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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. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
von John Mason Good - 1819
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 Seiten
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 Seiten
...AB, BC, a mean proportional DB is found. PROPOSITION XIV. THEOREM. 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 ; and parallelograms that have one...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...parallelogram BC. Therefore ri equai parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which haee one angle of the one equal to one angle of the other, haee their sides about the equal angles reciprocally proportional : and triangles which haee one angle...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1853
...About a given circle, to describe a triangle equiangular to a given triangle. 3. 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 figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...those angles equal which are opposite to the homologous sides, PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportional; then, if the remaining angles be each either less or...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 Seiten
...proportional DB 6 ' is found. Which was to he done. PROP. XIV. TIIEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sidei about the equal angles reciprocally proportional: and parallelograms that have one...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 Seiten
...parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. 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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General Report on Public Instruction in the Bengal Presidency

1843
...angle, and one of the other sides of a triangle are given ; construct it. 4. 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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The British Annals of Education for ...: Being The Scholastic ..., Bände 1-2

1844
...the touching line, shall be equal to the angles in the alternate segments. 12. 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. MECHANICS AND HYDROSTATICS....
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