| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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-... | |
| 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... | |
| 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... | |
| 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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