Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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dio loco proportionalis inter diametri ſeg
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menta IC, CO; ac proinde quadratum me
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diæ CF æquale eſt rectangulo ſub extremis. </
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Itaque quadrato ipſius CF diuiſo per IC ſeg
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mentum notum, Quotiens dabit CO, cui
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addatur CI, & habetur tota diameter IO
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quæſita. </
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LIV. </
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Decima me
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thodus, qua
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terræ dia
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meter inue
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nitur.
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LV. </
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Idem aliter.
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>Hæc mihi methodus magis arridet vtpo
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te breuior, qua quadratum CF diuido per
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IC: cæterùm ſi rem merè Trigonome
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tricè perficere quis malit, inuentis CF
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& IC, quærat angulum IFC; quem du
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plicet, & dupli ſinum ex Tabulis inue
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niat: tum fiat vt ſinus inuentus ad Ra
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dium ita inuenta CF ad quæſitam ſemidia
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metrum FT. </
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>Huius operationis ratio pa
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tet, quia cum angulus IFO in ſemicircu
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lo ſit rectus, triângulum ICF eſt ſimile trian
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gulo IFO, igitur angulus inuentus IFC æqua
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lis eſt angulo FOC; huius autem duplex eſt
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angulus ITF ad centrum, qui proinde inno
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teſcit, vnâ cum ſinu FC in partibus Radii
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hæc verò linea cum nota ſit etiam in men
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ſurâ homogeneâ altitudini datæ IG, manife
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ſtabit pariter in eâdem menſurâ Radium TF. </
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<
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>Placetne aliam adhuc inire viam? </
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Dionyſiodori Geometræ protritam veſtigiis;
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cuius in ſepulchro inuenta eſt epiſtola ad </
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