Newton's Principia is published as three books. The proposition, Proposition IV Problem II, I will discuss is in Book II, which is about the motion of bodies. However, Newton's first concept of the Principia did not include Book II. The original Book II was an early form of the Liber Tertius of the Principia. |

On 1st March 1686/7, Newton wrote to Halley, who was in charge of priniting the Principia, to announce that he was sending Book II. The following is what Newton said in the letter: |

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ You'll receive the 2nd book on Thursday night or Friday
by the coach. I have directed it to be left with Mr. Hunt at Gresham Coll.
Pray let me beg the favour of a line or two know of the receipt. I am
obliged to you for pushing on the edition, because of people's expextation,
tho' otherwise I could be as well satisfied to let it rest a year or two
longer. 'Tis a double favour, that you are pleased to double your pains
about it. Dr. Wallis's papers may be long, and I would not give you the
trouble of transcribing them all. The heads may suffice. The resistance,
in swift motions, is in a duplicate proportion to the celerity. The deduction
of the sun's parallax from the moon's variation, I cannot promise now
to consider. When astronomers have examined whether there be such an inequality
of her motion in the quadratures, as I mentioned in my last, and detemined
the quantity thereof, I may take some occasion perhaps to tell them the
reason. No more at present from |

From the letter, we know that there was a great expectation to Newton's mathematical work. However, in those days, the book-sellers were very unwilling to take the risk of publishing mathematical works. Therefore, only small amount of copies were published. And only small amount of people bought this book. |

Although publishing mathematical books were not
a profitable business, Halley still supported Newton to publish his Principia.
And it was lucky that Halley actually did so for us to have a complete copy
of Principia nowadays. |