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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: Also the Book of Euclid's Data ...cor. viz. The ... - Σελίδα 163
των Robert Simson - 1804
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

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...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If tix>o 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...

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

Pierce Morton - 1830 - 272 σελίδες
...of the ratios of the sides about the equal angles, or as the rectangles under those sides . G6 (/) Triangles which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal to one another; and, conversely,...

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 the sides...

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

John Playfair - 1832 - 333 σελίδες
...parallelogram AB is equal (9. 5.) to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which have one angle...the one equal to one angle of the other have their sides about the equal angles reciprocally proportional: Jind triangles which have one angle in the...

Library of Useful Knowledge: Natural philosophy, Τόμος 3

1834
...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 one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently...

The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 σελίδες
...the parallelogram AB is equal ° to the parallelogram BC. Therefore, " equal parallelograms" &c. QED Book VI. PROP. XV. THEOR. , — • — ' Equal triangles...the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the...

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

1835
...the altitude of the first, the two triangles will be equal to one another (11. Cor. 2.). PROP. 40. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles....

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

Euclid - 1835 - 513 σελίδες
...other, have their sides about the equal angles reciprocally proportional : And parallelograms that 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. Let AB,...

Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - 1836 - 220 σελίδες
...Multiply these equal ratios, and there will result ABС:DEF::AС.BG: DF.EH(th.T). THEOREM XXIV. 69. Two triangles which have one angle of the one equal to one angle of the other, are proportional to the products of the sides which contain those angles. E в Let AB С, DEF be two...

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

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...of the other, have their sides about the equal angles reciprocally proportional : And parallelograms 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. XV. Equal...




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