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" Iff a straight line be divided into any two parts, four 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 whole and that... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Strona 154
autor: Daniel Cresswell - 1817 - Liczba stron: 436
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - Liczba stron: 472
...of the difference of the lines. VIII. If a straight line be divided into any two parts, four 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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - Liczba stron: 390
...particular case of this problem in which the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure)...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - Liczba stron: 88
...+ AC*. CBD PROPOSITION VIII. Theorem. If a straight line be divided into any two parts, four 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 line made up of the whole...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - Liczba stron: 215
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice the rectangle contained by the whole line and one of the parts is equal to twice the square upon that part, together with twice the rectangle contained by the parts....
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 240
...square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four 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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided into any two parts, four 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...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...the half and the produced part. PROP. XI. PROB. 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 ;...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...half and the produced part. .n. . PROP. XI. 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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - Liczba stron: 351
...straight line, &c. QED PROP. VIII. THEOR. Iff a straight line be divided into any two parts, four 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - Liczba stron: 317
...equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four 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...
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