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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... "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 52
των John Playfair - 1837 - 318 σελίδες
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...expressed is (2a+b)b+a i =(a+b) s . PROP. XLVI. THEOR. 7 . 2 Eu . 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 str. line AB be divided into any two parts at the pt. C; then AB ! +BC«=2.AB.BC + AC*. A CB...

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...expressed is (2a+b)b+a8=(a+b)8. PROP. XLVI. THEOR. 7 . 2 Eu . 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 str. line AB be divided into any two parts at the pt. C; then AB 8 +BC8=2.AB.BC + AC8. ACB...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...CD. Wherefore, If a straight 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 at the point C : the squares of AB, BC shall...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1847 - 317 σελίδες
...multiplication, 6(2a+6)=2a6+62 ; therefore, by adding o2 to each member of the equality, we shall have, H PROP. VII. THEOR. If a straight line be divided into...part. L et the straight line AB be divided into any two parts in the point C ; the squares of AB, BC, ar.e equal to twice the rectangle AB.BC, together...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...made up of the half and the part produced. PROP. VII. THEOREM. 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. PROP. VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained...

Report of the Committee of Council on Education (England and Wales ..., Τεύχος 2

Great Britain. Council on Education - 1848
...parallels. Section 5. 1. If a right line be divided into any two parts, the squares 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. •>. If two circles cut each other,...

Minutes of the Committee of Council on Education, with Appendices, Τόμος 2

Great Britain. Committee on Education - 1848
...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...

Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...parallels. Section 5. 1. If a right line be divided into any two parts, the squares 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. 2. If two circles cut each other, they...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 317 σελίδες
...by b ; then, AD=2a+ b, and CD=a+ b. Now by multiplication, b(2a+b)=2ab+b2 ; therefore, by adding o2 to each member of the equality, we shall have, PROP....part. L et the straight line AB be divided into any two parts in the point C ; the squares of AB, BC, are equal to twice the rectangle AB.BC, together...

The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849
...PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and one of the parts, are equal to twice the rectangle...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...




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