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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 23
των Euclides - 1874
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Τόμος 1

Euclides - 1868 - 88 σελίδες
...Hyp. Cone. Sap. HP 24. HypConol. D. 5. 9. Concl. Recap. PROP. XXVI. THEOR. If tu-o triangles have t\co angles of the one equal to two angles of the other, each to and one side equal to one side, viz., either the sides adjacent to the equal angles in each, or the...

The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - 1858 - 422 σελίδες
...angle in each, contained by proportional sides, are similar to each other. Any two triangles having two angles of the one equal to two angles of the other, are similar triangles, because the three angles of the one triangle are equal to the three angles of...

Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 σελίδες
...line on one side of it, either arc two right angles, or are together equal to two right angles. 2. If two triangles have two angles of the one equal...other, each to each ; and one side equal to one side, namely, either the sides adjacent to the equal angles, or the sides which are opposite to equal angles...

The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 332 σελίδες
...these shall be less than the other two sides of the triangle, but shall contain a greater angle. 5. If two triangles have two angles of the one equal...other, each to each, and one side equal to one side, namely, the sides adjacent to equal angles in each triangle ; then shall the other sides be equal,...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 σελίδες
...right angle BED is equal to the right angle B FD ; (ax. 1 1 . ) therefore the two triangles EBD, FBD have two angles of the one equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore their...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 σελίδες
...angle EBC (b) : and the angle AEG is equal to the angle BEH (a) ; therefore the triangles AEG, BEH have two angles of the one, equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another ; wherefore they have their other...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 470 σελίδες
...the |_'s PFB and PEC, we have the remaining [_'s, AFC and AEB, equal. Hence, the A's, AFC and AEB, have two angles of the one equal to two angles of the other, each to each, and the included sides equal; the remaining sides and angles are therefore equal, (Cor., Prop. 9). Therefore,...

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 σελίδες
...logical sequence would not be affected by such transposition. It might then be demonstrated as follows : If two triangles have two angles of the one equal to two angles of the other, and a side of the one equal to a corresponding side of the other; the triangles are equal in every...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...Ex. 34. — Write down the obverse of Prop. 8. From what Proposition is it an immediate inference ? PROPOSITION 26. THEOREM. If two triangles have two...other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles or sides which are opposite to equal angles in...

Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 σελίδες
...D, for this necessitates that BC < EF. AA It remains .'. that A > D. Proposition 26. (First Part.) THEOREM — If two triangles have two angles of the...equal to two angles of the other, each to each, and have likewise the two sides adjacent to these angles equal ; then the triangles are identically equal,...




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