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" If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Side 39
av Euclides - 1834
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...straight line, &c. QED CB FE BOOK II. PROP. m. IV. • 46. 1. t 31. 1. PROPOSITION III. THEOK. — If a straight line be divided into any two parts,...rectangle contained by the whole and one of the parts, w equal to the rectangle contained by the two parts, together with the square of the aforesaid part....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C. Then the square of AB shall be equal to the squares of AC, and CB, together with twice the rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 sider
...multiplying both members of this equality by a, we shall have as=ab+ad FE K JL H PROP. III. THEOR. If a straight line be divided into any two parts,...aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B rectangle AB.BC is equal to the rectangle AC.BC, together with BC2....
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...A.BC = A.BD+A.DE+A.EC. Wherefore, if there be two str. lines, &c. PROP. XLII. THEOR. 3. 2 En. angle contained by the two parts, together with the square of the aforesaid part. Let the str. line AB be divided into two parts in the pt. C ; then AB . BC = AC. BC + BC 8 . Prop. 38 . On...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...there be two str. lines, &c. PROP. XLII. THEOR. 3 . 2E u. Prop. 10. Prop. 3. Prop. 30. Piop. 33. angle contained by the two parts, together with the square of the aforesaid part. Let the str. line AB be divided into two parts in the pt. C ; then AB. BC = AC. BC + BC". Prop 38 On BC descr....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1847 - 317 sider
...the rectangle contained by the whole and that 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, ar.e equal to twice the rectangle AB.BC, together with the square of AC, or AB2+BC2...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...two sides of it, the angle contained by these two sides is a right angle. Section 3. 1. Prove that if a straight line be divided into any two parts,...parts, together with the square of the aforesaid part. 2. Prove that if a straight line be divided into two equal and also two unequal parts, the squares...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...whole and each of the parts, are together equal to the square of the whole line. PROP. III. THEOREM. If a straight line be divided into any two parts,...parts, together with the square of the aforesaid part. PROP. IV. THEOREM. If a straight line be divided into any two parts, the square of the whole line is...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 sider
...contained by two straight lines AB, AC is sometimes simply called the rectangle AB, AC. PROP. III. THEOR. If a straight line be divided into any two parts,...contained by the whole and one of the parts is equal with the rectangle contained by the two parts, together with the square of the aforesaid part. Let...
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