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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: The Errors by which Theon, Or Others, Have Long ... - Page 141
by Robert Simson - 1827 - 513 pages
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The Quarterly Journal of Pure and Applied Mathematics, Volume 11

Mathematics - 1871 - 420 pages
...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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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volume 3

1858 - 398 pages
...I. — 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...equal which are opposite to the homologous sides. 7. PROP. XVIII. — Upon a given straight line to describe a rectilineal figure similar, and similarly...
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 694 pages
...I. — 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...equal which are opposite to the homologous sides. 7. PROP. XVin. — Upon a given straight line to describe a rectilineal figure similar, and similarly...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 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 - 672 pages
...the pound 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 angle, the...
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Parliamentary Papers, Volume 7

Great Britain. Parliament. House of Commons - Bills, Legislative - 1859 - 140 pages
...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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Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860 - 154 pages
...I. — Triangles of the same altitude are one to the other as their bases. fi. PROP. VI. — If two triangles have one angle of the one equal to one angle...equal which are opposite to the homologous sides. 7. PROP. XVIII. — Upon a given straight line to describe a rectilineal figure similar, and similarly...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...rectangle contained by the sides about the other, the triangles are equal. (ii.) Conversely: — If two triangles have one angle of the one equal to one angle of the other, the rectangle contained by the sides about one of those angles is equal to the rectangle contained...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
....-. a AC = a BF. (/3) is true. EUCLID Proposition 15. THEOREMS — (a) Triangles of equal area which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...the line joining two alternate vertices of a given length. 7. Prove that 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. 8. In a right-angled triangle, show...
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