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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 143
by Euclid, James Thomson - 1837 - 390 pages
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A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - Astronomy - 1831
...Ratios that are the same to the same ratio, are the same to one another. 13. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. M. In a plane triangle, of which...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then, if each of the remaining angles...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...is equiangular to the triangle DEF. Wherefore, if the sides, &c. <?. /.•./,. ' n. . 'PROPOSITION VI. THEOR. — If two triangles have one angle of...the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the funuologous...
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Library of Useful Knowledge: Natural philosophy, Volume 3

1834
...: A b, that is, A c : A 6 : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to...the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A"...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...equiangular to the triangle DEF. Wherefore, " if the sides," &c. QED Book VI. PROP. VI. THEOR. v— v—' If two triangles have one angle of the one equal to...the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . .66 (g) Two triangles are similar,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...DB is found. Which was to be done. a 11. 1. b 31. 3. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And parallelograms that have one...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...a mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...about the equal angles reciprocally proportional, are equal to one another. XV. 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 : And triangles which have one angle...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...lines AB, BC, a mean proportional DB is found. PROPOSITION XIV. THEOREM. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one...
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