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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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Pure mathematics, Volum 1

Edward Atkins - 1874
...BC, is equal to the square on AB. Therefore, if a straight line, &c. QED Proposition 3. — Theorem. If a straight line be divided into any two parts, the rectangle contaiiied by the whole and one of the parts is equal to the square on t/iat part, together with the...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major
...Give some account of it, and of the retribution exacted. Write an essay on " The House of Lords." 1. If a straight line be divided into any two parts,...contained by the two parts, together with the square on the aforesaid part. 2. If a straight line be divided into two equal, and also into two unequal parts,...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...its parts are together equal to the square on the whole line. . . - . . . . . . . . . . . . 145 3. 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. .. .. 145 6. If a straight...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 sider
...BC, is equal to the square on AB. 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 tJiat part, together with the rectangle contained by the two parts. Let the straight line...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 sider
...square on AB. If therefore a straight line, &c. QE ji. PROPOS1TION III. THEOREM. iJ a itraiyht line Tie divided into any two parts, the rectangle contained by the whole and one of the parti, is equal to the rectangle contained by the tun parti, together with the square. on the aforesaid...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - 1878
...square on a straight line is equal to four times the square on half the line, PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...the rectangle contained by the two parts together mth the square on the aforesaid part. J> Let the st. line AB be divided into any two parts in C. Then...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...divided Mo any two parts, the rectangle contained by the whole line and one of its parti is equal to th* rectangle contained by the two parts, together with the square of the for esaid part. And conversely, if there be a rectangle and the square of one of its sides, the rectangle...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...the line, and the two interior angles on the same side of it together equal to two right angles. 3. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. 4. From a given point, either without or in the circumference of a circle, draw a straight...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 sider
...AF+CE=AE; AF=AD.AC=AB.AC, CE=CF.CB = AB. CB, AE-AB * ; AB.AC+AB.CB=AB\ Proposition 3. Theorem.—If a straight line be divided into any two parts, the...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided in two parts in the point C, then AB.BC=AC.CB+BC\...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...this formula in terms corresponding to the enunciation of the proposition.] 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 AB be divided into any two parts at C. Then rect. AB, BC == rect. AC, BC,...
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