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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, with the Eleventh and ... - Seite 142
von Alexander Ingram - 1799 - 351 Seiten
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 Seiten
...is found. Which was to be done. - *' ' PROP. Book VI. PROP. XIV. THEO R. EQUAL parallelograms which have one angle of the one equal to one angle of the other, have their fides about the equal angles reciprocally proportional: And parallelograms that have one...
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 326 Seiten
...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 Elements of Euclid,: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 318 Seiten
...BC : Which was to be done. PROP. XIV. and XV. THEO R. E^JJ AL parallelograms and triangles, having one angle of the one equal to one angle of the other y have the fides about the equal angles reciprocally proportional-, and theje parallelograms and triangles...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 534 Seiten
...'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 - 552 Seiten
...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 - 296 Seiten
...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...of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF be two triangles, having the angle A...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 462 Seiten
...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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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - 1804 - 468 Seiten
...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 - 530 Seiten
..."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 - 546 Seiten
...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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