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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 Ago ... - Page 163
by Robert Simson - 1762 - 466 pages
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportionals, and if each of the remaining angles be not less...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...2. & H. 6 22, V. 7 6, VI. 8 Sim. 9 Cone. 10 H. 11 22, V. 16, V. PROP. 7. — THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861 - 572 pages
...the other, have their sides about the equal angles reciprocally proportional, and parallelograms that 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. 9. Prove...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...isosceles triangle having each of the angles at the base one-third of the third angle. 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 ; then if each of the remaining angles be either...
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The Messenger of Mathematics, Volume 4

Mathematics - 1868 - 276 pages
...Let the lines joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have 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 the sides. Applying this to the triangles...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863 - 482 pages
...sides produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...obtuse-angled, 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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. 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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...straight lines AB, BC, & mean proportional DB is iound. QBF PROPOSITION XIV. THEOREM. Equal parallelograms which have one angle of the one equal to one angle of the other, hate their sides about the equal angles reciprocally proportional: and conversely, parallelograms that...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the equal angles shall be those which are opposite to the homologous sides. Prop. 6. 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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