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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: With Select Theorems Out of Archimedes - Σελίδα 21
των Euclid, André Tacquet - 1727 - 239 σελίδες
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## Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 444 σελίδες
...confequently the Triangle ABC is equiangular to the Triangle DEF. Therefore if there are two Triangles having one Angle of the one, equal to 'one Angle of the other, and the Sides about other Angles proportional; and if the remaining third Angles are either both, left,...

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

Euclid, John Keill - 1733 - 444 σελίδες
...the equal Angles reciprocal, ere equal between tbfmfeives. LET the equal Triangles AB C, AD E, have one Angle of the one equal to one Angle of the other, viz. the Angle BAG equal to the Angle DAE. I fay the Sides about the equal Angles are reciprocal, that...

## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 488 σελίδες
...Therefore equal parallelograms, &c. Q^ED PROP, Book VI. PRO P. XV. THEO R. LJ AL 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...

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

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...are equal to one another. Which was to be demonftrated. PRO P. XV. THEO R. If equal triangles ha'je one angle of the one equal to one angle of the other ; the fides about the equal angles will he reciprocally proportional : and if triangles have one angle...

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

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...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 ...

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...triangle DEF. Wherefore, if the fides, &c. QED PKOP. Book VI. PRO P. VI. THEO R. TF two triangles have one angle of the one equal to one angle of the other, and the ftdes about the equal angles proportionals, the triangles Shall be equiangular, and fhall have...

## The Elements of Euclid,: In which the Propositions are Demonstrated in a New ...

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...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...

## The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 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 ...

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...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...

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

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...triangle DEF. Wherefore, if two triangles, &c. Q^ E. D f PROF. PROP. VII. THEO R. IF two triangles 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...