 | Euclides - 1840 - 192 pàgines
...half and the produced part. PROP. XI. PROB. To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ;... | |
 | Euclides - 1840 - 82 pàgines
...and the produced part. .n. . PROP. XI. PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the... | |
 | Euclides - 1841 - 378 pàgines
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB he bisected in C, and produced to the point D:... | |
 | Euclides - 1842 - 316 pàgines
...rectangle AB, BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. IF a straight line be divided into any two parts :...parts, together with the square of the other part, is equivalent to the square of the straight line, which is made up of the whole and that part. ELEMENTS... | |
 | John Playfair - 1842 - 332 pàgines
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D... | |
 | Scotland free church, gen. assembly - 1847 - 554 pàgines
...other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of... | |
 | John Playfair - 1844 - 338 pàgines
...This may be also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts,...one of the parts, together with the square of the olher part, is equal to the square of the straight line which is made up of the whole and thefirst-mentioned... | |
 | Euclid - 1845 - 218 pàgines
...together with the square of AC. Wherefore, if a 'straight line, &c. QED PROPOSITION VIII. THEOR. — If a straight line be divided into any two parts,...to the square of the straight line, which is made of the whole and that part. Let the straight line AB be divided into any two parts in the point C ;... | |
 | Euclid, James Thomson - 1845 - 382 pàgines
...to the square of their difference, together with four tunes their rectangle. PROP. VIII. THEOR. — If a straight line be divided into any two parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight... | |
 | Euclides - 1845 - 546 pàgines
...BC, together with the square of AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the reel" angle contained by the whole line, and one of the parts, together with the square of the other... | |
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IF a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... 
