. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. * ^=CHa ; consequently, FE* — CA* — 2C A-CI + CI*.And the root or side of this square is FE = CI—CA= the same manner is found f E = CI + CA = BI. Q. E, D. Cor. 1. Hence CH = CI is a fourth proportional , CF, CD. Cor. 2. AndfE-f FE = 2CH or 2CI ; or FE, CH,fE, are in continued arithmetical progression, the com-mon difference being CA the semitransverse. Cor. 3. From the demonstration it appears, that DE8- DH* — A
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. * ^=CHa ; consequently, FE* — CA* — 2C A-CI + CI*.And the root or side of this square is FE = CI—CA= the same manner is found f E = CI + CA = BI. Q. E, D. Cor. 1. Hence CH = CI is a fourth proportional , CF, CD. Cor. 2. AndfE-f FE = 2CH or 2CI ; or FE, CH,fE, are in continued arithmetical progression, the com-mon difference being CA the semitransverse. Cor. 3. From the demonstration it appears, that DE8- DH* — AG* = DH* — Ca*. Consequently DH is ev-ery where greater than DE ; and so the asymptote CGHnever meets the curve, though they be ever so far pro-duced : but DH and DE approach nearer and nearer to aratio of equality, as they recede farther from the vertex, tillat an infinite distance they become equal, and the asymp-tote is a tangent to the curve at an infinite distance from thevertex. proposition VI. The difference of two lines, drawn from the foci to meetin any point of the curve, is equal to the transverse axis. That is, IE — FE = AB, CONIG SECTIONS. 509. For, by the last Prop. FE = CI — C A = AI,and, by the same, f E = CI -f- C A = BI ;therefore, by subtraction, f E — FE = AB. Cor. Hence is derived the common method of describ-ing the curve mechanically by points, thus :
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