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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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The First Six Books with Notes

Euclid - 1822 - 179 pągines
...XVII. THEOR. If three right lines be proportional (A to B as B to Fig, 24. CJ the rectangle under the extremes is equal to the square of the mean. And if...three right lines are proportional. Part 1. Assume a line D equal to B, and A is to (i)Pro;'.n. B as D to C (1), therefore the rectangle under A and^-5C...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822
...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. Carol, t. Since it appears, by the rules of proportion In Arithmetic and Algebra,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 pągines
...EUCLID. £69 PROP. XVII. THEOR. Iflkree 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 projwrlionals....
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...PROPOSITION XVII.* THEOREM. If three right lines be proportional, the rectangle contained under the extremes is equal to the square of the mean ; and if the rectangle contained under the extremes be equal to the square of the mean, the three right lines will be proportional....
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pągines
...PROPOSITION XVII.* THEOREM. If three right lines be proportional, the rectangle contained under the extremes is equal to the square of the mean ; and if the rectangle contained under the extremes be equal to the square of the mean, the three right lines will be proportional....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 pągines
...&e. QED PROP. XVII. THEOR. If three straight lines be proportionals, the reetangle eontained by the extremes is equal to the square of the mean : And if the reetangle eontained by the extremes be equal to the square of the mean, the three straight lines are...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pągines
...&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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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 pągines
...proportional (A to B as B to C) the rectangle under the extremes is equal to the square of the mean. 2°. And if the rectangle under the extremes be equal to...right lines are proportional. Part 1°. — Assume a line D equal to B, and A is to B as D to C (hyp.), therefore the rectangle under A and C is equal to...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 pągines
...proportionals, the rectangle under the extremes shall be equal to the square of the mean ; and, conversely, if the rectangle under the extremes be equal to the square of the mean, the three straight lines shall be proportionals. Cor. 4. It appears from the proposition that rectangles which...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 pągines
...three right lines be proportional (A to B as B to C), the rectangle under the extremes is equal tothe square of the mean. And if the rectangle under the...three right lines are proportional. Part 1. Assume a line D equal to B, and A is to (i)Prop.i4. B as D to C(1); therefore the rectangle under A and ™\5A...
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