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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... "
The Elements of Geometry, Symbolically Arranged - Page 63
by Great Britain. Admiralty - 1846
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the diiferencc between the squares of half the line and the mean distance. PROPOSITION TIL THEOREM. to twice the rectangle contained by the whole and...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, BO, are equal to...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...of CB, is equal to the square of CD. Wherefore, if a straight line, Ac. «,in D. 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...
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...of CB, is equal to the square of CD. Wherefore, if a straight line, &c. a. ED PROP. VII. THEOR. Ir a straight line be divided into any two parts, the...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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...is equal to the square of the line made up of the half and the produced part. DA PROP. VII. THEOR. 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. PROP. VIII. THEOR. If a straight line...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...the produced part. PROP. VII. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the squares of the whole line and of one of the parts,...equal to twice the rectangle contained by the whole line and that part, together with the square of the other part. Upon AB construct the square ACDB ;...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...equal to the square of CD. Wherefore, if a straight line, &c. QED PROP. VII. THEOR. *36. 1. a * 43. 1. If a straight line be divided into any two parts,...whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 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,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...is equivalent to the square of C D. Wherefore, if a straight line, &c. QED РRОР. VII. ТНЕОВ, IF a straight line be divided into any two parts : the squares of the whole line, and one of the parts, are equivalent to twice the rectangle contained by the whole and that part, together...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...equal to the rectangles contained by the undivided line and the several parts of the divided line. 7. If a straight line be divided into any two parts,...part, together with the square of the other part. 8. If two circles touch one another internally, they shall not have the same centre. 9. Draw a straight...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...then, AD=2a+6, and CD=a+6. Now by multiplication, 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. two parts in the point C ; the squares of AB, BC, are equal to twice the rectangle AB.BC, together...
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