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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.
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 22
by John Mason Good - 1819

## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — 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 remaining angles are equal, each to each, viz....

## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...(v.9-) Therefore equal parallelograms, &c. QED PROPOSITION XV. THEOREM. 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 conversely, triangles which...

## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...proportional DB is found. Which was to be done. PROPOSITION 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...

## A system of practical mathematics; being no.xvi. of a new series of school-books

...and second terms AABD, we have AABC : ADBE=AB'BC : DB-BE, (Alg. 116) Cor. Parallelograms 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....

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

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...angles reciprocally proportional ; And triangles which have one angle in the one equal to one angle t'a the other, and their sides about the equal angles...reciprocally proportional, are equal to one another. Let ABC, ADE be equal triangles, which have the angle BAC equal to the angle DAE : the sides about...

## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3....

## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...a mean proportional DB has been found. O..E. p. 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, which have...

## A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 80 pages
...than the sum of the two sides by the diameter of the inscribed circle. 23. If two triangles have an angle of the one equal to one angle of the other, and also another angle of the one equal to the supplement of another angle of the other, the sides about...