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" If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 53
by Euclides - 1841 - 351 pages
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The Mechanic's Magazine, Museum, Register, Journal and Gazette, Volume 44

1846 - 536 pages
...the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 44

Perry Fairfax Nursey - Industrial arts - 1846 - 536 pages
...the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of...
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Arithmetic, in Two Parts

Frederic A. Adams - Arithmetic - 1846 - 230 pages
...what are the numbers ? The theorem on which the solution of this question depends is this, If a number be divided into two equal parts, and also into two unequal parts, the product of the two equal parts, that is, the square of half the number, will equal the product of the...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...the squares described upon the sides containing the right angle. SECTION III. 1. If a straight line be divided into two equal parts, and also into two...of section is equal to the square of half the line. 2. In any triangle the square of the side subtending contained by either of these sides, and the straight...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the...
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Report of the Committee of Council on Education (England and Wales ..., Issue 1

Great Britain. Council on Education - Education - 1848 - 532 pages
...to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts, and also into two...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less...
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Minutes of the Committee of Council on Education: with Appendices, Volume 1

Great Britain. Committee on Education - Education - 1848 - 514 pages
...to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts, and also into two...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less...
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The English Journal of Education, Volume 2

Education - 1848 - 542 pages
...&c. page 39, where a new proof is given of this important theorem. SECTION 3. 1. If a straight line be divided into two equal parts, and also into two...parts, the rectangle contained by the unequal parts, togelher with the square of the line between the points of section, is equal to the square of half...
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The Calendar of King's College, London

1850 - 400 pages
...produced, the exterior angle is greater than either of the interior opposite angles. 2. If a right line be divided into two equal parts, and also into two...section, is equal to the square of half the line. 3. In every triangle, the square of the side subtending either of the acute angles, is less than the...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...equal parts. In what case will the diameter bisect the angle of a parallelogram? 3. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. 4. Equal straight lines in a circle are equally distant from the centre ; and conversely, those which...
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