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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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National Society's Monthly Paper

1855
...the hase shall have the same ratio which the other sides of thi; triangle have. 2. 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 bhall be equiangular, and shall have...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of the...
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The Calendar of King's College, London

1857
...and the angle in a segment less than a semicircle is greater than a right angle. 9. 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 shall be equiangular, and shall have...
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The Quarterly Journal of Pure and Applied Mathematics

Mathematics - 1871
...the proposition and reduces it to a case of ambiguous equality. Let the triangles ABC, DEF (fig. 9) have one angle of the one equal to one angle of the other; namely, L ВАС = DEF, and the sides about two other angles ABC, EDF proportionals, so that AB :...
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The Educational record, with the proceedings at large of the ..., Volumes 3-4

British and foreign school society - 1857
...are due to the eighteenth century? HIGHER MATHEMATICS AND MATHEMATICAL PHfSCg. 1. If two triangles have one angle of the one equal to one angle of the other atid the sides "aboiift two other angles proportional ; then if each of the remaining angles be less...
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858
...Triangles of the same altitude are one to the other as their bases. 6. PROP. VI. — 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 shall be equiangular, and shall have...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 12 pages
...the angles at the base double of the third angle. 8 DIRECT COMMISSIONS. 2. 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. Show also how this follows from...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...is the income tax.? 10. Extract the square root of 6575-5881. Voluntary Portion. 2. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, each of the remaining angles being greater than a right...
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Parliamentary Papers, Volume 7

Great Britain. Parliament. House of Commons - Bills, Legislative - 1859
...a given circle, first, a regular hexagon ; secondly, a regular pentagon. 18. 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. 19. Investigate a trigonometrical...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...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 ;...the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Given two equal parallelograms...
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