Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
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ſtiganda ſunt ſegmenta BD, CD, inter perpendicularem, perea, quæ lib. </
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xlink:label
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note-192-01
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xml:space
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">Segmenta ba-
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ſis, quæ à per-
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pendiculari
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abſcinduntur,
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quo pacto cog-
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noſcatur.</
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3. </
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xml:space
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">Fiat vt latus BC, in quod cadit perpendicularis
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AD, (Semper autem eſſet demittenda perpendi-
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number
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122
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192-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/192-01
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cularis in maximumlatus, vtintra triangulum ca-
<
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deret) ad ſummam aliorum duorum laterum A B,
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AC, nimirum vt 21. </
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<
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<
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xml:space
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">ita differentia eorundem
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59
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laterum, videlicet 7. </
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<
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<
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numerus 9. </
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xml:space
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">(qui quoniam minor eſt latere BC, ar-
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gumento eſt, perpendicularem intra triangulum
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cadere. </
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<
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xml:space
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">Si enim maior eſſet, caderet extra, vt prop oſ. </
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<
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rumrectil. </
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<
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xml:space
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">oſtendimus) qui ablatus ex latere BC, id eſt, ex 21. </
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<
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ſemiſsis 6. </
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<
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xml:space
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">dabit minus ſegmentum B D, prope minus latus AB, quę eadem ſe-
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miſsis ex latere BC, ſubtracta reliquum faciet maius ſegmentum C D, nimirum
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15. </
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<
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<
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rurſus triangulum ABD, cuius latus AB, 12. </
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">& </
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tenda autem ſit perpendicularis ex D, ad AB. </
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<
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<
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aliorum duorum 31. </
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<
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xml:space
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<
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number
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123
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192-02
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/192-02
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mirum 9. </
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<
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23 {1/4}. </
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<
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xml:space
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">(qui quo niam maior eſt latere AB, argumen-
<
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to eſt, perpendicularem cadere extra triangulum,
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angulumque A, eſſe obtuſum,) ex quo latus A B,
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12. </
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<
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meri ſemiſsis 5 {5/8}. </
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<
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">dabit ſegmentum exterius A C,
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inter perpendicularem, & </
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<
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<
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">eademque ſemiſsis addita lateri
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AB, efficiet aliud ſegmentum BC, inter perpendicularem, & </
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<
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">angulum acutum
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17 {5/8}. </
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<
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">Atque hæc ratio expeditiſsima eſt.</
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</
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<
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<
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Sit ducenda perpendicularis ad maximum latus B C, in priori
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triangulo ABC, quæ neceſſario cadet intra triangulum; </
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<
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xml:space
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"> propterea, quod
<
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">18. primi.</
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gulus A, maior eſt vtrolibet BC; </
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<
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<
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<
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position
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xlink:label
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xml:space
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">13. ſecundi.</
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niam autem quadratum rectę A B, minus eſt quadratis rectarum A C, BC, re-
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<
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62
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<
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ctangulo bis comprehenſo ſub BC, & </
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<
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<
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rem: </
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<
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<
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A C, B C, id eſt ex 730. </
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<
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<
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ſub B C, & </
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<
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<
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">perpendicularem. </
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<
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ſis 315. </
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<
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<
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">ac proinde hoc rectangu-
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lo 315. </
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<
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">diuiſo per latus B C, 21. </
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<
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">dabit Quotiens 15. </
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<
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">ſegmentum C D, prope
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angulum acutum C, cui opponitur latus A B, cuius quadratum ex ſumma
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reliquorum quadratorum detractum fuit. </
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<
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</
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<
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<
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">remanebit alterum ſegmentum B D, 6. </
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<
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">Eodem pacto,
<
note
symbol
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c
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position
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xlink:label
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xml:space
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">13. ſecundi.</
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>
quadratum rectę A C, minus eſt quadratis rectarum A B, B C, rectangulo
<
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<
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<
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="
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63
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bis comprehenſo ſub CB, & </
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<
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<
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<
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quadratum rectę A C, 289. </
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<
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<
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rum A B, B C, reliquum fiet rectangulum 252. </
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<
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& </
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<
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<
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<
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<
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qualis erit illi rectangulo ſemel ſumpto: </
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<
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">ac proinde hoc rectangulo 126. </
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<
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uiſo per latus CB, 21. </
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<
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<
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">ſegmentum BD, iuxta acutum angu-
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lum B, cui latus A C, quadrati ex duobus aliis quadratis detracti opponitur.</
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