...definition will satisfy one of the tests of the former. 2. Give a proof of the following proposition : " If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either less, or not less...

...mean proportional between two given straight lines. PROP. XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and conversely, parallelograms...

...shall have to the second a greater ratio than the fifth has to the sixth. 8. Equal triangles which have one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional ; and conversely. 9. If two planes...

...similar to the whole triangle and to one another. PAPERS FOE THE SCHOOLHASTEB. 2. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms...

...: A b,. that is, A c : A b : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to...about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A!' F"E" are...

...triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras...

...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. If two triangles have (!•) one angle of the one equal to one angle of the other ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third...

...equiangular to the triangle def Wherefore, if two triangles, &c. QED PROPOSITION VII. — THEOREM. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then if each of tlie remaining angles...

...triangles on each side of it arc similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms...

...proportional DB is found. Which was to be done. PROPOSITION XIV. THEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and parallelograms that have one...