Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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to, ſumendus eſtille ſinus totusin aliqua recta bis, ter, aut quater, &</
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<
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<
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xml:space
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">ferrinequeat,
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quid agen-
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dum.</
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ita ex F, in G, transferendus. </
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<
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xml:space
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">Nam ſi Tangentium quæſitarum, vel ſinuũ, aut
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ſecantium reſpectu ſinus totius 100. </
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<
s
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xml:space
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">capiantur ſemiſſes, vel tertiæ partes, aut
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quartæ, &</
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<
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<
s
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xml:space
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">prout videlicet ſinus totus bis, ter, quateruè, &</
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<
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<
s
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">acceptus fuit,
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habebũtur Tangẽtes quæſitæ, vel ſinus, aut ſecãtes. </
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<
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">Vt ſi ſinus totus duplice-
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tur, & </
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<
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<
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">Tangens verbigratia ſit 378. </
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<
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189. </
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">&</
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<
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<
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xml:space
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">Sed commodiſsime res hæc peragetur, ſi ſinus totus, quiperpuſil-
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lus eſt, decupletur. </
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<
s
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xml:space
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">Ita enim poſito ſinu toto 100. </
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<
s
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xml:space
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">ſi ex Tangente verbi gra-
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tia propoſita (relicta prima figura ad dexteram) abijciatur vna figura ad de-
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xteram, quæ eſt ſecunda in tota Tangente, habebitur decima eius pars. </
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<
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benda tamen ſemper eſt ratio figuræ abiectæ, vt ſcilicet pro ea ſumatur 1. </
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<
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maior eſt quam 5. </
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<
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ſita (relictis {4/1000}.) </
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<
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xml:space
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pars decima Tangentis 241. </
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<
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</
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<
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<
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etiam, quando Tangens aliqua ſinum totum ſuperat, ne coga-
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mur primum ſinum totum aliquoties transferre, deinde vero reliquas partes,
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<
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xml:space
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">Quando Tã-
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gens ſuper{at}
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ſinum totum,
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quid agendũ,
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vt per vnicã
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tranſlationem
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punctũ quæſi-
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tum inuenia-
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tur.</
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vel contra; </
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<
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">ſed vt ſtatim punctum, quod quæritur, per vnam translationem
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poſsimus inuenire, diuidenda eſt tota Tangens tabulæ ad finem nouæ deſcri-
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ptionis Horologiorum poſitæ per 2. </
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<
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vt producatur in Quotiente Tangens trium figurarum. </
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prima figura ad dexteram, reliqua Tangens transferenda eſt reſpectu ſinus
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totius 100. </
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>
<
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">multiplicatiper eundem numerum, per quem Tangẽs diuiſa fuit.
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</
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<
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">eſt 1732. </
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2. </
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<
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<
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nus totius 100. </
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<
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<
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<
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quatuor ſacit 933. </
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<
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<
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100. </
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<
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<
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hoc eodem denique inſtrumento facile duabus rectis tertiam pro-
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portionalem, & </
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<
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<
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">Nam ſi, duabus propoſitis, pri-
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<
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">Quo pacto
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tertia, &
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quarta pro-
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portionalis
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reperiatur.</
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mæinrecta A F, regulæ A B, æqualis capiatur: </
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<
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">ſecunda à fine huius, aperto
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inſtrumento, per circinum transferatur in regulam A C, ad numerum ſimilem
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illi, qui in extremo primæ in regula AB, appoſitus eſt (ita vt pedes circini ſta-
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tuantur vel in ſimilibus partibus vtriuſque regulæ, vel in duobus punctis æ-
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qualiter diſtantibus à ſimilibus partibus) eidemque ſecundæ in regula A B, æ-
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<
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<
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qualis ſumatur, dabitinterualluminter finem huius ſecundæ, & </
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<
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regula A C, ſimilemilli, qui prope finem ſecundæ ſcriptus eſt, tertiam propor-
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tionalem; </
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<
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<
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<
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ratione, ſi, tribus rectis propoſitis, prima & </
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mentum transferantur, vt dictum eſt, tertiæ autem in regula A B, æqualis quo-
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<
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<
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que capiatur, dabit interuallum inter finem tertiæ, & </
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<
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xml:id
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">numerum regulæ A C, ſi-
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milem illi, qui ad extremum tertiæ in regula A B, notatus eſt, quartam propor-
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tionalem.</
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<
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<
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ſi lineæ propoſitæ tam magnæ ſint, velaliqua illarum, vt in inſtru-
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mentum tranſportari nequeant, ſumendæ erunt omnium ſemiſſes, vel tertiæ
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partes, vel quartæ &</
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<
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<
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">at que cum illis procedendum, vt dictum eſt. </
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<
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enim duplicata, vel trip licata, vel quadruplicata, &</
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<
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<
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">offeret tertiã aut quar-
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tam proportionalem quæſitam.</
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