Books Books 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. The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 60
by Robert Simson - 1806 - 518 pages ## A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845
...contact, and the diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii.... ## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...the first and third partu of whioh are, by the same curolla'y, tli» 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... ## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 contained by...parts shall be equal to the square of the other part. Upon AB describe the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. 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... ## An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 468 pages
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): = o2 - Zax + a?2, x- -... ## Minutes of the Committee of Council on Education, Volume 1

...the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the... ## The English Journal of Education, Volume 1

Education - 1847
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the... ## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so that the...parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute... ## Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that the...parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals of a parallelogram... 