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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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...(vi. def. 1) ; for the same reason the parallelogram ab С d is similar to the parallelogram fh С k. Wherefore each of the parallelograms ge, kh is similar...rectilineal figure are also similar to one another (vi. 21) ; therefore the parallelogram ge is similar to k h. Wherefore the parallelogram, &c. QED PBOPOSITION...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...first, to a similar and similarly described rectilineal figure upon the second PROPOSITION XXI. THEOB. Rectilineal figures, which are similar to the same...rectilineal figure, are also similar to one another. Let each of the rectilineal figures A, B be similar to the rectilineal figure C : the figure A is similar...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...AEFG ahout the equal angles are proportionals; and they are therefore similar to one another (e) ; and for the same reason, the parallelogram ABCD is similar...each of the parallelograms GE, KH, is similar to DB ; hut rectilineal figures which are similar to the same rectilineal figure are also similar to one...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...about the equal angles are proportionals ; and they are therefore similar to one another; (YI. def. 1.) for the same reason, the parallelogram ABCD is similar...parallelogram FHCK: wherefore each of the parallelograms GE, KHis similar to DB : but rectilineal figures which are similar to the same rectilineal figure, are...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...about the equal angles are proportionals ; and they are therefore similar to one another (e) ; and for the same reason, the parallelogram ABCD is similar to the parallelogram FHCK. Wherefore each of the parablelograms GE, KH, is similar to DB ; but rectilineal figures which are similar to the same rectilineal...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...angles are proportionals ; and they are therefore similar to one another (VI. Def. 9) ; for a like reason the parallelogram ABCD is similar to the parallelogram FHCK ; wherefore each of the parallelograms GE and KH is similar to DB; but rectilineal figures which are similar to the same rectilineal figure are...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...60 yards ? 7500 X 60X60 270000 The Area x = • ^ ^ = — ~ = Ю800 sq. yards. PROP. 21. — THEOn. Rectilineal figures which are similar to the same...rectilineal figure, are also similar to one another. DEM. Def 1, VI. Ax. 1, I. 11, V. Sen. This proposition follows evidently from Def. 1, VI., of similar...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 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...parallelogram FHCK: wherefore each of the parallelograms GE, KH\s similar to DB: but rectilineal figures which are similar to the same rectilineal figure, are also...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...AEFG about the equal angles are proportionals. and they are similar to one another ; (vi. def. 1.) For the same reason, the parallelogram ABCD is similar...FHCK ; wherefore each of the parallelograms GE, KH u similar to DB ; lint rectilineal figures which are similar to the same rectilineal figure, are also...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 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 FlICK: wherefore each of the parallelograms GE, KHis similar to DB: but rectilineal figures which are...
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