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" A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 4
by Euclides - 1821
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...a side of the other, as the remaining side of this other is to the remaiuing side of the first. 3. A right line is said to be cut in extreme and mean ratio when the whole is to the greater segment as the greater segment is to the less. 4. The altitude of any figure is the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...other, as the " remaining side of this other is to the remaining " side of the first." III. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. IV. The altitude of any figure is...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...each to each, and whose sides including equal angles are severally proportional. (514) II. A straight line is said to be cut in extreme and mean ratio when the whole line is to one segment as that segment is to the remaining one. This definition is thus expressed by Euclid :...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...the second, as the remaining side of the second is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. 4. The altitude of any figure is...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...as the remaining one of the second is to the remaining one of the first. II. A straight line maybe said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. III. When two magnitudes can be divided...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...the second, as the remaining one of the second is to the remaining one of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to one of the segments, as that segment is to the other. 4. The altitude of any figure is the straight...
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The First Six Books of the Elements of Euclid: With a Commentary and ...

Dionysius Lardner - Geometry - 1838 - 382 pages
...each, and whose sides including equal angles are severally proportional. (514) II. A straight line s said to be cut in extreme and mean ratio when the whole line is to one segment as that segment is to the remaining one. This definition is thus expressed by Euclid :...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...the second, as the remaining side of the second is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. 4. The altitude of any figure is...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...other, as the " remaining side of this other is to the remaining " side of the first." III. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. IV. The n/ti/>'(]<: of any figure...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...the second, as the remaining side of the second is to the remaining side of the first. 3. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment, as the greater segment is to the less. 4. The altitude of a triangle is...
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