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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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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane

Nathan Fellowes Dupuis - 1889 - 294 páginas
...the construction of 183° solves the problem, " To divide a given segment so that the rectangle on the whole and one of the parts is equal to the rectangle on the other part and the segment which is the sum of the whole and the first part." r i. Construct...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - 1890 - 132 páginas
...an expression for the number of factors a1, a2, a3, &c. II.— EUCLID AND TRIGONOMETRY. 1. Show that if a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. To what algebraical formula does this proposition correspond ? 2. Describe a square that shall be equal...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 páginas
...shall be equal to the square on a given straight line greater than half A B. 1 See p. 235. Ex. 505. — If a straight line be divided into any two parts, the rectangle contained by the diagonals of the squares on the whole line and one of the parts is equal to twice the rectangle contained...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 páginas
...contained by the whole and each of the parts are together equal to the square on the. whole line. 3. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. 4. If a straight line be divided into any two parts, the square on the whole line is equal to the squares...
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The Educational Record of the Province of Quebec: The Medium ..., Volumen11

1891
...9. If a straight line be divided into any two parts, then the rectangle .contained by the whole line and one of the parts is equal to the rectangle contained...parts together with the square on the aforesaid part. Prove this proposition. ALGEBRA (GRADE II. ACADEMY.) SECTION I. 1. Find the GCM of 9 (a2*5 - 4) and...
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Plane and Solid Geometry

Seth Thayer Stewart - 1891 - 406 páginas
...follows, etc. Exercises, i. Parallelograms about the diagonals of a square are themselves squares. 2. If a straight line be divided into any two parts, the rectangle of the whole line and one of the parts is equal to the square of that part, together with the rectangle...
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A Text-book of Geometrical Deductions: Corresponding to Euclid ..., Libro 2

James Blaikie - 1892
...line shall be equal to the sum of the rectangles contained by the whole line and each of the parts. 3. If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts shall be equal to the square on that part, together with the rectangle contained...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 páginas
...+ &) a + (a + &) I. PROPOSITION 3. THEOREM. If a straight line is divided into any two parts, tlie rectangle contained 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. Let the straight line AB...
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Euclid's Elements of Geometry, Libros 1-6

Henry Martyn Taylor - 1893 - 504 páginas
...BC, DC be equal to the squares on AB, AC respectively, the angle BAC is a right angle. PROPOSITION 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 sum of the square on that part and the rectangle contained...
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - 1893 - 225 páginas
...at 0, each = IL; .-., DE = E 0, and OH — HB (B. п., P. vIn.) ; and £^"and HG are Ds (P. Iv.). 2. If a straight line be divided into any two parts, the rectangle of the whole line and one of the parts equals the square of that part, together with rectangle of the...
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