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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. "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Strona 81
autor: Daniel Cresswell - 1817 - Liczba stron: 436
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - Liczba stron: 264
...BC : Which was to be done. PROP. XIV. and XV. THEO R. EQJJ . AL parallelograms and triangles, having one angle of the one equal to one angle of the other, have the ftdes about 5 the equal angles reciprocally proportional ; and thefe parallelograms and triangles...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - Liczba stron: 520
...parallelograms, &c. Q^ED PROP. Book VI. 14. r. • ..• J PRO P. XV. THEO R. QtJAL triangles which have one angle of the one equal to one angle of the other, have their fides >ut the equal angles reciprocally proportional : And Jangles which have one angle...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - Liczba stron: 272
...DEF will be equiangular with the triangle AGH (I. 7.) or ABC, as was to be fhewn. PROP. VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF be two...
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Elements of Geometry: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - Liczba stron: 400
...parallelograms, &c. a 14. i. b 7-. $• c i. 6. a ii. 5. PROP. XV. THE OR. s. .•»-*• " triangles which have- one angle of the one equal to one angle of the other, have their iides about the equal angles reciprocally proportional : And triangles which have one angle...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - Liczba stron: 351
...parallelogram BC. Therefore equal parallelograms, Sec. Q^ ED PROP. XV. THEOR. EQUAL triangles which have one angle of the one equal to one angle of the other, have their fides about the equal angles reciprocally proportional : And triangles which have one angle...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
..."parallelogram BC. Therefore equal parallelograms, &c. D. Book VI. PROP. XV. THEOR. EQUAL triangles which have one angle of the one equal to one angle of the other, have their fides 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 ...

Euclid, John Playfair - 1804 - Liczba stron: 440
...triangle DEF. Wherefore, if two triangles, fitc. Q^ ED PROP. PROP. VII. THE OR. IF two triangles have ow angle of the one equal to one angle of the other, and the fides about two other angles proportionals, then, if each of the remaining angles be either lefs,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - Liczba stron: 518
...is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QE D, PROP. VII. THEOR. See N. 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 less,...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Tom 5

John Mason Good - 1813
...a mean proportional between two given straight lines. Prop. XIV. Theor. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proport ional : and parallelograms that have one...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Tom 2

Charles Butler - 1814
...a •••• b : ai=the square of the product, wherefore ^/afc=the product. 234. Prop. 23. Hence, if two triangles have one angle of the one equal to one angle of the other, they will have to each other the ratio compounded of the ratios of the sides about their equal angles;...
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