Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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<
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xml:space
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EVCLIDIS LIBRVM</
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<
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<
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">Animaduertimus tamen permultos ſumma
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difficultate
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type
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demonstr ationes percipere. </
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<
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">Prœ
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unsure
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-
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cipuè ubi quint a, aut ſeptima deffinitiones eiuſ-
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dem libri neceſſariœ
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ſunt. </
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<
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">Illœ enim adeo obſcurœ
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uidentur, ut longè facilius admißuri ſint hœc no-
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ſtra poſtulat at anquam clarior a. </
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<
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">At que etiam tanquam intellectui
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commodiora, quam ſit illud quintum
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idemque
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">idemq́ꝫ</
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ultimum postulatum
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eiuſdem in primo libro poſitum, de line a duas alias ſecante. </
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<
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">Quan-
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doquidem
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noſtris postulatis admißis, ſequentia Theoremata per
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facillima reddentur.</
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<
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">Horum autem primum est.</
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<
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tota compoſita ex æquali numero partium æqualium, ſunt inuicem
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æqualia.</
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<
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">Vtſi quis diceret omnes proportiones quæ
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ſunt ex æquali numero alia-
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rum proportionum inuicem æqualium, ſunt etiam inuicem æquales, quod Eucli-
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des conatur demonſtrare in .22. et .23. quinti libri.</
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<
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ſi à totis æqualibus detractæ fuerint æquales partes, quæ remanent erunt
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partes inuicem æquales.</
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<
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">Et è conuerſo ſi æqualibus æqualia addas compoſita erunt inuicem æqualia.</
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<
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">Quod in ipſis proportionibus hoc loco ſemper intelligendum eſt.</
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<
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">Quę est εuclidis ſeptima propoſitio.</
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<
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ſi fuerint plures termini æquales inuicem, ratio ſeu proportio vnius ip-
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ſorum ad alium tertium terminum maiorem, minoremúe, ſed eiuſdem generis, erit
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cadem quæ cuiuſuis alterius termini ad eundem tertium. </
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<
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xml:space
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">Et è conuerſo, quæ fuerit
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proportio tertij termini ad vnum prædictorum æqualium, eadem erit, ſpecie, cum
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alio eorundem terminorum.</
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