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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.
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 127
των John Playfair - 1837 - 318 σελίδες
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Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With ...

Euclid, Isaac Barrow - 1714 - 536 σελίδες
...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 - 1723 - 444 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 - 280 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...

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

Euclid - 1728 - 236 σελίδες
...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 - 1733 - 444 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...

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

Euclid - 1751 - 420 σελίδες
...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...

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

Robert Simson - 1762 - 488 σελίδες
...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's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 492 σελίδες
...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 - 1772 - 462 σελίδες
...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; and becaufe BC...

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

Benjamin Donne - 1775 - 338 σελίδες
...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...