 | Euclides - 1840 - 82 pages
...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 - 1840 - 192 pages
...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 - Geometry - 1841 - 378 pages
...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 pages
...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 : four times the rectangle...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 - Euclid's Elements - 1842 - 332 pages
...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 pages
...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 - Euclid's Elements - 1844 - 338 pages
...derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...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 - Geometry - 1845 - 218 pages
...square of AC. Wherefore, if a 'straight line, &c. QED PROPOSITION VIII. THEOR. — If a straight line be divided into any two parts, four times the rectangle...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 ;... | |
 | Euclides - 1845 - 546 pages
...nf, That is, If a number be divided into any two parts, four times the product of the whole number and one of the parts, together with the square of the other part, ig equal to the square of the number made up of the whole and that part. Prop. ix. Algebraically. Let... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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... | |
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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... 
