Books Books 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 Books: Together with the Eleventh and Twelfth - Page 170
by Euclid - 1781 - 520 pages Report on the examination for admission to the Royal military academy at ...

...prove that the centre of the circumscribing circle is outside of the triangle. 11. 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. 12. Let ABODE be a... The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...EC. (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 reciprocallg proportional : and converselg, triangles which... Report on Education in the Parochial Schools of the Counties of Aberdeen ...

...angles." ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar polygons... The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...the equal angles reciprocally proportional, are equal to one another. Prop. 15. 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's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 504 pages A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 404 pages
...of 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 equal. 6. The circumferences of circles... The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...and shall have those angles equal about which the sides are proportionals. Let the triangles ABC, DEF have one angle of the one equal to one angle of the other, namely, the angle BA C equal to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,... The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate... Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868
...of a pair of corresponding sides involves the identity of the triangles. THEOREM 7. If two triangles have one angle of the one equal to one angle of the other; and the sides about the equal angles proportionals, then will the triangles be similar. Let the triangles... 