Clavius, Christoph
,
Geometria practica
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LIBER SEXTVS.
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ta proportionalis E atque inter AB, & </
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& </
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<
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xml:space
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">ſupra FG, figura conſtruatur ſimilis datæ figuræ AB, ſimiliterque poſita. </
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circulus deſcribatur circa diametrnm FG. </
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<
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xml:space
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">Dico tam rectilineum A B, eſſe ter-
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tiam partem rectilinei FG, quam circulum AB, circuli FG, nimirum eandem ha-
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bere proportionem AB, ad FG, quam habet C, ad D. </
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<
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xml:space
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AB, FG, & </
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<
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">E, continuè proportionales ſunt, erit figura A B, ad figuram
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vel 20. ſexti.</
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vt AB, ad E, hoc eſt, vt C, ad D. </
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<
s
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xml:space
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"> Quia verò eſt, vt quadratum ex A B, ad qua- dratum FG, ita circulus AB, ad circulum FG; </
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<
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xml:space
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">eſtque quadratum AB, ad quadra-
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<
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tum FG, vt AB, ad E; </
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<
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">erit quoque circulus AB, ad circulum FG, vt AB, ad E, vel
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vt C, ad D.</
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deinde figura, vel circulus H I, oporteatque conſtruere minorem figu-
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ram, vel circulum in proportione K, ad L, nimirum tripla. </
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I, inueniatur quarta proportionalis M: </
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nalis inueniatur N O, ſupra quam conſtruatur figura ſimilis ſimiliter que poſita
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figuræ HI: </
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HI, ad figuram NO, quam circulum HI, ad circulum NO, habereproportionem
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triplam, eandem videlicet, quam habet K, ad L. </
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20. ſexti.</
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NO, & </
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<
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"> erit figura HI, ad figuram NO, vt recta HI, ad M, hoc eſt, vt K, ad L. </
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tum NO, ita circulus HI, ad circulum NO, eſt que quadratum HI, ad quadra-
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tum NO, vt recta HI, ad M; </
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cta HI, ad M, vel vt K, ad L.</
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<
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">Ex his conſtat, qua ratione, dato foramine rotundo, vel etiam quadrato ali-
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cuius fontis, aliud foramen rotundum, vel quadratum maius, vel minus in qua-
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cunque proportione conſtruendum ſit.</
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lib. </
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figuræ ſolidæ ſunt parallelepipedum, Pyra-
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mis, Priſma, ſphæra, Conus, Cylindrus, & </
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gularia.</
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ergo figura ſolida, cuius latus A, vel ſphæra, cuius dia-
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meter A, augenda primum in proportione B, ad C. </
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ctis B, C, A, inueniatur quarta proportionalis D: </
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& </
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dum lateris A, ad ſolidum ſupra latus E, nimirum ſupra me-
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diam proportionalem, quæ propinquior eſt lateri dato A,
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conſtructum ſimile, ſimiliter que poſitum ſolido ſupra latus A,
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conſtituto, habere proportionem, quam B, habet ad C. </
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ſphæram datam diametri A, ad ſphæram diametri E, eſſe, vt B,
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ad C. </
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<
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">Quoniam enim figura ſolida lateris A, ad figuram ſoli-
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dam lateris E, ſimilem ſimiliter que poſitam habet proportio-
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nem triplicatam lateris A, ad latus E, vt lib. </
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