A treatise of algebra, in three parts. Containing

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struction'wil serve for determining the piant i , is In stea of the right line V be sub tute another c. parallel o C at an equa distances m in minibu on the contrar see. -

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oo ENERA PROPERTIE orbe in a line give in position by the fame . No the compositio of the problem is asil performe stom. at has been said. et a VC and E e threelines iue in position and let the parallelogram DF VH

Anoster fri6. et an right line drawn rom the give potire meet right lines give in position in the politis A, B, C, Ε, cc md in his right line let there bestahen

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is eques to this sum, and when the linei is give inposition, and the right lines AK, L, CN, M. e- main fixed whilst the right line PD revolves a ut themle P thesmin M,illae in a right line, by the precedin Article; hich may be determine by hathas Men hewn above sto the siveo tange iis AK, 648. A the right line P is a mean harmonical

. line terminate by the Dint rana the curve, the minim ill e in a right line. For . . illis and theresere 'uris to M as cto unity and since thei, iiii Mas in a right line, by the preceding the potui

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tio of the orderis V iis la tet into hie thoordinate or rooto oes no enter, 'the coe Scient of the rus term ut ne limine armonica mea b

tionsor conae sectio alven in Art. I. y - . In a cubic equation, Whola three roota are et in , Μ Will

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ineis in quantity Whicli Ne cal -- . et here betara n

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Ἀ GENERA PROPERTIES OF

essicient of the la term ut ne, ill e eques to

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right line gi ven in position a we have otherwise mem in Theor. . More ove ali ille aut of the linea His that whicli in Art. 20. e have determine dis another method and the right line 13 cut ali right Iine drawn throughi harmonicatly accordin to the desinitio of harmonica section sive in genera in Art. 28.

Sections. 6 33. Ut L . , Rhiat has been demonstra ted in gene- a concernin geometrica lines in the first sectiori, the proper ies of linc os second third, and superior order naturali flow What relate to theconi sections are est crived sto in the properties of the circle, hicli figure is the a se of the cinae. Butthat the use of the preceding theorem ma more clearly appear, and the analog of the figures be illustraled itwii be orth, lille to deduce the properties of thesealso froni,hat has cen premi sed No the wholeconi doctrine about diameters, and their ordinates towhicli right lities ouching the section a the vertices . of the diametercare par illet an a ut ille segmenis os parallela hic meet an right Enes, an a ut simp

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GEOMETRICA LINEs. 467

line P meet the curve in minis D andra est Lae But to the segmenis,hicli are o the sameside of the poliati the fame sigias area be prefixed, and to thos inhicli are on the opposite fides of P contrary