I've seen numerous explanation of why two negatives make a positive and I did understand most of them. Now, I found the following explanation :
If now we consider the product arising from the multiplication of the two quantities $a-b$, and $c - d$, we know that it is less than that of $(a-b)\times c$, or of $ac-bc$; in short, from this product we must subtract that of $(a - b) \times d$; but the product $(a - b)\times(c - d)$ becomes $ac-bc-ad$, together with the product of $-b\times-d$ annexed; and the question is only what sign we must employ for this purpose, whether $+$ or $-$. Now we have seen that from the product $ac-bc$ we must subtract the product of $(a-b)\times d$, that is, we must subtract a quantity less than $ad$; ◈ we have therefore subtracted already too much by the quantity $bd$; this product must therefore be added; that is, it must have the sign $+$ prefixed; hence we see that $-b\times-d$ gives $+bd$ for a product; or $-$ minus multiplied by $-$ minus gives $+$ plus.
The ◈ mark is the part where I'm not having the same conclusion... Does it seem convincing to you or valid ?
If so, could you rephrase it or explain it for me?? I'm not sure of following why this is THE conclusion!Thank you!