Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s5719" xml:space="preserve">
              <pb o="149" file="179" n="179" rhead="LIBER TERTIVS."/>
            & </s>
            <s xml:id="echoid-s5720" xml:space="preserve">EG, ad ED, vt SL, ad SR. </s>
            <s xml:id="echoid-s5721" xml:space="preserve">Ideoque exæquo AE, ad ED, vt OS, ad SR: </s>
            <s xml:id="echoid-s5722" xml:space="preserve">Atque
              <lb/>
            ita de alijs. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">Similis ergo ſunt figuræ ABCDE, OPQRS.</s>
            <s xml:id="echoid-s5724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5725" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">
              <emph style="sc">Iam</emph>
            vero vt longitudines laterum AB, BC, CD, DE, EA, & </s>
            <s xml:id="echoid-s5727" xml:space="preserve">rectarum ex
              <lb/>
            F, vel G, ad angulos in prima figura ductarum inueniamus, diuidendum erit in fi-
              <lb/>
            gura inuenta, id eſt, in ſecunda, interuallum KL, in quotcunq; </s>
            <s xml:id="echoid-s5728" xml:space="preserve">partes æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s5729" xml:space="preserve">Deinde inquirendum, quotnam exillis partibus in ſingulis lateribus, & </s>
            <s xml:id="echoid-s5730" xml:space="preserve">rectis
              <lb/>
            eiuſdem figuræ ſecundæ ex K, vel L, prodeuntibus contineantur. </s>
            <s xml:id="echoid-s5731" xml:space="preserve">quod vel per
              <lb/>
            cir cinum fieri poteſt, repetendo ſæpius vnam particulam in dictis lateribus re-
              <lb/>
            ctis: </s>
            <s xml:id="echoid-s5732" xml:space="preserve">vel (quod magis probo) hoc modo. </s>
            <s xml:id="echoid-s5733" xml:space="preserve">Repetatur tota KL, in quolibetlate-
              <lb/>
            re, velrecta, quoties fieri poteſt, & </s>
            <s xml:id="echoid-s5734" xml:space="preserve">in reliquo ſegmento v@a etiam particula in-
              <lb/>
            terualli KL, circino iteretur, quoties fieri poteſt. </s>
            <s xml:id="echoid-s5735" xml:space="preserve">Nam quoties repetita fuerit
              <lb/>
            KL: </s>
            <s xml:id="echoid-s5736" xml:space="preserve">toties numerus particularum ipſius KL, in latere continebitur, cum tot in-
              <lb/>
            ſuper particulis, quot per circinum in reliquo r
              <unsure/>
            egmento fuerint deprehenſæ. </s>
            <s xml:id="echoid-s5737" xml:space="preserve">
              <lb/>
            Aut certe per ea, quæ lib 1. </s>
            <s xml:id="echoid-s5738" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s5739" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5740" xml:space="preserve">ad finem N@m. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5742" xml:space="preserve">ſcripſimus, inueſtigetur in in-
              <lb/>
            ſtrumento partium, quot particulæ inter@alli KL, in dictis lateribus, & </s>
            <s xml:id="echoid-s5743" xml:space="preserve">rectis cõ-
              <lb/>
            prehendantur. </s>
            <s xml:id="echoid-s5744" xml:space="preserve">Deinde fiat, vtnumerus particularum interualli K L, aſſumptus
              <lb/>
            in 2. </s>
            <s xml:id="echoid-s5745" xml:space="preserve">figura, ad numerum pedum inter puncta F, & </s>
            <s xml:id="echoid-s5746" xml:space="preserve">G, in prima figura aſſumptum,
              <lb/>
            ita numerus particularum in quolibet latere, vel recta in ſecunda figura inuen-
              <lb/>
            tarum, ad aliud. </s>
            <s xml:id="echoid-s5747" xml:space="preserve">Quotiens enim numerus indicabit, quot pedes in aſſumpto
              <lb/>
            latere, vel recta contineantur. </s>
            <s xml:id="echoid-s5748" xml:space="preserve">Ratio eſt, quia cum eandem proportionem ha-
              <lb/>
            beat KL, in 2. </s>
            <s xml:id="echoid-s5749" xml:space="preserve">figura ad quodlibet latus, vel rectam eiuſdem figuræ, quam habet
              <lb/>
            FG, in prima figura ad reſpondens latus, vel rectam, propter ſimilitudinẽ figu-
              <lb/>
            rarũ, erit ꝑmutando KL, ad interuallũ FG, vt latus adlatus, &</s>
            <s xml:id="echoid-s5750" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5751" xml:space="preserve">Verbi gratia, In
              <lb/>
            2. </s>
            <s xml:id="echoid-s5752" xml:space="preserve">figura interuallum KL, ſectum eſt in 5. </s>
            <s xml:id="echoid-s5753" xml:space="preserve">particulas, qualium 17. </s>
            <s xml:id="echoid-s5754" xml:space="preserve">in latere OP, in-
              <lb/>
            uentæ ſunt: </s>
            <s xml:id="echoid-s5755" xml:space="preserve">Et quia ſpatium FG, in 1. </s>
            <s xml:id="echoid-s5756" xml:space="preserve">figura poſitum eſt 100. </s>
            <s xml:id="echoid-s5757" xml:space="preserve">pedum: </s>
            <s xml:id="echoid-s5758" xml:space="preserve">ſi fiat,
              <lb/>
              <note style="it" position="right" xlink:label="note-179-01" xlink:href="note-179-01a" xml:space="preserve">
                <lb/>
              Vt KL, quinque parti- \\ cularum # ad FG. 100. pedum: # Ita OP, 17. particu- \\ larum # ad AB,
                <lb/>
              </note>
            hoc eſt, ſi, vt regula aurea præcipit, 100. </s>
            <s xml:id="echoid-s5759" xml:space="preserve">ducantur in 17. </s>
            <s xml:id="echoid-s5760" xml:space="preserve">ſecundus numerus in
              <lb/>
            tertium, & </s>
            <s xml:id="echoid-s5761" xml:space="preserve">productus numerus 1700. </s>
            <s xml:id="echoid-s5762" xml:space="preserve">diuidatur per 5. </s>
            <s xml:id="echoid-s5763" xml:space="preserve">id eſt, per primum nume-
              <lb/>
            rum, reperientur in Quotiente 340. </s>
            <s xml:id="echoid-s5764" xml:space="preserve">pedes pro latere AB, & </s>
            <s xml:id="echoid-s5765" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s5766" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5767" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5768" xml:space="preserve">
              <emph style="sc">Evndem</emph>
            ſitum campi propoſiti A B C D E, delineabimus etiam ex vno
              <lb/>
              <note position="right" xlink:label="note-179-02" xlink:href="note-179-02a" xml:space="preserve">Sit{us} campi
                <lb/>
              cuiſuis qua
                <lb/>
              ratione ex v-
                <lb/>
              no loco intra
                <lb/>
              ipſum aſſum-
                <lb/>
              pto deſcriba-
                <lb/>
              tur.</note>
            tantumloco F, intra ipſum aſſumpto, hacratione. </s>
            <s xml:id="echoid-s5769" xml:space="preserve">Dioptra ad ſingulos bacu-
              <lb/>
            los ex angulis erectos, dirigatur, notatis angulis, quos lineæ, p
              <unsure/>
            er dioptram de-
              <lb/>
            ſignatæ inter ſe faciunt; </s>
            <s xml:id="echoid-s5770" xml:space="preserve">diſtantiæ que ab F, ad ſingulos angulos inquirantur in
              <lb/>
            aliqua menſura, vel per catenulã aliquã ferream, quæ nec intendi poſsit, nec re-
              <lb/>
            mitti, vel per chordam ex F, ad ſingulos angulos extenſam vel certe, ſi diſtantiæ
              <lb/>
            illæ magnæ ſint, per problema 2. </s>
            <s xml:id="echoid-s5771" xml:space="preserve">vel 36. </s>
            <s xml:id="echoid-s5772" xml:space="preserve">beneficio quadrati, alteriuſue inſtrumẽ-
              <lb/>
            ti. </s>
            <s xml:id="echoid-s5773" xml:space="preserve">Nam ſi in charta aliqua ad quo dlibet punctum K, ijdem anguli conſtituan-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s5774" xml:space="preserve">in rectis illos angulos effi cientibus accipiantur tot particulæ inter ſe æ-
              <lb/>
            quales cuiuſuis magnitudinis, quot menſuræ inuentæ ſunt in rectis reſponden-
              <lb/>
            tibus, quæ ex F, exeunt: </s>
            <s xml:id="echoid-s5775" xml:space="preserve">extrema autem puncta vltimarum particularum rectis
              <lb/>
            lineis coniungantur, deſcripta erit figura OPQRS, ſimilis omnino campo AB-
              <lb/>
            CDE: </s>
            <s xml:id="echoid-s5776" xml:space="preserve"> propterea quod triangula ad punctum F, collecta ſimilia ſunt
              <note symbol="a" position="right" xlink:label="note-179-03" xlink:href="note-179-03a" xml:space="preserve">6. ſexti.</note>
            ad punctum K, collectis, ob æqualitatem angulorum in F, & </s>
            <s xml:id="echoid-s5777" xml:space="preserve">K, conſtitutorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s5778" xml:space="preserve">latera circa illos angulos proportionalia, ex conſtructione.</s>
            <s xml:id="echoid-s5779" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5780" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5781" xml:space="preserve">
              <emph style="sc">Latervm</emph>
            autem longitudines in campo ABCDE, cognoſcentur, </s>
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