A treatise of algebra, in three parts. Containing

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parallel to the tangent harmonicali cui res that

anditiaco P m PQ it sollows that in line parallel to the harmonical in., 97. Corol. 2. In like manner iste alien ille pomi

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GENERA PROPERTIES F

b is parallel to the lineis tauching the figure in

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tineat eques in Firi an Vn Uire Wil cui the line i . Rop. XXII. et be draWn through u si. an minii in the directio of the infinite leva line to meet the curve in a and e and throuo the same potnt an line culting the curve in theminis D, E, F, and hic may meet the linest ching the curve in a an in E an and

the asymptote of the infinite leg in I and is theroinis hi, his, , arein the fame fide os ribu the piant Ron the continu, it Willie i

os ever term is tot cham dis osten a thesegmen mes orto the opposite side of Ρ. .

the conmutae of the tangent a an em; andra Ibe ahen qua to an harmonica ni ean etween the

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three minis os contin are in the fame right linei and the three tangent parallel, letae taken the potnt 'as in Prop. XIX. an let be parallel to the asymptot

Io . Gra 3. The sameris tote Did of thecas in Prop. XX. here threeioints of contacti, E, F, are in the sanie right lines ichiastes through P the centre. os gravi nos the triangle TZ containe by the tam genis. ut is ne of the lines ouehing the curve in a

meter, since this necessarii passe through the doublepoin V, hom theloint of the curve F here the tangent FZ is bisecte letae a n stoma loward U, αβ FU let eΡ, betarawn parallelao the asymptote, and the tangent ast hic may meet the diameter in and on the oster side theloint' et bestilen upon the

line PV, Pici an a line dr Withmus tiara in the ordinate Will bestii a pote tot in e Butis the tangent a be parallel to the diameter, the latus ine

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Hie mire Milybe, ille parabolae End. Maiesptatum a ut the agmenis os in right line ternumted by three asymptotes and the curve asili sollows hom

is a circle of the iam curvature Mith the Pr posta line of the miro orde in D meet the litae

IH κ DR and sum is to LM in Q to 2DR. IIo, CorOL I. Let therelare hestahen Dr in the line D a third proportional to the lines HG and QU, and a perpendicula toste linem at the pomi r illo a perpendiculii to the tangent Drat the piant in the centre of the osculator circle orabe circle of the