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" AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. "
The First Six Books: Together with the Eleventh and Twelfth - Page 167
by Euclid - 1781 - 520 pages
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...draw a straight line AC making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off A from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...draw a straight line AC making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off A from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...required, Let AB be the given straight line; it is required to cut off any part from it. part which U to be cut off from it; join BC, and draw DE parallel to CB: then AE shall be the part required to be cut off Because ED is parallel to BC, one of the sides...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...; and in AC take any point D, and take AC such that it shall contain AD, as oft as AB is to contain the part, which is to be cut off from it ; join BC,...to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the 17 B c DA : DC (4. 6.) BA : BD (46.) CA : CD (46.)....
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...draw a straight line AC, making any angle with AB ; and in AC take any point D, and take A c the same multiple of AD, that AB is of the part which is to be cut off from it ; join B, c, and draw DE parallel to it (31. 1.) : then AE is the part required to be cut off. ' " " Because...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the / same multiple of AD, that AB is of the part which is to...to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so * 2....
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to...cut off from it ; join BC, and draw DE parallel to CB. Then AE shall be the part required to be cut off. Because ED is parallel to BC, one of the sides...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...it. Draw a straight line AC making any angle with AB ; in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it ; .join BC, and (I. 31) draw DE parallel to it: AE is the part required. Because ED isparallel to BC, one of the sides...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...a straight line AC, making any angle with A. 13 ; and in AC take any point D, and take AC the same multiple of AD that AB is of the part which is to...DE parallel to it : then AE is the part required. For, because ED is parallel to BC, one of the sides of the triangle ABC, therefore BE is to EA as CD...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...; and in AC take any point D, and take AC such that it shall contain AD, as oft as AB is to contain the part, which is to be cut off from it ; join BC,...to it: then AE is the part required to be cut off. 130 triangle ABC, viz. to BC, CD : DA : : BE : EA (2. 6.) ; and by composition (18. 5), CA : AD : :...
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