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" AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Σελίδα 54
των Robert Simson - 1781 - 466 σελίδες
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...the half and the part produced. Prop. XI. Prob. To divide a given straight lint into tu'o parts, so that the rectangle contained by the whole, and one of the parts, shall be equal tu the fquare of the other part. Prop. XII. Theor. In obtuse angled triangles, if a...

Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 σελίδες
...equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of a given line, which is less than the line to be divided. L,etAB be the...

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John Playfair - 1819 - 333 σελίδες
...the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. I.) the square ABDC; bisect (10....

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...the other part. Let AB be the given straight line ; it is required to divide .it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC in E,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 σελίδες
...of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. e 47. 1. Upon AB describe » the square ABDC ; bisect5...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...the other part. Let AB be the given straight line : it is required to divide it into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8....

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...= 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 σελίδες
...the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line;...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...of the other part. Let AB be the given straight line: it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. From the point A draw* AC perpendicular and *" o™4...




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