 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
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...with the square of CB, is equal to the square of CD : which was to be proved. PROP. VII. THEOB. — 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... | |
 | Great Britain. Council on Education - 1845 - 696 pages
...described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into any two parts,...part, together with the square of the other part. 62. To divide a given straight line into two parts, so that the rectangle contained by the whole, and... | |
 | Euclid - Geometry - 1845 - 218 pages
...line, &c. QED PROPOSITION VII. THEOR. — If a straight line be divided into any two parts, the iquares of the whole line, and of one of the parts, are equal...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... | |
 | Euclides - 1845 - 546 pages
...CB, is equal to the square of CD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOREM. If a straight line be divided into any two parts,...line, and of one of the parts, are equal to twice ihe rectangle contained by the whole and that part, together with the square of the other part. Let... | |
 | James Wood - Algebra - 1845 - 442 pages
...the two parts into which the given line is divided; then a + b is the whole line, and (a + b)* + a1 = the squares of the whole line, and of one of the parts; = 2 (a + 6) a + b' = twice the rectangle &c. together with the square of the other part. QBD Ex. 2.... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...line be a, and the part produced b, the proposition algebraically expressed is (2a+b)b+a i =(a+b) s . PROP. XLVI. THEOR. 7 . 2 Eu . If a straight line be...be divided into any two parts at the pt. C; then AB ! +BC«=2.AB.BC + AC*. A CB Upon AB descr. sq. ADEB, join BD. D I CGF || AD or BE, r \ HGK || AB or... | |
 | Euclides - 1846 - 292 pages
...square of CB, is equal to the square of CD. Wherefore, If a straight 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 at the point C : the squares of AB, BC shall be equal... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...equality, we shall have, .-. i(2a+6)+o2=(a+i)2. 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 two parts in the point C ; the squares of AB, BC, are... | |
 | Euclides - 1848 - 52 pages
...square of the straight line which is made up of the half and the part produced. PROP. VII. THEOREM. If a straight line be divided into any two parts,...part, together with the square of the other part. PROP. VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...parallels. Section 5. 1. If a right line be divided into any two parls, the squr.res of the whole line and 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. If two circles cut each other, they... | |
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