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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 49
av Euclid, Robert Simson - 1829 - 516 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...D FE QED PROP. III. THEOR. If a straight line be divided into any to parts, the reetangle eontained by the whole and one of the parts, is equal to the reetangle eontained by the two parts, together with the square of the foresaid part. Let the straight...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...angle AB, BC, is equal to the square of AB. fore a straight line, &c. QED If thereFD 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: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...contained by the whole line and each of the parts are together equal to the square of the whole line. ..If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...divided into any tico parts, the rectangle contained by the tchole line and one of the parts, ihali be equal to the rectangle contained by the two parts, together with the tquare of the aforesaid part. Let the straight line AB be divided into any two parts А С, С В :...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...AB'. Therefore AB.AC+AB.BC=AB'. Therefore, if a straight line, &c.QED G F K. LH A PROP. III. THEOR. If a straight line be divided into any two parts,...the rectangle contained by the two parts, together ivith the square of the aforesaid part. Let the straight line AB be divided into two parts in the point...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...AB.AC+AB.BC=AB2. Therefore, if a straight line, &c. QED D IT E: 14 i A. PROP. III. THEOR. If a straight line he divided into any two parts, 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 rectangle AB.BC...
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The Quarterly Journal of Education, Volum 5

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 sider
...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,...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 rectangle AB, BC is equal...
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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 sider
...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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