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" If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Σελίδα 66
των John Keill - 1733 - 397 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

The Practical Teacher, Τόμος 2

1883
...coincide with the vertex of the given angle and then the construction would fail. 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz., either the sides adjacent to the equal angles in...

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

Euclid, Isaac Todhunter - 1883 - 400 σελίδες
...I. n ; and therefore EF is less than EG. I. 26. It will appear after I. 32 that two triangles which have two angles of the one equal to two angles of the other, each to each, have also their third angles equal. Hence we are able to include thu two cases of I....

Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...[Alternative proofs, (i) by Theors. 16 and 5. (ii) By Theors. 7 and 5.] THEOR. 19. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides opposite to one pair of equal angles equal, then the triangles...

The Eclectic School Geometry: A Revision of Evan's School Geometry

Evan Wilhelm Evans - 1884 - 155 σελίδες
...angles are equal. But the angle A is common to the two triangles BAD and BAC. Hence, these triangles have two angles of the one equal to two angles of the other, and are consequently similar (Cor., Theo. IX). Therefore, Cor.—If from a point without a circle a secant...

The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884
...sixteenth, it would be a proof of both the sixteenth and seventeenth. It shows us that, if two triangles have two angles of the one equal to two angles of the other, each to each or together, their third angles are also equal. The corollaries to this proposition are...

An introduction to geometry, consisting of Euclid's Elements, book ..., Τόμος 1

Euclides - 1884
...which is the greater of the angles R and V. TV 65. PROPOSITION XXVI. — THEOREM. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles...

Questions and exercises in elementary mathematics

Palaestra Oxoniensis - 1884
...three given straight lines, of which any two are together greater than the third. (5) If two triangles have two angles of the one equal to two angles of the other, each to each, and have one side equal to one side, viz. either the sides adjacent to the equal angles...

The Eclectic School Geometry

Evan Wilhelm Evans - 1884 - 149 σελίδες
...angles A and B by AF and BF, and the angles a and 6 by af and bf. Now, since the triangles ABF, abf, have two angles of the one equal to two angles of the other, they are similar (Cor., Theo. IX) ; hence, ABF : abf= AB2 : o&2 (Theo. XIV). Multiplying first couplet...

Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884
...another. What other converse proposition may be obtained from Proposition V., Book I.? 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, namely, the sides opposite to the equal angles in each,...

The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...such that AB is equal to AC, and AD to AE : shew that BE is equal to CD. THEOR. 6. If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the sides between the vertices of these angles equal, then the triangles...




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