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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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...straight line, &c. QED 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 equivalent to the square of the straight line, which...
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Proceedings

Scotland free church, gen. assembly - 1847
...on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - Liczba stron: 352
...particular case of this problem m which the given lines are equal. PROP. XXIII. PROR. — 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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - Liczba stron: 199
...line, &c. QED PROPOSITION 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 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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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...of the other part. PROP. 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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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - Liczba stron: 108
...straight line, &c. QED 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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University of Durham

University of Durham - 1851
...square of the parts together with 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 of the parts shall be equal to the square of the other part. 6. If two circles cut one another...
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Papers for the schoolmaster, Tom 3

1867
...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 one of the parts, together with the square of the other part, is equal to the square of the straight liue which is made...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852
...kc added together.] 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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