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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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Proceedings

Scotland free church, gen. assembly - 1847 - 554 Seiten
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 338 Seiten
...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 olher part, is equal to the square of the straight line which is made up of the whole and thefirst-mentioned...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 Seiten
...'straight 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...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, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 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 D ; the rectangle...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 Seiten
...nf, That is, If a number be divided into any two parts, four times the product of the whole number and one of the parts, together with the square of the other part, ig equal to the square of the number made up of the whole and that part. Prop. ix. Algebraically. Let...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 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 line and the part produced. Let the str. line AB be bisected in C, and produced to D; then AD....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 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 D : the rectangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 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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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846 - 128 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 line and the part produced. Let the str. line AB be bisected in C, and produced to D; then AD....
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 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. PROP. VII. THEOREM. If a straight line be divided into any two parts, the...
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