| Euclid, John Playfair - Circle-squaring - 1804 - 440 pages
...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... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...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... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...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... | |
| Miles Bland - Euclid's Elements - 1819 - 377 pages
...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... | |
| Miles Bland - Euclid's Elements - 1819 - 377 pages
...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... | |
| Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...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... | |
| James L. Connolly (mathematician.) - Arithmetic - 1829 - 250 pages
...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... | |
| John Hind - Algebra - 1837 - 539 pages
...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 : .-.... | |
| 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... | |
| 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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