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Bøker Bok 4150 av 144If a straight line be divided into any two parts, the rectangle contained by the...
" 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 - Side 41
av Euclid - 1838 - 416 sider
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...BOOK II. PROP. m. IV. • 46. 1. t 31. 1. PROPOSITION III. THEOK. — If a straight line be divided into any two parts, the 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
...square of AB. Wherefore, If a straight line Sjc. QED PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the...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 ...

John Playfair - 1846 - 317 sider
...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, the rectangle contained by the...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 - 1847 - 317 sider
...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 - 1848
...contained by these two sides is a right angle. Section 3. 1. Prove that if a straight line be divided into any two parts, the rectangle contained by the...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
...are together equal to the square of the whole line. PROP. III. THEOREM. If a straight line be divided into any two parts, the rectangle contained by the...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 ...

Euclides - 1849
...AC is sometimes simply called the rectangle AB, AC. PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle 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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Papers for the Schoolmaster, Volum 2

1852
...squares described upon the sides which contain the right angle. III. If a straight line be divided into any two parts, the rectangle contained by the...by the two parts, together with the square of the aforesaid part. following sentence, shewing the variou» clauses, &c. :— " Not to do your best when...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852
...multiplied together.] 90 BOOK II. • xlvi. 1. THE ELEMENTS PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the...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 rectangle AB,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...If QED df therefore a straight line, &c. PROPOSITION III. — THEOREM. If a slraigM line be divided into any two parts, the rectangle contained by the...rectangle contained by the two parts, together with tlie square of the aforesaid part. LET the straight line ab be divided into any two parts in the point...
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