...reciprocally proportional : And 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. Let AB, BC be equal parallelograms, which have the angles at B equal,, and let the sides DB, BE be...

...and have those angles equal about tnhich 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...

...reciprocally proportional: and parallelograms that have one angle of the o.he equal to one angle of the o(hsr, and their sides about the equal angles reciprocally proportional are equal to one another. Let AB,BCbe equal parallelograms, which have the anglesat B equal, and let the sides DB, BE be placed...

...equiangular, and have those angles equal about which the tides art proportionals. Let the triangle« ABC, DEF have one angle in the one equal to one angle in the other, riz. the angle ВАС to the angle EDF, and the sides about two other angles ABC, DEF, proportional!!,...

...of the other have their sides about the equal angles reeiproeally proportional : And triangles whieh have one angle in the one equal to one angle in the other, and their sides about the equal angles reeiproeally proportional, are equal to one another. Let ABC, ADE be equal triangles, whieh have the...

...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...

...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...

...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...

...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...

...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...