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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 53
by Euclid, Robert Simson - 1829 - 516 pages
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...is equal to the fquare of AB. If therefore a ftraight be, &c. Q^ED PROP. HI. THEO R. TF a ftraight line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with the fquare of the forcfuid part. Let the ftraight line AB be divided into any two parts in the point C;...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...a itraight line, &c. QED PROP. III. THEOR. tF a fbaight line be divided into any two parts, thd *. rectangle contained by the whole and one of the parts,...rectangle contained by the two parts, together with the fquare of the forefaid part. T> ° Let the ftraight line AB be divided into any two parts in the point...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 351 pages
...ftraight line, &c. Q^ED PROP. III. THEOR. IF a ftraight line be divided into any two parts, the redtangle contained by the whole, and one of the parts, is equal...rectangle contained by the two parts, together with the fquare of the forefaid part. Let the ftraight line AB be divided into any two parts in the point C...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...equal to the fquare of AB. If therefore a ftraight line, &c. Q^ED PROP. III. THEOR. j IF a ftraight line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with the fquare of the forefaid part. Let the ftraight line AB be divided into any two parts in the point C;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...Therefore AB.AC+ AB.BC=AB2. Therefore, if a straight line, &c. QED CB D a 46. 1. b 31. 1. PROP. III. THEOR. IF a straight line be divided into any two parts,...parts, together with the square of the foresaid part. sr~"~~-~^ i - f ^ I .... > . ;i Let the straight line AB be divided into two parts in the point C;...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...whole and each of the parts, are together equal to the square of the whole line. Prop. III. Theor. If a straight line be divided into any two parts,...rectangle contained by the two parts, together with the aquarc of the foresaid part. Prop. IV. Theor. If a straight line be divided into any two parts, the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
..."Y"*"' 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 ofthe parts is equal to the rectangle contained by the two parts, together with the square of the aforesaid...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1819
...the whole and each of the parts, are together equal to the square of the whole line. Prop. HI. Theor. If a straight line be divided into any two parts, the rectangle contained by the «•hole and one of the parts, is 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 - Circle-squaring - 1819 - 333 pages
...AE = AB2. Therefore AB.AC + AB.BC =AB2. Therefore, if a straight line. &c. QED D PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whoj.e and one of the parts, is equal to the rectangle contained by the two parts, together with the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...BC, is equal to the gquare of AB. If therefore a straight line, &c. QED Propotition III. Tlieorem. If a straight line be divided into any two parts,...contained 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 С ; the rectangle...
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