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" AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 136
by John Playfair - 1844 - 317 pages
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Annual Report

Canada. Department of the Interior - 1888 - 756 pages
...a given rectilineal angle. 5. From a given straight line oat off any part required. < 6. Show that rectilineal figures which are similar to the same...rectilineal figure, are also similar to one another, 7. Describe a rhombus which shall be equal to any quadrilateral figure. 8. Show that if the sum of...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...to the two A s into which the whole trapezoid is divided by either diagl. PROPOSITION 21. THEOREM. Rectilineal figures which are similar to the same...rectilineal figure are also similar to one another. Let each of the rectl. figs. H, h be similar to the rectl. fig. X ; they shall be similar to one another....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...figures and therefore are to one another in the duplicate ratio of their sides. PROPOSITION 21. THEOREM. Rectilineal figures which are similar to the same rectilineal figure, are also similar to each other. Let each of the rectilineal figures A and B be similar to C: then shall A be similar to...
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Books 3-9

Euclid - Mathematics, Greek - 1908 - 456 pages
...described on the first be to the similar and similarly described figure on the second." PROPOSITION 2i. Figures which are similar to the same rectilineal figure are also similar to one another. For let each of the rectilineal figures A, B be similar to C; I say that A is also similar to B. For,...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...porism is standard. For the proof Ricci & Xu refer to the proof of the previous theorem (19): Heath Figures which are similar to the same rectilineal figure are also similar to one another. (If two rectilineal figures each are similar to another rectilineal figure, then they are similar to...
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The Thirteen Books of Euclid's Elements

Euclid - 452 pages
...described on the first be to the similar and similarly described figure on the second." PROPOSITION 21. Figures which are similar to the same rectilineal figure are also similar to one another. For, since A is similar to C, it is equiangular with it and has the sides about the equal angles proportional....
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