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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. "
Manual of Euclid. Books IV. V. VI. - Page 66
by Euclid - 1859
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...parallelograms, are such See KK " as have their sides about two of their angles proportionals " in such manner, that a side of the first figure is to a side •• of the other, as the remaining side of this other is to the reK maining side of the first." III. A straight...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...triangles and parallelograms, are such as have their sides about two of their angles proportionals in such manner, that a side of the first figure is to a side of the other, as the remaining side of this other is to the remaining side of the first. 3. A straight line...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...reciprocally proportional to two sides of another, when one of the sides of the first is to one of the sides of the second, as the remaining side of the second is to the remaining side of the first. A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment,...
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Universal Technological Dictionary: Or, Familiar Explanations of ..., Volume 2

George Crabb - Industrial arts - 1823 - 704 pages
...two of their angles proportionals in such manner, that a side of the one is to a side of the other, as the remaining side of the second is to the remaining side of the other. The Base of a figure is the lowest part of the perimeter, as KL, fig. 11. The vertex of a figure...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...each, and the sides about the equal angles proportional. 2. Reciprocal figures are such as have their sides about two of their angles proportional in such...that a side of the first figure is to a side of the other, as the remaining side of this other is to the remaining side of the first. 3. A right line is...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...each, and the sides about the equal angles proportional. 2. Reciprocal figures are such as have their sides about two of their angles proportional in such...that a side of the first figure is to 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...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...reciprocally proportional to two sides of another, when one of the sides of the first is to one of the sides of the second, as the remaining side of the second is to the remaining side of the first. III.— The altitude of any figure is the straight line drawn from its vertex perpendicular to its...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...triangles and parallelograms, " are such as have their sides about two of their " angles proportionals in such a manner, that a side " of the first figure is to a side of the other, as the " remaining side of this other is to the remaining " side of the first." III. A straight...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...triangles and parallelograms, are " such as have their sides about two of their angles pro" portionals in such a manner, that a side of the first figure " is to a side of the other, as the remaining side of this " other is to the remaining side of the first." III. A straight...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...parallelograms, are such See N. " as have their sides about two of their angles proportionals " in such manner, that a side of the first figure is to a side " of the other, as the remaining side of this other is to the " remaining side of the first." III. A straight...
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