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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. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Side 247
av Euclid - 1765 - 464 sider
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 466 sider
...'Wherefore if two triangles, &c. Q._ ED 4. 6. ii. i. f- y- i. T •*, , Book VI. PROP. VII. THEO R. riangles have one 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, or not lefs than...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 sider
...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 - 272 sider
...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...and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF be two triangles, having the angle A equal to the angle...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 sider
...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 - 351 sider
...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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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 sider
...to the triangle DEF. Wherefore, if the fides, &c. <ED b 32. i. c4.<f. fS. I. S4-i' PROP. VI. THEOR. IF two triangles have one angle of the one equal to one angle of the other, and the lides about the equal angles proportionals, the triangles fball be equiangular, and fhall have thofe...
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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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 sider
...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, or...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 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 ..., Volum 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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