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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 165
von Robert Simson - 1806 - 518 Seiten
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 540 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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Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - 399 Seiten
...Angle of the other, have the Sides *ibout the equal Angles reciprocal; and tbofe Parallelograms that have one Angle of the one equal to one Angle of the other, and the Sides that are about the equal Angles reciprO' tal, are equal. TETAB, BC, be equal Parallelograms, having...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 298 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 one angle of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF be two triangles,...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - 444 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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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 Seiten
...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 ...

John Playfair - 1804 - 470 Seiten
...ABC is equiangular 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
...Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore if the fides, &c. C^E. JJ, a. 33, PROP. VI. THEOR. IF two triangles have one angle of the one eqoal to one angle of the other, and the fides abou; the equal angles proportionals, the triangles...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 Seiten
...Wherefore, if two triangles, &c. QED PROP. VII. THEOR. Book vi. IF two triangles have one angle of one equal to one angle of the other, and the sides about two other angles proportional ; and if each of the remaining angles be either less, or not less, than...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 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 ..., Band 2

Charles Butler - 1814 - 528 Seiten
...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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