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1. □HA=bb+dd as above.
2 Putting x for NO, as sought, we may infer from a new Property of the Parabola, which we have demonstrated Prop. 6. lib. 2
as L to NO so OR to AO, i. e. (putting a for BA or FO given; that NO−OF i. e. NF or OR shall be = x−a) as L to x so x−a to 〈 math 〉〈 math 〉 = AO.
Therefore having substracted AD i. e. b from AO, you'l have DO or HP = 〈 math 〉〈 math 〉; whose □ is
〈 math 〉〈 math 〉.
But PN also is = NO−PO or HD, = x−d is = 〈 math 〉〈 math 〉.
Therefore having added the □ □ PH and PN, there will come out □ HN 〈 math 〉〈 math 〉, = □ HA i. i. bb+dd; and taking away from both sides 〈 math 〉〈 math 〉; and multiplying every where by L{powerof2} and diving by 〈 math 〉〈 math 〉.
3. And now comparing this Equation with another form, which shall be like an Equation arising from the Solution of some Problem, e. g. with this 〈 math 〉〈 math 〉; to this you'l have = this other, 〈 math 〉〈 math 〉.
4. Wherefore, because in these equal forms, first, 2a is = p, a will be = 〈 math 〉〈 math 〉 i. e. the line BA. Secondly, Because aa (or 〈 math 〉〈 math 〉) 〈 math 〉〈 math 〉;
Therefore 〈 math 〉〈 math 〉, and dividing by 〈 math 〉〈 math 〉 = AD.
Thirdly, Because 〈 math 〉〈 math 〉 i. e. 〈 math 〉〈 math 〉; therefore dividing by 2L{powerof2}, d will be = 〈 math 〉〈 math 〉 i. e.
〈 math 〉〈 math 〉 i. e. resolving 〈 math 〉〈 math 〉 into equivalent Terms ex∣pressed by p and q, 〈 math 〉〈 math 〉; which is the other mem∣ber of the Central Rule to be found. viz. a is = 〈 math 〉〈 math 〉
Therefore ab will be = 〈 math 〉〈 math 〉
Therefore 〈 math 〉〈 math 〉.