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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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...first to a similar and similarly described rectilineal figure on the second. 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 the rectilineal figure C: the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...about their equal angles are proportional, and the parallelograms are therefore similar to one another. For the same reason the parallelogram ABCD is similar to the parallelogram FHCK. Therefore each of the parallelograms EG and HK is similar to BD ; therefore the parallelogram EG is...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...about the equal angles are proportionals ; and they are therefore similar to one another; (VI. def. 1.) for the same reason, the parallelogram ABCD is similar to the parallelogram FUCK: wherefore each of the parallelograms GE, Kffis similar to DB: but rectilineal figures which are...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...the > equal angles are proportionals ; and they are therefore similar to one another (VI. Def. 1). For the same reason, the parallelogram ABCD is similar to the parallelogram FHCK; wherefore 6. Each of the parallelograms GE, KH is similar to DB ; but rectilineal figures which are similar to...
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The Elements of Euclid, with Many Additional Propositions and Explanatory ...

Euclid - 1876 - 240 pages
...about the equal angles are proportionals ; and they are therefore similar to one another () ; and for the same reason, the parallelogram ABCD is similar...rectilineal figure are also similar to one another (/) ; therefore the parallelogram, GE is similar to KH. PROPOSITION XXV. PROBLEM. To construct a rectilineal...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...about the equal angles are proportionals ; and they are therefore similar to one another; (vi. def. 1.) for the same reason, the parallelogram ABCD is similar...rectilineal figure, are also similar to one another: (vi. 21.) therefore the parallelogram GE is similar to KH. Wherefore, parallelograms, &c. QED PROPOSITION...
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Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi ...

James Hamblin Smith - Euclid's Elements - 1879 - 378 pages
...shall be to a given triangle in a given ratio. PROPOSITION XX. THEOREM. (EucL vi. 21.) Rectilinear figures, which are similar to the same rectilineal figure, are also similar to each other. B Let each of the rectilinear figures A and B be similar to the rectilinear figure C. Then...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...first to a similar and similarly described rectilineal figure on the second. PROPOSITION 21. THEOREM. Rectilineal figures which are similar to the same rectilineal figure, are also similar to each other. Let each of tho rectilineal figures A and B bo similar to the rectilineal figure C: the...
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The Cambridge Examiner, Volume 4

Education, Higher - 1884 - 538 pages
...equiangular to one another, and shall have these angles equal which are opposite to the homologous sides. 15. Rectilineal figures which are similar to the same rectilineal figure, are also similar to each other. 16. From the same point in a given plane, there cannot be two straight lines at right angles...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...about their equal angles are proportional, and the parallelograms are therefore similar to one another. For the same reason the parallelogram ABCD is similar to the parallelogram FHCK. Therefore each of the parallelograms EG and HK is similar to BD ; therefore theparallelogram EG is...
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