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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 First Six Books: Together with the Eleventh and Twelfth - Seite 160
von Euclid - 1781 - 520 Seiten
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 364 Seiten
...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...
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The Elements of Euclid: With Select Theorems Out of Archimedes

Euclid, André Tacquet - 1727 - 239 Seiten
...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...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1733 - 397 Seiten
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 Seiten
...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...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid, Edmund Stone - 1765 - 464 Seiten
...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...
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The Geometrician: Containing Essays on Plane Geometry, and Trigonometry ...

Benjamin Donne - 1775 - 159 Seiten
...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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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 Seiten
...is found. Which was to be done. - *' ' PROP. Book VI. PROP. XIV. THEO R. EQUAL 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 parallelograms that have one...
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 264 Seiten
...BC : Which was to be done. PROP. XIV. and XV. THEO R. EQJJ . AL parallelograms and triangles, having one angle of the one equal to one angle of the other, have the ftdes about 5 the equal angles reciprocally proportional ; and thefe parallelograms and triangles...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1781 - 466 Seiten
...BC, a mean proportional DB is found.' Which was to be done. Book VI. I^XYX^ PROP. XIV. THE OR. EOU AL parallelograms which have one angle of the one equal...the one equal to one angle of the other, and their fidesabout the equal angles reciprocally proportional, arc equal to one another. Let AB, BC be equal...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - 399 Seiten
...the one equal to one Angle of the other, have the Sides *ibout the equal Angles reciprocal; and tbofe Parallelograms that have one Angle of the one equal to one Angle of the other, and the Sides that are about the equal Angles reciprO' tal, are equal. TETAB, BC, be equal Parallelograms,...
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