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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. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 127
των John Playfair - 1837 - 318 σελίδες
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...to FE so is вс to FE, therefore the parallelogram AB is equal to PROPOSITION XV. THEOREM. If equal triangles have one angle of the one equal to one angle of the other, the sides about the equal angles are reciprocally proportional; and if triangles have one angle of...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...the parallelogram ac.d Therefore if equal parallelograms, &C. QED PROPOSITION XV. THEOREM. If equal triangles have one angle of the one equal to one angle of the other, the sides about the equal angles are reciprocally proportional ; and if triangles have one angle of...

Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...the other, have their sides about the equal angles reciprocally proportional ; and 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 equivalent. Let the triangles be...

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

Euclid, John Playfair - 1826 - 320 σελίδες
...a mean proportional DB is found. Whieh was to be done. PROP. XIV. THEOR. Equal parallelograms whieh have one angle of the one equal to one angle of the pther, have their sides about the equal angles reeiproeally proportional : And parallelograms whieh...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...parallelogram BC. Therefore equal pa- * 9' 5rallelograms, &c. QED PROP. XV. THEOR. • 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 whichhave one angle...

Natural Philosophy: With an Explanation of Scientific Terms, and an ..., Τόμος 3

1829
...: A b, that is, A c : Ab : : 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: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...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 ...

Pierce Morton - 1830 - 272 σελίδες
...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 ...

John Martin Frederick Wright - 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...

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

John Playfair - 1833 - 333 σελίδες
...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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