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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 ... - Σελίδα 156
των Robert Simson - 1781 - 466 σελίδες
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 364 σελίδες
...reci frotalt are equal between themfelves. if - • • . * • T ET the equal Triangles ABC, ADE, have one •*-' Angle of the one equal to one Angle of the other, viz the Angle BAC equal to the Angle DAE. I lay the Sides about the equal Angles are reciprocal, th.it...

The Elements of Euclid: With Select Theorems Out of Archimedes

Euclid, André Tacquet - 1727 - 239 σελίδες
...the firft Part. i PROP. XXVI. Theorem. IF two Triangles (XandZ) have two Angles equal&g. 2;. to two, one Angle of the one equal to one Angle of the other ( B to F and C to /), and one Side of one Equal to one of the other, whether it be that •which is...

Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - 1733 - 393 σελίδες
...is equal to the Angle GFL ; and BA is to AE, as GF is to F L. Therefore the two Triangles BAE, GFL, have one Angle of the one equal to one Angle of the other, viz. the Angle BAE equal to the Angle GFL, and the Sides about the equal Angles proportional. Wherefore...

Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 σελίδες
...and accordingly the triangles ABC, DBF are equiangular. . .v : ... .- ..: If therefore two triangles have one angle of the one equal ,to one angle of the othsr, and the fides about two other angles proportional, and have alfo each of the remaining angles...

The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - 1775 - 159 σελίδες
...Angle in one is equal to the remaining Angle in the other Triangle. 8 1. Co ROLL. 3. If two Triangles have one Angle of the one equal to one Angle of the other, then the Sum of the two remaining Angles of one Triangle is equal to the Sum of the two remaining Angles...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 σελίδες
...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...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...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...

Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 272 σελίδες
...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, having...

Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - 400 σελίδες
...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...

The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 σελίδες
...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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