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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 First Six Books with Notes - Page 118
by Euclid - 1822 - 179 pages
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

Euclid, John Keill - Geometry - 1723 - 364 pages
...in each figure. III. A Right Line is faid to be cut into mean and extreme Proportion, when the Whole is to the greater Segment, as the greater Segment is to the leffer. IV. The Altitude of any Figure, is a Perpendicular Line drawn from the "Top, or Vertex, to...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - Trigonometry - 1733 - 397 pages
...in each Figure. III. A Right Line is faid to be cut into mean and extreme Proportion, when the whole is to the greater Segment, as the greater Segment is to the le/er. IV. The Altitude of any Figure, is a perpendicular Line drawn from the Top, or Vertex to the...
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The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - Geometry, Plane - 1775 - 159 pages
...one of the firft. 176. Def. 24. A Line is faid to be cut in extreme and mean Ratio, when the Whole is to the greater Segment as the greater Segment is to the lefs. • 177. Axiom i. Equimultiples of the fame, or equal Magnitudes, are equal to one another ;...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 the straight line drawn from its vertex perpendicular to the base....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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 the straight line drawn from its vertex perpendicular to the base....
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 the straight line drawn from its vertex perpendicular to the base....
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814
...figure, but the idea of ratio does not occur ; here we are to divide a line, so that the whole may be to the greater segment, as the greater segment is to the less, and tlie idea of figure has no place ; but our business is solely with the agreement of certain ratios....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...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 the straight line drawn from its vertex perpendicular to the base....
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...line. 3. The altitude of any figure is the right line from the vertex perpendicular to the base. 4. A right line is said to be cut in extreme and 'mean...greater segment as the greater segment is to the less. 5. A J'iglit line is said to be cut harmonically when it is divided into three segments, such that...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...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 perpendicular drawn from the vertex to the base. PROPOSITION I....
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