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" To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Σελίδα 57
των Euclid, James Thomson - 1837 - 390 σελίδες
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 σελίδες
...PROP. XI. PR OB. TO divide a given ftraight line into two parts, fo that the.rectangle contained by the whole, and one of the parts, may be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required to divide it into two...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...PROP. XI. PROB. TO divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...be done. x Otherwise. •' Divide the radius of the given circle, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other (11. 2.). Apply in the circle, on each side of a given point, a line equal to thegreater of these parts...

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

Miles Bland - 1819 - 377 σελίδες
...the given square. (9.) To divide a straight line into two 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 fhe line to be divided. Let AB he tlie given line to be divided. Upon...

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

Miles Bland - 1819 - 377 σελίδες
...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 given line to be divided. Upon...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 σελίδες
...to be done. Otherwise : "Divide the radius of the given eirele, so that the reetangle eontained by the whole and one of the parts may be equal to the square ef the other (tl. 2.). Apply in the eirele, on eaeh side of a given point, a line equal to the greater...

Connolly's Arithmetic: Or, The Ohio Accomptant: Being a Plain Practical ...

James L. Connolly (mathematician.) - 1829 - 250 σελίδες
...EXAMPLE. 13. Let it be required to divide 100 into two such parts, that the product of the whole, into one of the parts, may be equal to the square of the other part ? 1st. Suppose 38 and 6-i Error in this, 4i — 5 ,,, .._ , 2nd. Suppose 38.2 and 61.8. Error...

The Elements of Algebra: Designed for the Use of Students in the University

John Hind - 1837 - 539 σελίδες
...which answer the symbolical condition. • Ex. 3. Divide 20 into two parts, so that the product of the whole and one of the parts, may be equal to the square of the other part. Let a? = one part : .-. 20 - as = the other : whence, 20a? = (20 - off = 400 - 40a? + of : .-....

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the square of the side subtending the obtuse...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ; join EB, and produce CA towards F till EF...




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