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" Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. "
A Supplement to the Elements of Euclid - Σελίδα 309
των Daniel Cresswell - 1819 - 410 σελίδες
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 454 σελίδες
...AB at the circumference of the given circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it...

Elements of Geometry: With Notes

John Radford Young - 1827 - 246 σελίδες
...which it is included, without violating one of the most obvious rules of logic. PROPOSITION XXXII. PROBLEM. To divide a given straight line into two parts, such that the greater part may be a mean proportional between the whole line and the other part. Let AB be the proposed...

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

Euclid, James Thomson - 1837 - 410 σελίδες
...the lines forming a given angle, to draw a straight line cutting off the least possible triangle. 40. To divide a given straight line into two parts, such that the square of one of them may be double of the square of the other, or may be in any given ratio to it....

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

Euclid, James Thomson - 1845 - 382 σελίδες
...(I. 47) equal to the squares of GA, AM, the sides of the hexagon and decagon. PROP. XXII. PROB. — To divide a given straight line into two parts, such that the square of one of them may be equal to the rectangle contained by the other, and a given straight line....

University of Durham

University of Durham - 1851 - 222 σελίδες
...line is equal to the square of the parts together with twice the rectangle contained by the parts. 5. To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 6. If two circles cut one another...

Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - 1853 - 474 σελίδες
...both are answers to the question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x...

The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 σελίδες
...will bo the greatest possible when the segments of the given straight line are equal. PROP. XXVIII. PROBLEM. To divide a given straight line into two parts such that of the two parallelograms having the same altitude described upon tliem, one may be similar to a given...

Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 σελίδες
...figure ABED is the square required. (46. I.) PBOB. 15. To divide a given line, AB, into two parts, so that the rectangle contained by the whole line and one of its parte, AB-BH, Khali be equal to the square of the other part, AH. On AB, by 46. 1. , describe the square...

The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 332 σελίδες
...bisected, shall be equal to the square of the straight line made up of the half and the part produced. 8. Divide a given straight line into two parts, such...the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. PRELIMINARY GENERAL EXAMINATION. Christmas,...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...parts is equal to the sum of the squares described on the parts, the straight line is bisected. 135. Divide a given straight line into two parts such that the rectangle contained by them shall be the greatest possible. 136. Construct a rectangle equal to the difference of two given...




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