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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 First Six Books: Together with the Eleventh and Twelfth - Page 170
by Euclid - 1781 - 520 pages
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Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - Dick bequest for elevating the character and position of the parochial schools and schoolmasters in the counties of Aberdeen, Banff and Moray - 1865 - 401 pages
...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...
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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...
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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...
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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,...
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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...
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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...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...the segments BG, GD, GC of the base shall be in harmonical proportion. 12. 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. ALGEBRA. 1. Prove that se и х...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...parallelogram BC. [V. 9. Wherefore, equal parallelograms &c. QED PROPOSITION 16. 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 triangles which have one angle...
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AN ELEMENTARY TREATISE ON MENSURATION

GEORGE BRUCE HALSTED - 1881
...both sides of a rectangle from their ratio m : n, and its area R. \mR Ans. n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental....
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The Cambridge Examiner, Volume 3

Education, Higher - 1883
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle...
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