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Bøker Bok 3140 av 143If 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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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837
...CE ; and that these are = AB x AC + AB x BC. PROPOSITION 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. Proved by showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*....
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...by a, we shall have azs=ab+ad FE, 6 • F K J. H A 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 E rectangle...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 sider
...manner similar to this, several of the following propositions nay be 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 square of that part, together with the rectangle contained by the two parts. Let the straight line...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...restriction of the number of parts to two is unnecessary. PROP. III. THEOR. If a straight line be dieided 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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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...square of AB. If therefore a straight line, &c. 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: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...square of A B. If therefore a straight line, &c. 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 two parts in the point c : the rectangle AB,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by tke whole and one of the parts, is equal to the rectangle...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...
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The British Annals of Education for ...: Being The Scholastic ..., Volum 1

1844
...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, the rectangle contained by the...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 ...

Robert Potts - 1845
...of AB. If therefore a straight line, &c. QED PROPOSITION 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. 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 ...

James Thomson - 1845 - 358 sider
...established by continual appeals to original principles. 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 to the square of that part, together with the rectangle contained by the two parts. Let the straight line...
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