 | George Lees - 1826 - 266 σελίδες
...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... | |
 | Robert Simson - 1827 - 513 σελίδες
...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... | |
 | Hirsch - 1827 - 690 σελίδες
...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... | |
 | Meyer Hirsch - 1827 - 294 σελίδες
...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... | |
 | John Playfair - 1829 - 186 σελίδες
...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... | |
 | Pierce Morton - 1830 - 584 σελίδες
...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... | |
 | John Playfair - 1832 - 333 σελίδες
...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-... | |
 | John Playfair - 1833 - 333 σελίδες
...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... | |
 | Euclides - 1834 - 518 σελίδες
...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... | |
 | 1835 - 684 σελίδες
...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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... 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. 
