A treatise of algebra, in three parts. Containing

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theresere si i. o. e. P is an bari onicalmeanaetinee the two lines PB and PC terminated atthe curve. hic is a properi os linest the studorde es admirabie simplicith, 66. bra. r. A line hic cui an right ynestaris sto a piant os contrar flexure in thecurve harmonicassy, Wil also cui an othe two lines drawn rom the potat and terminared b the curve har

Fig. V. 6 68. PROP. X. A right line Oini it . potnis os contrar flexure esther passe thro haud ptant os contrar flexure or is in the fame direction,ith an infinite latos the curve.

I et Maia a be two potnis os contrary exure let Aacioine meet the curve in a, a, ill alio besa polyto contrar flexure. For is a tangen to the figure in theloint a liould meet the curve in an other potiat

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Wwhere the curve cui me asymptote.

Foru et the line-meet FH in Q , and BC the samo in H; et he cine u and in and sincerit is as

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a litie of the thir orde is deternia tred hicli palles through these seven pollit A, B, C, b, Μ, , and has it contrar flexure in A. For Do the potnis Mand mare ive the potnis mand where M and Ani e in drawn ut the curve, an fro these ineconditions the line is determined. No i three potnis

determine by drawing AV, whic let L parallel to AH meet in , and by biserent L in X sor AX, bcino vines, Willie ste tangent at the oin A. For

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meet the curve in H, and et a tangent at the

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86 GENERA PROPERTIES F

curo,

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and the linem C illae harmonicali cui in mandi, so that tways N is ommas C to Bri this sol-lows sto Corol. 2. of the preceding. No the lines FG and fg meet in the potnt of the curvem; and in like manne the lines fand G me et in andand in in x and Danda,ill beioints of the curve, is heciam corollary. An this is the alter of the two properties of lines of the hircorde vini I de

the curve'.

9 79. Corol. Therelare since the lines ΗΚ, ΗΒ, Hrianum Me harmonimiis i the lines HB and Hameetine curve in blandia; the potnis A, M K willae in the fame right line. For let Abjoined meet ille curve in ban L and F in , and ΗΚ in , and sinces, isto is asscto p cito ears that eris in the line HC; an reciprocali is cie in the lineminandis in tholine HB, A, oti,iilae in the fame right line.