Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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las AD, BC, & </
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<
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catur AC, & </
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<
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">beneficio perpendicularis AE, area trianguli ABC, inquiratur, quod
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hæc duplicata aream exhibeat totius parallelogrammi, quippe cum
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lum ABC, ſemiſsis ſit parallelogrammi. </
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<
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expeditius area inueniatur ſi perpendicularis in totum latus BC, ducatur, quam
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ſi in ſemiſſem multiplicetur, ac productus deinde numerus dupletur.</
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<
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per quadrantem cap. </
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<
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<
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<
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<
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laris inuentio.</
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B, reperietur perpendicularis AE, perſinus, hacratione. </
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<
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gulirecti E, ad latus oppoſitum AB, ita ſinus anguli B, ad aliud. </
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<
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ctil.</
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nim numerus erit perpendicularis AE, cognita in partibus lateris dati AB.</
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<
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<
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, in quo duo latera oppoſita ſint parallela AB, BC, & </
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latera nota, area producitur ex perpendiculari A E, inter duo latera parallela
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multiplicata in ſemiſſem ſummæ ex lateribus parallelis conflatæ. </
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<
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habentis duo
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lateraparalle-
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la.</
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diametro AC, area trianguli ABC, producitur ex perpendiculari A E, in ſemiſ-
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ſem baſis BC, vt cap. </
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<
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<
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128
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200-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/200-01
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</
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guli ACD, ex eadem perpendiculari A E, in ſemiſſem baſis
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AD: </
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<
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">Acproinde hæ duæ areæ ſimul aream totius Trapezij A-
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BCD, conficient. </
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<
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xml:space
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"> Cum igitur idem fiat ex AE, in ſummam
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ſemiſſe rectæ B C, & </
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ſemiſſem rectarum BC, AD, ſimul: </
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<
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lateris B C, & </
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<
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aream Trapezij gigni ex perpendiculari AE, in ſemiſſem ſum-
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mæ laterum AD, BC. </
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Trapezio habente vnum angulum rectum, vel duos rectos.</
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<
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vero AE, inuenietur, vt in Rhombo, & </
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de diximus, duobus modis, ſi per quadrantem angulus B, inueſtigetur, &</
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<
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Trapezio autem FGHI, in quo nulla ſunt latera parallela, omnia tamen
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<
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nulla haben-
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tis latera pa-
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rallela.</
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latera ſunt nota, menſuranda primum eſt diameter. </
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<
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tium. </
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<
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">Deinde vtriuſque trianguli FGI, GHI, area inuenienda, vt cap. </
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</
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<
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<
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<
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<
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ſi malueri angulum F, vel H, per quadrantem inuenire, cognoſce-
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mus diametri GI, magnitudinem, per doctrinam ſinuum, ac Tangentium,
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vt lib. </
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<
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<
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<
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<
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<
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ctil. Num. 2.</
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ipſis comprehenſo, vel ex duobus lateribus HG, HI, & </
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tinent.</
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<
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<
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aliter aream conſequemur cuiuſcun que quadrilateri irregularis, et-
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<
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">Area figuræ
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quadrilateræ
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irregularis.</
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iamſi non habeat omnes angulos introrſum, ſicut Trapezium. </
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<
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zio FGHI, ducantur ex G, & </
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<
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">I, duæ rectæ GK, IK, conſtituetur quadrilaterum
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GHIK, irregulare, cum ſolum habeat tres angulos GHI, HIK, HGK. </
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<
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K, non fit angulus GKI, introrſum verſus H, cum illud ſpatium ſit duo-
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bus rectis maius, ſed verſus F, extrorſum. </
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<
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drilateræirregularis aream colligemus, ducta diametro
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K H, ex duabus areis triangulorum IKH,
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GKH, vt de Trapezio FGHI,
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dictum eſt.</
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