If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. A Shorter Geometry - Page xviLimited preview - About this book
| Euclid, Isaac Barrow - Geometry - 1714 - 520 pages
...together) then is the remaining angle of the one equal to the remaining angle of the other. In like manner, **if two triangles have one angle of the one equal to one** of the other, then is the fumof the remaining angles of the one triangle equal to the fum of the remaining... | |
| Euclid, John Keill - Geometry - 1723 - 364 pages
...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... | |
| Euclid, André Tacquet - Euclid's Elements - 1727 - 239 pages
...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 - 1728
...then is the remaining Angle of the one, equal to the remaining Angle of the other. In like manner, **if two Triangles have one Angle of the one, equal to one** of the other j then is the Sum of the remaining Angles of the one Triangle, equal to the' Sum of the... | |
| Euclid, John Keill - Geometry - 1733 - 397 pages
...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 - Euclid's Elements - 1751 - 384 pages
...together) then is the remaining angle of the one equal to the remaining angle of the.other. In like manner, **if two triangles have one angle of the one equal to one** of the other, then is the fum of the remaining angles of the one triangle equal to the fum of the remaining... | |
| Robert Simson - Trigonometry - 1762 - 466 pages
...to be done. a. 1i. i. b. 31.3, Book VI. v^rvw . PROP. XIV. THE OR. "C1 QJJ AL 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 pa. rallelograms that have... | |
| Euclid - Geometry - 1765 - 464 pages
...angle at F : 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... | |
| John Keill - Geometry - 1772 - 399 pages
...that are about the equal Angles of the Triangles ABG, DEF, are reciprocal : But thofe Triangles that **have one Angle of the one equal to one Angle of the other, and the Sides about** the equal Angles reciprocal, are J equal. Therefore the Triangle t ABG is equal to the Triangle DEF;... | |
| Benjamin Donne - Geometry, Plane - 1775 - 159 pages
...the remaining 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... | |
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