...lines, to find the ratio which is its sub-duplicate, or the ratio of which it is duplicate. PROPOSITION 14. In equal and equiangular parallelograms the sides...equal angles are reciprocally proportional are equal. Let AB, BC be equal and equiangular parallelograms having the angles at B equal, and let DB, BE be...

...square on it is also equal to BD ; therefore BD is equal to GF. But it is also equiangular with it ; and in equal and equiangular parallelograms the sides...about the equal angles are reciprocally proportional ; [vi. 14] therefore, proportionally, as BC is to EG, so is EF to CD. Therefore also, as the square...

...contained) by CD and E. For CH (is) equal to E. BG is thus equal to DH. And they are equiangular. And for equal and equiangular parallelograms, the sides about the equal angles are reciprocally proportional [Prop. 6.14]. Thus, as AB is to CD, so С H (is) to AG. And С H (is) equal to E, and AG to F. Thus,...

...the mean proportional between its parts) This theorem was taken from Peletarius by Clavius (p. 258) 14. In equal and equiangular parallelograms the sides...equal angles are reciprocally proportional are equal. (If two parallelograms are equal and also one angle is equal, then the two sides about the equal angle...

...square on it is also equal to BD ; therefore BD is equal to GF. But it is also equiangular with it ; and in equal and equiangular parallelograms the sides...about the equal angles are reciprocally proportional ; [vi. 14] therefore, p-opcrtionally, as BC is to EG, so is EF to CD. Therefore also, as the square...

...rectangle CD, E is DH, for CH is equal to E, therefore BG is equal to DH. And they are equiangular But in equal and equiangular parallelograms the sides...about the equal angles are reciprocally proportional. [vi. 14] Therefore, as AB is to CD, so is CH to AG. But CH is equal to E, and AG to F; therefore, as...