Clavius, Christoph, Geometria practica

Table of figures

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            <s xml:id="echoid-s14190" xml:space="preserve">
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            AC, baſis maior baſe CE. </s>
            <s xml:id="echoid-s14191" xml:space="preserve">Deinde ex F, per B, ducatur recta FBK, ſecans rectam
              <lb/>
            AC, in puncto K; </s>
            <s xml:id="echoid-s14192" xml:space="preserve">Item ex D, per G, punctum ducaturrecta DGH, ſecansre-
              <lb/>
            ctam CE, in H. </s>
            <s xml:id="echoid-s14193" xml:space="preserve">Et quia latera AF, FB, trianguli AFB, æqualia ſunt lateribus CF,
              <lb/>
              <note symbol="a" position="right" xlink:label="note-331-01" xlink:href="note-331-01a" xml:space="preserve">8. primi.</note>
            FB, triãguli CFB, & </s>
            <s xml:id="echoid-s14194" xml:space="preserve">baſis AB, baſi BC, æqualis, erit angulus AFB, angulo CFB, æqualis. </s>
            <s xml:id="echoid-s14195" xml:space="preserve">Rurſus quia latera AF, FK, trianguli AFK, æqualia ſunt lateribus CF,
              <lb/>
            FK, trianguli CFK, & </s>
            <s xml:id="echoid-s14196" xml:space="preserve">angulus AFK, angulo CFK, æqualis, vt probatum eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s14197" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-331-02" xlink:href="note-331-02a" xml:space="preserve">4. primi.</note>
            erunt baſes AK, KC, æquales, & </s>
            <s xml:id="echoid-s14198" xml:space="preserve">anguli ad K, æquales quoque, hoc eſt, recti.</s>
            <s xml:id="echoid-s14199" xml:space="preserve"> Eadem ratio cinatione concludemus rectam CE, in puncto H, diuidi bifariam,
              <lb/>
            anguloſque ad H, eſſerectos. </s>
            <s xml:id="echoid-s14200" xml:space="preserve">Producatur recta DH, ad partes H, ſumatur que
              <lb/>
            HL, æqualis rectæ DH, & </s>
            <s xml:id="echoid-s14201" xml:space="preserve">extendatur à puncto L, per punctum C, recta LCN.
              <lb/>
            </s>
            <s xml:id="echoid-s14202" xml:space="preserve">Quoniam verò latera DH, HC, trianguli DCH, æqualia ſunt lateribus LH,
              <lb/>
            HC, trianguli LCH, & </s>
            <s xml:id="echoid-s14203" xml:space="preserve">anguli ad H, æquales, vtpote recti; </s>
            <s xml:id="echoid-s14204" xml:space="preserve"> erunt baſes DC,
              <note symbol="c" position="right" xlink:label="note-331-03" xlink:href="note-331-03a" xml:space="preserve">4. primi.</note>
            æquales, & </s>
            <s xml:id="echoid-s14205" xml:space="preserve">anguli DCH, LCH, æquales etiam: </s>
            <s xml:id="echoid-s14206" xml:space="preserve">Atqui angulus DCH, maior
              <lb/>
            eſt angulo GCH, & </s>
            <s xml:id="echoid-s14207" xml:space="preserve">angulus GCH, æqualis eſt angulo FAK, propter ſimilitu-
              <lb/>
            dinem triangulorum GCE, & </s>
            <s xml:id="echoid-s14208" xml:space="preserve">FAC, hoc eſt, angulo FCA, qui angulo FAC, æqualis eſt. </s>
            <s xml:id="echoid-s14209" xml:space="preserve">Erit igitur angulus DCH, hoc eſt, angulus LCH, qui illi oſtenſus
              <lb/>
              <note symbol="d" position="right" xlink:label="note-331-04" xlink:href="note-331-04a" xml:space="preserve">5. primi.</note>
            eſt æqualis, hoc eſt, angulus NCK, qui angulo LCH, ad verticem eſt
              <note symbol="e" position="right" xlink:label="note-331-05" xlink:href="note-331-05a" xml:space="preserve">15. primi.</note>
            lis, maior etiam angulo FCA: </s>
            <s xml:id="echoid-s14210" xml:space="preserve">& </s>
            <s xml:id="echoid-s14211" xml:space="preserve">obid CN, recta extra rectam CF, cadet ne-
              <lb/>
            ceſſariò; </s>
            <s xml:id="echoid-s14212" xml:space="preserve">& </s>
            <s xml:id="echoid-s14213" xml:space="preserve">rectæ LC, CB, propterea comprehendent ad partes K, angulum
              <lb/>
            BCL. </s>
            <s xml:id="echoid-s14214" xml:space="preserve">Quare ſi ducatur recta B L, ſecabit ea lineam C K, in aliquo puncto in-
              <lb/>
            ter puncta C, & </s>
            <s xml:id="echoid-s14215" xml:space="preserve">K, quod ſit M. </s>
            <s xml:id="echoid-s14216" xml:space="preserve">Quoniam verò rectæ AB, BC, CD, DE, ſimul
              <lb/>
            æquales ſunt rectis AF, FC, CG, GE, ſimul, propter triangula iſoperimetra,
              <lb/>
            erunt quoque dimidia earum æqualia inter ſe, nimirum rectę BC, CD, hoc eſt,
              <lb/>
            BC, CL, ſimul æquales ipſis FC, CG, ſimul: </s>
            <s xml:id="echoid-s14217" xml:space="preserve"> Sunt autem rectæ BC, CL,
              <note symbol="f" position="right" xlink:label="note-331-06" xlink:href="note-331-06a" xml:space="preserve">20. primi.</note>
            maiores recta BL. </s>
            <s xml:id="echoid-s14218" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s14219" xml:space="preserve">FC, CG, ſimul maiores erunt eadem recta BL:
              <lb/>
            </s>
            <s xml:id="echoid-s14220" xml:space="preserve">
              <figure xlink:label="fig-331-01" xlink:href="fig-331-01a" number="224">
                <image file="331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/331-01"/>
              </figure>
            ideo que quadratum ex F C, C G, tanquam ex vna linea, deſcriptum maius erit
              <lb/>
              <note symbol="g" position="right" xlink:label="note-331-07" xlink:href="note-331-07a" xml:space="preserve">9. hui{us}.</note>
            quadrato BL. </s>
            <s xml:id="echoid-s14221" xml:space="preserve"> Quod autem ex F C, CG, tanquam ex vna linea, deſcribitur quadratum, æquale eſt quadrato ex F K, G H, tanquam ex vna linea deſcripto,
              <lb/>
            vna cum quadrato, quod ex K C, C H, tanquam ex vna linea deſcribitur.
              <lb/>
            </s>
            <s xml:id="echoid-s14222" xml:space="preserve">
              <note symbol="h" position="right" xlink:label="note-331-08" xlink:href="note-331-08a" xml:space="preserve">9. hui{us}.</note>
            Quadratum verò ex L B, deſcriptum æquale eſt quadrato ex B K, L H, hoc eſt, ex B K, D H, tanquam ex vna linea, deſcripto, vna cum quadrato, quod ex
              <lb/>
            KM, MH, tanquam ex vna linea, deſcribitur; </s>
            <s xml:id="echoid-s14223" xml:space="preserve">quod triangula rectangula BKM,
              <lb/>
              <note symbol="i" position="right" xlink:label="note-331-09" xlink:href="note-331-09a" xml:space="preserve">15. primi.</note>
            LHM, ſint ſimilia inter ſe. </s>
            <s xml:id="echoid-s14224" xml:space="preserve"> Sunt enim anguli M, ad </s>
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