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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 ... - Page 49
by Euclid, Robert Simson - 1829 - 516 pages
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...the square on AB. Conclusion. — Therefore, if a straight line, &c. QED PROPOSITION 3.— THEOREM. If a straight line be divided into any two parts,...by the whole and one of the parts, is equal to the square on that part, together with the rectangle contained by the two parts. (References— Prop. I....
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...straight line be divided into any two parts ; then the rectangle contained by the whole and one of Ihe parts is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. (References— Prop. i. 31, 46.) Let the straight line AB be divided into any two parts...
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Responsions

University of Oxford - Education, Higher - 1863 - 316 pages
...of its angles equal to a given rectilineal angle. 6. Describe a square on a given straight line. 7. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. 8. If a straight line be bisected, and produced to any point, the rectangle...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...AB, BCis equal to the square on AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts in the point C. Then...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...AB, BCis equal to the square on AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...rectangle contained by the whole and one of the parts, it equal to the rectangle contained by the two parts, together with the square on the aforesaid part....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...BC is equal to the square on AB. If therefore a straight line, &c. QED PROPOSITION III. THEOREM. lf a straight line be divided into any two parts, the...contained by the two parts, together with the square on the aforemid part. Let the straight line AB\>& divided into any two parts in the point C. Then the...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...equal to the rectangles under the whole and each of the parts . . . . . II. 2. 2. The rectangle under the whole and one of the parts, is equal to the rectangle under the two parts, together with the square on the aforesaid part . . . . . . . n. 3. 3. The square...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 350 pages
...multiplying both members of this equality by a, we shall have a2=ŤA + a</ PE Q KLD PROP. III. THEOR. tf a straight line be divided into any two parts, the...the parts, is equal to the rectangle contained by the tttm parts, together with the square of the aforesaid part. Let the straight line AB be divided...
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Examination papers collected by A. Clark as a student and as an examiner

1867 - 224 pages
...one another, and likewise those which are terminated at the other extremity equal to one another. 3. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point (7: the...
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