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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; viz. the first six books, together with the eleventh ... - Side 153
av Euclides - 1814
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 sider
...equiangular, and shall have 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 not less than a...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 sider
...the parallelogram BC. Therefore equal parallelograms, &c. QED 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 triangle* which have one angle...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 sider
...parallelogram 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 - 332 sider
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • 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 which have one...
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General Report on Public Instruction in the Bengal Presidency

1843 - 570 sider
...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 ..., Volumer 1-2

1844 - 688 sider
...this line makes with 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...proportionals, the triangles shall be equiangular. MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON, TRINITY COLLEGE. Pint Division...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 380 sider
...to DFE, and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two triangles have one angle...the sides about the equal angles proportionals; the remaining angles are equal, each to each, viz. those which are opposite to the homologous sides. Let...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 sider
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 sider
...AB, BC, a mean proportional -DB is found. QEF ^ 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 conversely, parallelograms...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 sider
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of...
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