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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; viz. the first six books, together with the eleventh ... - Page 138
by Euclides - 1834

Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With ...

Euclid, Isaac Barrow - Geometry - 1714 - 536 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's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - Logarithms - 1723 - 444 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...

The Elements of Euclid: With Select Theorems Out of Archimedes

Euclid, André Tacquet - Euclid's Elements - 1727 - 280 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...

Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund Stone

Euclid - 1728 - 236 pages
...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's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - Geometry - 1733 - 444 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...

Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated: with ...

Euclid - Euclid's Elements - 1751 - 420 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...

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

Euclid - Geometry - 1765 - 492 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...

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

John Keill - Geometry - 1772 - 462 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;...