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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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...other, as the " remaining side of this other 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 the...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...as the other about this angle is to the other about the angle in the first figure. III. A straight line is said to be cut in extreme and mean ratio, when it is divided into two parts such, that the whole line is to the greater part as the greater part is...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...the second as the remaining side of the second is to the remaining side of the first. m. 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. rv. The altitude of any figure is...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...pair, as the remaining опе of the second pair is to the remaining one 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. A straight line is said to be cut...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...line AB. (29. VI.) PEOB. 10. To cut a given straight line, AB, in extreme and mean ratio, ie, so that the whole line is to the greater segment as the greater segment to the less. On AB, by 46. I. , describe the square BC ; and, by 29. VI. , apply to AC the parallelogram...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...the other, as the remaining side of the 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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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...extreme and the other a mean: thus, if AB : BF = CD : EF, the proportion is direct. 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 ; thus in the line AB and its parts,...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...second, as the remaining side of the second is to the remaining side of the firbt. III. A straight line is said to be cut in extreme and mean ratio when tho whole is to the greater segnwut as ths greater segment is to tho less. IV. The altitude of any...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...the other, as the remaining side of the 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 College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the other, as the remaining side of the other is to the remaining side of the first.' m. 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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