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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 - Página 118
por Euclid - 1822 - 179 páginas
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 páginas
...remaining 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 oase. PROPOSITION I....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 páginas
...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 First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 páginas
...one segment as that segment is to the remaining one. This definition is thus expressed by Euclid : ' The whole line is to the greater segment as the greater segment is to the lesser.' But it is objectionable to assume in one part of a definition a property which may be deduced...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 páginas
...when any two corresponding segments of them have the same ratio as the lines have. ED. 3. A straight line is said to be cut in extreme and mean ratio,...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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 páginas
...are harmonicals (def. 20.). SECTION 7. — Probleme. Def. 21. A straight line is said to be divided in extreme and mean ratio, when the whole line is...greater segment as the greater segment is to the less. A straight line so divided is also said to b« divided medially ; and the ratio of its segments is...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 216 páginas
...demonstrated, that D has not a less ratio to E than A has to B ; and therefore A is to B as D to E. THE ELEMENTS OF EUCLID. BOOK VI. DEFINITIONS. 1. Similar...perpendicular to the base. 4. A parallelogram described upon aright line is said to be applied to that right line. 5. A parallelogram, described upon a part of...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 páginas
...are harmonicals (def. 20.). SECTION 7. — Problems. Def. 21. A straight line is said to be divided in extreme and mean ratio, when the whole line is...greater segment as the greater segment is to the less. A straight line so divided is also said to be divided medially ; and the ratio of its segments is called...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 páginas
...of the first." III. A straight line is said to be cut in the 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 Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 páginas
...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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The Element of Geometry

John Playfair - 1836 - 148 páginas
...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 into any number of equal parts, so that a part of one is equal...
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