Casati, Paolo
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Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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480, aſſumatur BC 1 ℞: tum fiat vt particu
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læ OA ad particulas AS, ita ped. 1 ℞ + 480
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ad aliud, & proueniet quartus terminus CD
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æqualis ipſi CB 1 ℞: atque adeò factâ Anti
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theſi, & inſtitutâ diuiſione habetur quanti
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tas ipſius CD. </
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XXXIII
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Idem aliter
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ſine Trigo
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nometria.
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>Quid? </
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>quod ſinè Algebrâ res tam facilis
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eſt, vt penè non audeam dicere, ne vulgata
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vilecat. </
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>Fiat vt OI, differentia inter OA &
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AS, ad ipſam AS, ita nota altitudo AB ad
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aliud, & proueniet CD quæſita terræ ſemi
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diameter. </
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>Eſt nimirum AB differentia inter
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AC & CD, & vt tota AC ad totam AO, ita
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ablata CB ad ablatam AI; igitur & reliqua
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AB ad reliquam IO vt tota AC ad totam
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AO: ergo permutando, & diuidendo, vt
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AB ad BC, hoc eſt CD, ita OI ad IA, hoc
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eſt AS. </
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XXXIV
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Idem ſine
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Trigonome
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tria & ſine
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Algebra.
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<
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>Et hæc quidem dicta ſint, ſi fortè angu
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lum CAD præcognoſcere non libeat. </
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<
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>Cæ
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terùm illo cognito rem aggredi licet ſine
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Algebrâ ope ſoliûs Trigonometriæ, quæ
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multiplicem ſubminiſtrare poterit metho
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dum. </
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>Et primò datâ altitudine AB, & an
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gulo ad A obſeruato ex. </
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>gr.gr.89.m.36.ſec.
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33., notus eſt angulus ad centrum C gr.o.
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m. 23. ſec. 27, ac proinde eius ſubtenſa iņ
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partibus Radij innoteſcit. </
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>Igitur ductâ BD, </
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