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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 Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 199
των Euclides - 1874
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...Wherefore, if the sides &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of one triangle equal to one angle of the other, and the sides about the equal angles proportional, the triangles will he equiangular, and will have those angles equal which are opposite...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...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 (j) Two triangles are similar,...

A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 σελίδες
...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...

Library of Useful Knowledge: Natural philosophy, Τόμος 3

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...: 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...about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A" F'E" are so...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 σελίδες
...to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of the one equal to...equal angles proportionals, the triangles shall be eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the...

Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

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...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,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...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...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

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...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...

The Element of Geometry

John Playfair - 1836 - 114 σελίδες
...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...