Ancient Mathematics Question?

Question

A heap and its 1/7 part become 19. What is the heap?

Solution:
Assume 7
(Then) 1 (heap is) 7
(and) 1/7 (of the heap is) 1
(making a) Total 8
(But this is not the right answer, and therefore)
As many times as 8 must be multiplied to give 19, so many times 7 must be multiplied to give the required number.
The text then finds (by rather complicated arithmetic) the solution (7) x (19/8) = 16(5/8)

Today we would solve the problem by the equation

This question is run by the principle of proportionality.
But I cannot find out proportionlity in this question.

Running question by assuming 'sth' also seems to be strange for me. Can you help me?

Answer 1

8/7(heap)=19

8/7(heap)=19
8(heap)=7x19
heap= (7 x 19)/8 = 133/8 = 16 & 5/8


in terms of the original question
8/7(heap)=19
7/7 =heap
8 is to 19 as 7 is to heap
8/19= .421 7/.421= 16.627 or if you prefer
19/8 as heap is to t
19/8= 2.375 7 x2.375 = 16.625 = 16 & 5/8

Answer 2

(8/7) x heap = 19 which can be looked upon as the proportion of
(7/7)/([7+1]/7) = heap/19