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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 student's guide to the University of Durham, with information respecting ... - Página 136
1880 - 144 páginas
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The Quarterly Journal of Education, Volumen5

1833
...subtending the right angle is equal to the squares described upon the sides containing the right angle. 4. If a straight line be divided into any two parts, the rectangle contained OCT. 1832— JAN. 1833. B by the whole and one of the parts is equal to the rectangle contained by...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...AB, BC, is equal to the square of AB. " If, therefore, a straight line," &c. QED PROP. III. THEOH. If a straight line be divided into any two parts,...contained by the two parts, together with the square of the foresaid part. AC Let the straight line AB be divided into any two parts in the point C; the...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 páginas
...AB, BC, is equal to the 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 whole and one of tJie parts, is equal to the rectangle contained by the two parts, together with the square of the foresaid...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...each of the parts, shall be together equal to the square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 páginas
...therefore, multiplying both members of this equality by a, we shall have a'=ab+ad. PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by Ike whole and one of the parts, is equal to the rectangle contained by the two parts, together with...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...contained by the whole and each of the parts, are together equal to the square of the whole line. III. If a straight line be divided into any two parts,...contained by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the square of the whole...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...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,...contained 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...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 páginas
...showing that AB* = figures AF + CE ; and that these are = AB x AC + AB x BC. PROPOSITION III. Theorem. If a straight line be divided into any two parts,...contained 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...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 páginas
...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...contained 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...
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