Ceva, Giovanni
,
Geometria motus
,
1692
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pora per AB, AK iuxta ipſa imagines. </
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">Vel enim hæ ima
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gines ſunt ſimplices, hoc eſt tantùm parallelogrammę, aut
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tantùm acuminatæ, & tunc ſupra oſtendimus propoſitum,
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quemadmodum etiam ſi vna acuminata, altera parallelo
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gramma; vel non ſunt huiuſmodi & componentur ex illis.
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Sint ergo in imagine ADFB partes ab æquidiſtantibus di
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ſtinctæ ADEN, OFB acuminatæ & NEFO paralellogram-
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mum, erunt hæ procul dubio inter ſe, totique imagini ho
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mogeneæ; ſint pariter in alia imagine partes GHCM,
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MCKL, per æquidiſtantem MC diſtinctæ inter ſe acumi
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natæ, quæ itidem inter ſe, & imagini, cuius ſunt partes, ho
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mogeneæ erunt. </
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iuxta imaginem ADEN acuminatam ad tempus per HC
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iuxta aliam imaginem item acuminatam HGMC, habet
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eandem rationem, ac imago ADEN ad
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imaginẽ
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GHCM.
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ſimiliter tempus per HC iuxta imaginem GHCM ad tem
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pus per CK iuxta imaginem acuminatam MCKL eſt vt
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illa ad hanc imaginem; componendo, inde per conuerſio
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nem rationis, & conuertendo, tempus per HC ſecundùm
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imaginem GHCM ad tempora ſimul per HC, CK,
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quorũ
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imagines GHCM, MCKL, hoc eſt ad tempus per HK iux
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ta imaginem GHKL habebit
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eãdem
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rationem, quam ima
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go GHCM ad imaginem GHCL; & ideo ex æquali tem
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pus per AN, cuius imago ADEN, ad tempus per HK, iux
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ta imaginem GHKL, erit in eadem ratione, in qua eſt ima
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go ADEN ad imaginem GHKL. </
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AN iuxta imaginem ADEN ad idem ipſum tempus habet
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eandem rationem, quam imago ADEN ad eandem ipſam;
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tempus per NO iuxta imaginem rectangulum NEPO ad
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tempus prædictum per AN eſt in eadem ratione
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imaginũ
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NEPO ad ADEN, & ſimiliter tempus per OB iuxta ima
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ginem OPFB habet ad tempus per AN eandem rationem,
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ac imago OPFB ad imaginem ſæpè dictam ADEN;
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itaq;
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ex
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lem. 18. Toric. in lib. de dim: parabolæ, erunt tria
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per </
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