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" If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. "
Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ... - Side 56
av Association for the improvement of geometrical teaching - 1876 - 58 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 sider
...CD : : E : F. Wherefore, if four straight 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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 sider
...equal the rectangle contained by the means ; and conversely. ED. Cor. 4. If three straight lines be proportional the rectangle contained by the extremes is equal to the square of the mean ; and conversely. ED. Cor. 5. Equal triangles, or equal parallelograms, have their bases...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 sider
...Prop. IB). But since D = B, the rectangle B'D is the same as B'B, or the square of B ; and therefore, if three straight lines are proportional, the rectangle contained by the extremes is equal to the square of the mean. And conversely, if three straight lines be such that the rectangle contained by the extremes...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 sider
...the means, the four straight lines are proportional. 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 (of three given straight lines) be equal...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 sider
...the means of the proportion be equal, the rectangle formed by them will be a square. Hence, " when three straight lines are proportional, the rectangle...contained by the extremes is equal to the square on tie mean ;" and conversely. PROPOSITION LXV — THEOREM. If two chords, AB, CD, cut one another in...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 sider
...7.) Wherefore, if four, &c. QED PROPOSITION XVH. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. r Let the three straight...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 sider
...therefore AB is to CD as E toF. PROPOSITION XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 sider
...7.) Wherefore, if four, &c. QED PROPOSITION XVII. THEOREM. If three straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. Let the three straight...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 sider
...(v. 7.) Wherefore, if four, &c. QED PROP. XVH.— THEOREM. //" Him', straight lines be proportionals, the rectangle contained by the extremes is equal to...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. (References— Prop....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 sider
...QED PROPOSITION XVII. .THEOREM. lf (hree straight lines be proportionals, the rectangle contained Jy the extremes is equal to the square on the mean ;...conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals. Let the three straight...
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