Clavius, Christoph, Geometria practica

Table of contents

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[321.] I. QVADRA TRICEM lineam deſcribere.
Page: 350 (320)
[322.] COROLLARIVM.
Page: 353 (323)
[323.] II.
Page: 354 (324)
[324.] COROLLARIVM I.
Page: 355 (325)
[325.] COROLLARIVM II.
Page: 356 (326)
[326.] COROLLARIVM III.
Page: 356 (326)
[327.] III.
Page: 357 (327)
[328.] IV.
Page: 359 (329)
[329.] COROLLARIVM.
Page: 359 (329)
[330.] V.
Page: 359 (329)
[331.] FINIS LIBRI SEPTIMI.
Page: 359 (329)
[332.] GEOMETRIÆ PRACTICÆ LIBER OCTAVVS.
Page: 360 (330)
[333.] Varia Theoremata, ac problemata Geometrica demonſtrans.
Page: 360 (330)
[334.] THEOR. 1. PROPOS. 1.
Page: 360 (330)
[335.] SCHOLIVM.
Page: 361 (331)
[336.] LEMMA I.
Page: 361 (331)
[337.] LEMMA II.
Page: 362 (332)
[338.] EEMMA III.
Page: 362 (332)
[339.] THEOR. 2. PROPOS. 2.
Page: 364 (334)
[340.] SCHOLIVM.
Page: 365 (335)
[341.] THEOR. 3. PROPOS. 3.
Page: 365 (335)
[342.] COROLLARIVM.
Page: 366 (336)
[343.] PROBL. 1. PROPOS. 4.
Page: 366 (336)
[344.] PROBL. 2. PROPOS. 5.
Page: 367 (339)
[345.] ALITER.
Page: 367 (339)
[346.] PROBL. 3. PROPOS. 6.
Page: 367 (339)
[347.] THEOR. 4. PROPOS. 7.
Page: 368 (340)
[348.] SCHOLIVM.
Page: 368 (340)
[349.] PROBL. 4. PROPOS. 8.
Page: 369 (341)
[350.] PROBL. 5. PROPOS. 9.
Page: 370 (342)
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            <s xml:id="echoid-s13894" xml:space="preserve">
              <pb o="293" file="323" n="323" rhead="LIBER SEPTIMVS."/>
            rectæ B E, G H, ipſi A D, æquidiſtantes, eritque G H, ęqualis
              <note symbol="a" position="right" xlink:label="note-323-01" xlink:href="note-323-01a" xml:space="preserve">34. primi.</note>
            A D. </s>
            <s xml:id="echoid-s13895" xml:space="preserve"> Quoniamigitur rectangulum BCFE, duplum eſt trianguli ABC; </s>
            <s xml:id="echoid-s13896" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-323-02" xlink:href="note-323-02a" xml:space="preserve">41. primi.</note>
            duplum rectanguli BEHG: </s>
            <s xml:id="echoid-s13897" xml:space="preserve">erit rectangulum BEHG, quod continetur ſub per-
              <lb/>
              <note symbol="c" position="right" xlink:label="note-323-03" xlink:href="note-323-03a" xml:space="preserve">36. primi.</note>
            pendiculari GH, vel AD, & </s>
            <s xml:id="echoid-s13898" xml:space="preserve">dimidio baſis BG, æquale triangulo ABC.</s>
            <s xml:id="echoid-s13899" xml:space="preserve"/>
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            <s xml:id="echoid-s13900" xml:space="preserve">
              <emph style="sc">Secetvr</emph>
            iam perpendicularis AD, vel G H, bifariam in I, agaturque per I,
              <lb/>
            ipſi BC, parallela KL. </s>
            <s xml:id="echoid-s13901" xml:space="preserve">Dico triangulum idem ABC, æquale quoque eſſe rectã-
              <lb/>
            gulo BCLK, in 1. </s>
            <s xml:id="echoid-s13902" xml:space="preserve">& </s>
            <s xml:id="echoid-s13903" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13904" xml:space="preserve">figura, Item rectangulo BCLM, in 3. </s>
            <s xml:id="echoid-s13905" xml:space="preserve">figura, comprehen-
              <lb/>
            ſo nimirum ſub ID, vel IG, ſemiſſe perpendicularis AD, vel HG. </s>
            <s xml:id="echoid-s13906" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-323-04" xlink:href="note-323-04a" xml:space="preserve">41. primi.</note>
            enim triangulum ABC, dimidium eſt rectanguli E C, eiuſdemque dimidium et-
              <lb/>
            iam eſt rectangulum BL; </s>
            <s xml:id="echoid-s13907" xml:space="preserve"> quod rectangula BL, LE, ſuper æquales baſes
              <note symbol="e" position="right" xlink:label="note-323-05" xlink:href="note-323-05a" xml:space="preserve">36. primi.</note>
            lia ſint: </s>
            <s xml:id="echoid-s13908" xml:space="preserve">æqualia inter ſe erunt triangulum A B C, & </s>
            <s xml:id="echoid-s13909" xml:space="preserve">rectangulum B L. </s>
            <s xml:id="echoid-s13910" xml:space="preserve"> Et
              <note symbol="f" position="right" xlink:label="note-323-06" xlink:href="note-323-06a" xml:space="preserve">41. primi.</note>
            rectangulum B F, contentum ſub perpendiculari A D, vel B E, & </s>
            <s xml:id="echoid-s13911" xml:space="preserve">baſe trianguli
              <lb/>
            BC, duplum eſt trianguli ABC; </s>
            <s xml:id="echoid-s13912" xml:space="preserve">erit triangulum ſemiſsiillius rectanguli ęquale.
              <lb/>
            </s>
            <s xml:id="echoid-s13913" xml:space="preserve">Area igitur cuiuslibet trianguli æqualis eſt, &</s>
            <s xml:id="echoid-s13914" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13915" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s13916" xml:space="preserve"/>
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          <head xml:id="echoid-head319" xml:space="preserve">PROBL. 2. PROPOS. 2.</head>
          <note position="right" xml:space="preserve">Regularis fi-
            <lb/>
          gura quæcun-
            <lb/>
          que cuirectã-
            <lb/>
          gulo @qualis
            <lb/>
          ſit.</note>
          <p>
            <s xml:id="echoid-s13917" xml:space="preserve">AREA cuiuslibet figuræ regularis æqualis eſt rectangulo contento ſub
              <lb/>
            perpendiculari à centro figuræ ad vnum latus ducta, & </s>
            <s xml:id="echoid-s13918" xml:space="preserve">ſub dimidia-
              <lb/>
            to ambitu eiuſdem figuræ.</s>
            <s xml:id="echoid-s13919" xml:space="preserve"/>
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            <s xml:id="echoid-s13920" xml:space="preserve">
              <emph style="sc">Sit</emph>
            figura regularis quæcunque ABCDEF, & </s>
            <s xml:id="echoid-s13921" xml:space="preserve">centrum eius punctum G, à
              <lb/>
            quo ducatur GH, perpendicularis ad vnum latus, nempe ad AB: </s>
            <s xml:id="echoid-s13922" xml:space="preserve">Sit quoq; </s>
            <s xml:id="echoid-s13923" xml:space="preserve">re-
              <lb/>
            ctangulum I K L M, contentum ſub I K, quæ æqualis ſit perpendiculari G H, & </s>
            <s xml:id="echoid-s13924" xml:space="preserve">
              <lb/>
            ſub KL, recta, quæ æqualis ponatur dimidiæ parti ambitus figuræ ABCDEF. </s>
            <s xml:id="echoid-s13925" xml:space="preserve">Di-
              <lb/>
              <figure xlink:label="fig-323-01" xlink:href="fig-323-01a" number="214">
                <image file="323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/323-01"/>
              </figure>
            co huic rectangulo æqualem eſſe figuram regularem ABCDEF. </s>
            <s xml:id="echoid-s13926" xml:space="preserve">Ducantur enim
              <lb/>
            ex G, ad ſingulos angulos lineæ rectæ, vt tota figura in triangula reſoluatur, quæ
              <lb/>
            omnia æqualia inter ſe erunt, vt in corollario propoſ. </s>
            <s xml:id="echoid-s13927" xml:space="preserve">8. </s>
            <s xml:id="echoid-s13928" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13929" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13930" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s13931" xml:space="preserve">demonſtra-
              <lb/>
            tum eſt à nobis: </s>
            <s xml:id="echoid-s13932" xml:space="preserve">propterea quòd omnia latera triangulorum à puncto G, ex-
              <lb/>
            euntia ſint inter ſe æqualia, habeantq; </s>
            <s xml:id="echoid-s13933" xml:space="preserve">baſes æquales, nempè latera figuræ regu-
              <lb/>
            laris. </s>
            <s xml:id="echoid-s13934" xml:space="preserve"> Hinc enim effi citur, omnes angulos ad G, æquales eſſe, ac proinde, ex
              <note symbol="g" position="right" xlink:label="note-323-08" xlink:href="note-323-08a" xml:space="preserve">8. primi.</note>
            cto corollario, triangula ipſa inter ſe quo que eſſe æqualia. </s>
            <s xml:id="echoid-s13935" xml:space="preserve"> Quoniam igitur
              <note symbol="h" position="right" xlink:label="note-323-09" xlink:href="note-323-09a" xml:space="preserve">1. hui{us}.</note>
            ctangulum contentum ſub GH, perpendiculari, & </s>
            <s xml:id="echoid-s13936" xml:space="preserve">medietate baſis AB, æquale
              <lb/>
            eſt triangulo ABG, ſi ſumantur tot huiuſmodi rectangula, in quot triangula di-
              <lb/>
            uiſa eſt figura regularis, erunt omnia ſimul figuræ ABCDEF, ęqualia; </s>
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