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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 of the other part.
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838

## Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850 - 912 pages
...figures, and duplicate ratio. 3. Solve Euc. II. 11. To divide a given finite straight line into two part*, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other jjart. '2. Prove Kuc. 1. 36. Parallelograms upon equal bases,...

## A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...upon the necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that...parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner....

## Papers for the schoolmaster, Volumes 1-6

582 pages
...every respect." Enumerate tlie cases proved in Book 1 and state what ease is omitted. SECTION IT. 1. Divide a given straight line into two parts, so that...parts, shall be equal to the square of the other part. 2. If a straight line be divided into any two parts, the square of the whole line is equal to the squares...

## The Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - Mathematics - 1851 - 144 pages
.../. 4 (BE2 + CF2) = 4 (ABa + AC2) + 4AE2 + 4AF2, = 4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). Divide a given straight line into two parts, so that...parts shall be equal to the square of the other part. (ii. 11.) (B). Shew that in Euclid's figure, four other lines, beside the given line, are divided in...

## University of Durham

University of Durham - Education, Higher - 1851 - 222 pages
...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...parts shall be equal to the square of the other part. 6. If two circles cut one another they cannot have the same centre. 7. Equal straight lines in a circle...

## Bonnycastle's Introduction to Algebra: Containing the Indeterminate and ...

John Bonnycastle - Algebra - 1851 - 288 pages
...to divide a line y of 20 inches in length, into two such parts that the rectangle of the whole arid one of the parts shall be equal to the square of the other. Ans. 10^/5 — 10, and 30— 10 ^5. 5. It is required to divide the number 60 into two such parts,...

## Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...two sides which contain the right angle. Is this proposition included in any more general one ? (2.) To divide a given straight line into two parts, so...parts, shall be equal to the square of the other part. Can this be solved arithmetically ? if so, find approximately into how many parts the given line must...

## The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...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 ABDC; • x hi. i. bisect* AC in E, " x . i. and join BE; produce CA to...