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" PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 59
von Robert Simson - 1806 - 518 Seiten
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 Seiten
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced. Let the straight line AB be bisected in c, and produced to the point D...
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Minutes of the Committee of Council on Education, Band 1

Great Britain. Committee on Education - 1850 - 790 Seiten
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half, and the part produced. 2. If a point be taken within a circle from which there tall more than...
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The English Journal of Education, Band 4

1850 - 488 Seiten
...line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. SECTION IV. 1. If two circles cut each other they shall not have the same...
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Papers for the schoolmaster, Band 3

1867 - 336 Seiten
...cannot be less than twice their rectangle. 3. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and...other part, is equal to the square of the straight liue which is made up of the whole and that part. Prove this also algebraically. SECTION VI. 1. If...
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Papers for the Schoolmaster, Band 2

1852 - 314 Seiten
...rectangle contained by the whole line thus produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. ANSWERS TO THE EXAMINATION PAPER ON SCHOOL MANAGEMENT* (CONTINUED FROM...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 Seiten
...produced, and the part of it produced, together with the square of half the line bisected, is eqaul to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D;...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 Seiten
...straight line, etc. QED PROPOSITION VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and...to the square of the straight line, which is made of the whole and that part. Let the straight line AB be divided into any two parts in the point C ;...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 Seiten
...and difference. 7. If a straight line be divided into five equal parts, the square of the whole line is equal to the square of the straight line which is made up of four of those parts, together with the square of the straight line which is made up of three of those...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - 1853 - 474 Seiten
...question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Bücher 1

Euclides - 1853 - 334 Seiten
...other part. Let AB be the given straight line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing...
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