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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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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...AB, AC, together with the rectangle AB-BC, is equal to the square of AB. PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...by the two parts, together with the square of the foresaid 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 and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...equal to the square of A B. In a manner similar to this, several of the following propositions nay be 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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...square of AB. If therefore a straight line, &c. Q^ ED PROP. III. THEOR. IF a straight line be diyided into any two parts, the rectangle contained by the...by the two parts, together with the square of the foresaid part. Let the straight line AB be divided into two parts in the point C ; the rectangle AB,...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...is equal in 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 ; the square of AB shall be equal to the squares of AC, CB, and to twice the rectangle AC'CB. Upon...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...the sum of the rectangles contained by the whole line and each of its parts. ED f B PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole line and either of its parts, is equal to the square of that part, together with the rectangle under...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...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; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...rectangle AB, BC, is equal to the square of A B. If therefore a straight line, &c. QED 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 rectangle AB, вc is equal to the rectangle AC, c B, together with the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...multiplying both members of this equality by a, we shall have a~=ab+ad FE J o $ DEC K JL B 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 contained by the two parts, together with...
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The British Annals of Education for ...: Being The Scholastic ..., Volumer 1-2

1844
...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,...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. 9. If a point...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...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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