 | John Keill - Logarithms - 1723 - 444 pages
...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, John Keill - Geometry - 1733 - 444 pages
...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... | |
 | Robert Simson - Trigonometry - 1762 - 488 pages
...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 - Geometry - 1765 - 492 pages
...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... | |
 | Benjamin Donne - Geometry, Plane - 1775 - 338 pages
...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... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...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... | |
 | Euclid - Geometry - 1776 - 318 pages
...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... | |
 | Euclid - 1781 - 552 pages
...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... | |
 | Euclid - Euclid's Elements - 1789 - 296 pages
...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... | |
 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...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... | |
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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. 
