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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 ... - Page 49
by Euclid, Robert Simson - 1829 - 516 pages
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...squares described upon the other two sides of it, the angle contained by these two is a right angle. 6. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. 7. Describe a square equal to a given rectilineal figure. 8. Find the centre of a circle....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...AB, BC is equal to the square of AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C. Then the rectangle...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...them, instead of being established by continual appeals to original principles. PROP. III. THEOR. — If a straight line be divided into any two parts,...by the whole and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let the straight line...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...rectangle AB, BC, is equal to the square of AB. Wherefore, If a straight line Sjc. QED PROP. III. THEOR. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part, Let the straight line AB be divided into any two parts in the point C : the rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1847 - 340 pages
...parts, is equal to the rectangle contained by. the two parts, together with the square of the 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. Upon BC describe (Prop. 46. 1.)...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...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,...by the two 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,...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...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,...by the two 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...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...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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