...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 to... | |
 | Mathematics - 1836 - 488 pages
...is 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,...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 - Geometry - 1837 - 410 pages
...figure, as there will remain the rectangle AM and the square LG, together equal to tb« square CF. IF a straight line be divided into any two parts,...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 to... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 - Euclid's Elements - 1837 - 112 pages
...these = 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,...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*... | |
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