Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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GO, ſint verò in ambitu triangula, ABC, FIG; </
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BC, OIG, ergo tria hęc tribus iam dictis ſimilia erunt, ergo & </
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<
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ſes, ACH, FGO, ſimiles erunt, nam cum ſit, AC, ad, CB, vt,
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FG, ad, GI; </
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<
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">BC, ad, CH, vt, IG, ad, GO, erit ex ęquali, AC,
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ad, CH, vt, FG, ad, GO, eadem ratione oſtendemus, CH, ad,
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">5. Sexti
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HA, eſſe vt, GO, ad, OF, ex quo habebitur ex ęquali, CA, ad,
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AH, eſſe vt, GF, ad, FO, ergo triangula, ACH, FGO, ſimilia
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erunt. </
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<
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">Eodem modo probabimus triangula, AHD, FLO, ACD,
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FGL, eſſe ſimilia, ex quo concludemus ipſas pyramides ſimiles eſſe.
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<
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">Quod ſi tria triangula ad, B, I, terminantia omnia non ſint in am-
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bitu, oſtendemus tamen illa eſſe ſimilia, erunt.</
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<
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">n. </
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<
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">vel baſes pyrami-
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dum, quarum tria triangula verticalia erunt in ambitu, vel ſaltem
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aliarum pyramidum, quarum triangula ſimilia eſſe probabuntur,
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quia erunt baſes pyramidum tria triangula verticalia in ambitu ha-
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bentium, ad hæc.</
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<
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">n. </
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eſt, quod proponebatur.</
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<
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">_Q_Via verò in pyramidibus triangulatis, BAHC, IFGO, exiſten-
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tibus ſimilibus illarum triangulis verticalibus, baſes, ACH, F
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GO, neceſſiriò ſimiles eſſe oſtenſæ ſunt, ideò ex hoc colligimus ſi
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in duabus pyramidibus triangulatis tria verticalia triangulatribus ver-
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ticalibus triangulis ſimilia ſint, etiam baſes ſimiles eſſe.</
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">SI duo ſimilia triangula fuerint ſubiectis planis æquè ad eandem
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partem inclinata, ita vt communes cum illis ſectiones ſint ea-
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rum latera homologa, quæ tanquam baſes aſſumantur; </
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<
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">ab eorum
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autem verticibus rectæ lineæ in ſublimi fuerint conſtitutæ, angulos
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æquales cum eorum lateribus homologis continentes, illæ erunt ſu-
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biectis planis æqualiter inclinatæ, vel eiſdem ambo parallelæ; </
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<
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tem fuerint inclinatæ, & </
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<
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">vſque ad ſubiecta plana producantur, iun-
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ganturq; </
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<
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">pucta occurſuum cum extremis baſium dictorum triangu-
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lorum, pariter hinc conſtitutæ pyramides ſimiles erunt.</
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<
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">Sint ſimilia triangula, ABD, HPO, ſubiectis planis ęquè incli-
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nata, in baſibus, BD, PO, à quorum verticibus, A, H, rectæ li-
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neæ, AC, HN, in ſublimi conſtitutæ contineant cum homologis
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eorum lateribus angulos æquales, ſint nempè anguli, CAB, NH
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P, necnon, CAD, VHO, inter ſe æquales. </
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N, ſubiectis planis eſſe ęqualiter inclinatas, vel eiſdem ambo </
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