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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 ... - Page 26
by Euclides - 1821
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

Euclid, John Keill - Geometry - 1723 - 442 pages
...PROPOSITION XVII. THEOREM. If three Right Linet be proportional, the Re&tingle contained under the Extremes, is equal to the Square of the Mean ; and...the Extremes, be equal to the Square of the Mean, then the three Right Lines are proportional, - • T ET there be three Right Lines A, B, C, propor-....
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Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - Geometry - 1733 - 448 pages
...demonftrated. PROPOSITION XVII. THEOREM. If three Right Lines be proportional, the RfRangle contained under the Extremes, is equal to the Square of the Mean ; and if the Rett angle under the Extremes be equal to the Square of the Mean, then the three Right Lines are proportional...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - Geometry - 1782 - 399 pages
...PROPOSITION XVII. THEOREM. If three Right Lines be proportional, the Reflatgle contained1 under the Extremes is equal to the Square of the Mean ; and if the Rettangle under the Extremes be equal to the Square of the Mean, then the three Right Lines are proportional....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...&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 - Euclid's Elements - 1806 - 320 pages
...lines, &c. PROP. XVII. THEOR. IF three straight lines be proportional, 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 proportional....
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...rectangle of the two extremes is equal to the 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. Since it appears, by the rules of proportion in Arithmetic and Algebra,...
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A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

Charles Hutton - Mathematics - 1812
...rectangle of the two extremes is equal to the 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. 2. Since it appears, by the rules of proportion in Arithmetic and Algebra,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...&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 ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...ED S i PROP. XVII. THEOR. If three straight hues 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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...proportionals. 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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