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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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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...this, and ifm=a + b, shew that its symbolical expression is m? = am + bin. PROPOSITION 3. THEOREM. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point C: the rectangle AB, BC shall be...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...&c. QED PROPOSITION 3. — Theorem. If a straight line be divided into any two parts, the rectangU contained by the whole and one of the parts is equal...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts in the point C. AC .. B Then the rectangle AB,...
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Pure Mathematics, Volumen1

Edward Atkins - 1874
...parts AF+ CE. And;.= AB-AC+ AB-BC. AB-BC= BCa+ AC • BC. For AE=AD +CE. 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 t/tnt part, together with the rectangle contained liy the two parts. Let the straight line...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...BAandAC, together with that contained by AB and BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) 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 square of that part, together with the rectangle contained...
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Pure mathematics, Volumen1

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,...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, the squares on the...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 páginas
...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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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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 páginas
...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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