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" ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another. "
The Elements of Euclid, containing the first six books, with a selection of ... - Seite 209
von Euclides - 1874
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 Seiten
...angle ACB equal to DFE. Wherefore, if the sides, &c. QED , . , ; PROP. VI. THEOREM. If two triangles have one angle in the one, equal to one angle in the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 Seiten
...shall have those angles equal about which the sides are proportionals. Let the two triangles ABC, DEF have one angle in the one equal to one angle in the other, viz, the angle BAC to the angle EDF, and the sides about two other angles ABC, DEF proportionals, so...
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Hirsch's Collection of Examples Formulae and Calculations on the Literal ...

Hirsch - 1827 - 690 Seiten
...Д ABC = • 2 ab Sin. л or q =• Сок. 1. Hence it follows : that two triangles, which contain one angle in the one equal to one angle in the other, are as the products of the sides which include these triangles. Since every parallelogram is divided...
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Hirsch's Geometry: Or, A Sequel to Euclid

Meyer Hirsch - 1827 - 288 Seiten
...Therefore AABC=2 ab Sin. a ОГ q — COR.'l. Hence it follows : that two triangles, which contain one angle in the one equal to one angle in the other, are as the products of the sides which include these triangles. Since every parallelogram is divided...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 Seiten
...proportional ; and parallelograms, and also • triangles, which have one angle of one equal to one angle of the other, and their sides about the equal angles...reciprocally proportional, are equal to one another. In a right angled triangle if a perpendicular be drawn from the right angle to the hypothenuse, it...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 Seiten
...it may be shown, that any two parallelograms which have one angle of the one equal to one angle of the other, and their sides about the equal angles...reciprocally proportional, are equal to one another ; and conversely. For, if the equal angles be placed vertically as in the figure, and the parallelogram...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 358 Seiten
...of the other have their sides about the equal angles reciprocally proportional: Jind triangles which have one angle in the one equal to one angle in the...ABC, ADE be equal triangles, which have the angle BAG equal to the angle DAE: the sides about the equal angles of the triangles are reciprocally proportion-...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 346 Seiten
...the other have their sides about the equal angles reciprocally proportiontil : And triangles which have one angle in the one equal to one angle in the...and their sides about the equal angles reciprocally pro~ fortional, are equal t<f one another. Let ABC, ADE be equal triangles, which have the angle BAC...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 Seiten
...to one another. Let ABC, ADE be equal triangles, which have the angle BAC equal to the angle DAE : the sides about the equal angles of the triangles...reciprocally proportional ; that is, CA shall be to AD, as EA to AB. Let the triangles be placed so that their sides CA, AD be in one straight line ; wheret...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 Seiten
...angles (37.). PROP. 41. (Eue. vi. 15.) Triangles which have .one angle of the one equal to one angle of the other, and their sides about the equal angles...reciprocally proportional, are equal to one another ; and, conversely, equal triangles which have one angle of the one equal to one angle of the other,...
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