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" IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Page 161
by John Keill - 1733 - 397 pages
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Woolwich mathematical papers [aftwerw.] Mathematical papers for admission ...

Woolwich roy. military acad - 1884
...angle ECD is equal to CED, CD will touch the circle described about ACB. ro. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular to one another,...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...same ratio are equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. £ B = £ G, and AB : BC :...
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...circles from' any point \n Afí produced aro equal to one another. 9. Equal parallelograms, which have one angle of the one equal to one angle of the other, havo their eidos about the equal angles reciprocally proportional. FRIDAY, October 10, 1884. О—1Ц....
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 pages
...same ratio are equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. £ B = $. G, and AB : BC :...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888
...angles at A, B, C respectively equal to the angles at D, E, FV i. QED THEOR. 5. If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite the equal angles...
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Annual Report of the Schools of New Brunswick

New Brunswick. Board of Education - Education - 1889
...Parallelograms of the same altitude are to one another as their bases. 6. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about 'the equal angles reciprocally proportional. NB — Female candidates will receive credit for any correct work on the...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889
...their sides about the equal angles reciprocally proportional ; and, conversely, triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. n. From...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890
...the base. What is the corresponding proposition for the external bisector ? 8. Triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides about the equal angles. 9....
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pages
...the construction. 5. Show how to describe a circle about a given triangle. 6. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular to one another,...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...ABC, DEF are equiang. to each other, and /. simr. Proposition 7. THEOREM — If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite the equal angles...
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