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" IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Pągina 24
per Euclides - 1821
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pągines
...E : F. PROP. XVII. THEOR. If three straight lines lie proportionals, the rectangle contained by the extremes is equal to the square of the mean : And if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals....
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 pągines
...PROPOSITION XVII. THEOR. — If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals....
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 pągines
...contained by the extremes is equal to the square of the mean : and (2) if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. Let the three straight lines A, B, C be proportionals, viz. A : B...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...contained by the extremes is equal to the square of the mean; and conversely, if tke rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. Let the three straight lines A, B, C be proportionals, viz. as A...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...B as B to C), the rectangle under the extremes will be equal to the square which is constructed on the mean. And if the rectangle under the extremes be equal to the square constructed on the mean, the three right lines shall be proportional. PART 1. — Assume D equal to...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 pągines
...AG; that is, AB : CD :: E : F. 17 Th. If three straight lines be proportionals, the rectangle of the extremes is equal to the square of the mean: and if the rectangle of the extremes be equal to the square of the mean, the three straight lines are proportionals. The...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...%c. QED PROP. XVII. THEOR. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and, if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 pągines
...rectangle contained by the extremes is equal to the square of the mean : And if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals. Let the three straight lines, A, B, C be proportionals, viz. as A...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 pągines
...proportionals, the rectangle of the extremes is equal to the square of the mean: and if the rectangle of the extremes be equal to the square of the mean, the three straight lines are proportionals. Given three straight lines A, B, C ; such, that AistoBasBistoC: then...
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Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 pągines
...rectangle of the two extremes is equal to the square of the mean ; and, conversely, if the rectangle of the extremes be equal to the square of the mean, the three lines are proportionals. Corol. 2. If the sides about the equal angles of parallelograms or triangles...
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