A treatise of algebra, in three parts. Containing

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and the minis uanam coincide contrar to the hypothesis. 36. For the fame ea n it appears that the right Iines AG andi meet ach ther in the pol ni et orthe right linea: and there fore the potnis P, , , L are in the fame right in . MIente alving three αpoints of contae A, B, and F gi ven wit two tangent AK and FK, the conic section is eastly describes. Hlat the right line Κω revolve bout the con- course of the tangent mas a pole, hic te meet the

37. The tam things rem alii in γ, et the right. Fig a , lines AF and BG meet ach other in the potnit, thetangent A and BL inra, and tangent Finand GLin in and thc pomis R, in and , illae in the fame right line in like manne let the tangenis AK and G Q meet ni the tangent BR and Κ in, and the. potnis P, ni, p, illae in the samo right line Thisis demonstrared in the fame manne as in Art. 35.6 38. Ience having urioints of contacti, B, F, G given with ne tangent AK, the concourse of the

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F and the coni station a b describe a in Art. 35. Fig.46. y a Let inere bellum seu tangent Κ4, L, LR, and Ria illi one potnt os contacti os the conic

B ut this proposition is more generat. For is Domn. a. atly Oilli Κ-drawn Wo lines Κ Aa, Bb cuti intili secti in in the potiris A a, and B, b , an frona the politis A and a b drais to the se nion the lines AF

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et II

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Is in his casei be a diameter, G, and B DR,

D. I. n. a.

No i the tangent AK be parallel o DΕ' in hic he Me the tangenis A and DT PIahe qua ut siles .ith the linem Rhic is heresore perpendicula tothe axis of the figure the poenis' an E ill coincide, and the osculator circle, ill pas through theptanti est sol loWs also uom 'stat has been sal that

a be

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Vmto D D to ΕΝ and so the trian gles DUranda DN,ill e si initar, and the angi DVr equa to isto angle EDO This,hthod os determining the oiaculator circle I have demonstrate in the reatis of Fluxionis Art. 375. ut notio ibo xly.6 49. The variation os curvature, orithe tangent of the angle os contae made by a mic section and the. osculator circle is directi as the tangent of the angle

valui is a the tangent of the angle EDO. ut is the linem me et the osculator circle in a parabola describe Wit in diameter an parameter Du, and