Page:Œuvres de Fermat, Tannery, tome 1, 1891.djvu/204

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Sublatis communibus, et reliquis ipsi E applicatis,

B + O bis adclquabitur E bis 4- A quater.

Expungatur EB is ex methodo: ergo

B + O bis æquabitur A quater,

ideoque

A quater - B tequabitur O bis,

et

A bis - dimid. B æquabitur 0.

Hac equalitate ex methodo stabilita, redeundum ad priorem, in qua ponebamus

A + lat.(B in A - A quad.) æquari O.

Quum igitur inventa sit

O æqualis A his - dimid. B,

ergo

A bis - dimid. B æquabitur A + lat. (B in A - A quad.),

ideoque

A - dimid. B wequabitur lat. (B in A - A quad.),

omnibusque in quadratum ductis,

A quad. - B quad. - B in A æquabitur B in A - A quad.,

et tandem

B in A -A quad. æquabitur B quad.1/8;

quæ ultima sequalitas dabit valorem A in quawsita determinatione.

Hoc artificio uti possumus ad inventionem coni maximi ambitus sphæræ inscribendi ^[1].

Sit sphæræ datœ diameter AD (fig'. 99). Conus quysitus habeat altitudinem AC, latus AB, semidiametrum baseos BC. Rectangulum AB