Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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IO. BAPT. BENED.
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              <p>
                <s xml:id="echoid-s1979" xml:space="preserve">
                  <pb o="166" rhead="IO. BAPT. BENED." n="178" file="0178" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0178"/>
                cto
                  <var>.c.</var>
                vnde linea
                  <var>.g.m.</var>
                mediante
                  <var>.K.</var>
                continget circunferentiam circuli minoris in pun
                  <lb/>
                cto .b: et
                  <var>.K.g.</var>
                ex .34. primi Eucli. æqualis erit ipſi
                  <var>.f.l.</var>
                quia ex .17. tertii, anguli
                  <var>.f.</var>
                et
                  <var>.g.</var>
                  <lb/>
                ſunt æquales, vnde ex .28. primi
                  <var>.f.l.</var>
                et
                  <var>.g.K.</var>
                ſunt parallelæ. </s>
                <s xml:id="echoid-s1980" xml:space="preserve">& ſic erunt
                  <var>.k.l.</var>
                cum
                  <var>.f.g.</var>
                ex
                  <lb/>
                eadem ſupradicta. </s>
                <s xml:id="echoid-s1981" xml:space="preserve">Ratio autem, qua arcus
                  <var>.g.b.</var>
                tranſierit lineam
                  <var>.g.K.</var>
                maiorem ipſa,
                  <lb/>
                eſt, quia dum mouetur, quodlibet punctum ipſius
                  <var>.g.b.</var>
                virtute reuolutionis ipſius
                  <var>.f.c.</var>
                  <lb/>
                omne punctum eiuſdem arcus
                  <var>.g.b.</var>
                vlterius verſus
                  <var>.K.</var>
                quam ſi moueretur virtute re-
                  <lb/>
                uolutionis ipſius
                  <var>.g.b.</var>
                ſuper lineam
                  <var>.g.m.</var>
                defertur. </s>
                <s xml:id="echoid-s1982" xml:space="preserve">vt exempli gratia, quando virtute
                  <lb/>
                reuolutionis maioris circuli, centrum
                  <var>.a.</var>
                reperitur in ſitu lineæ
                  <var>.l.K.</var>
                punctum
                  <var>.g.</var>
                confe
                  <lb/>
                cerit iter
                  <var>.g.u.</var>
                & punctum
                  <var>.b.</var>
                iter
                  <var>.b.K.</var>
                etiam reliqua omnia puncta inter
                  <var>.g.b.</var>
                magna
                  <lb/>
                itinera egerint, cum à magno circulo ſint ante delata. </s>
                <s xml:id="echoid-s1983" xml:space="preserve">Imaginemur quoque hos cir
                  <lb/>
                culos eſſe delatos virtute reuolutionis circuli minoris, &
                  <reg norm="partem" type="context">partẽ</reg>
                  <var>.g.t.</var>
                rectè
                  <var>.g.m.</var>
                dimen-
                  <lb/>
                ſam fuiſſe ab arcu
                  <var>.g.b</var>
                . </s>
                <s xml:id="echoid-s1984" xml:space="preserve">
                  <reg norm="Quando" type="context">Quãdo</reg>
                ergo
                  <var>.b.</var>
                erit in
                  <var>.t.</var>
                factum erit iter
                  <var>.b.t.</var>
                ab ipſo
                  <var>.b.</var>
                et
                  <var>.g.</var>
                fa-
                  <lb/>
                ciet iter
                  <var>.g.n.</var>
                quę itinera alijs multò breuiora ſunt, quia breuioribus cruribus reuolu-
                  <lb/>
                ta ſunt dicta puncta; </s>
                <s xml:id="echoid-s1985" xml:space="preserve">& ſic dico de reliquis omnibus punctis inter
                  <var>.g.</var>
                et
                  <var>.b.</var>
                & in hoc ca
                  <lb/>
                ſu punctum
                  <var>.f.</var>
                erit in
                  <var>.q.</var>
                & punctum
                  <var>.c.</var>
                erit in
                  <var>.e</var>
                . </s>
                <s xml:id="echoid-s1986" xml:space="preserve">Quamobrem omnia puncta
                  <reg norm="contingen- tiæ" type="context">cõtingen-
                    <lb/>
                  tiæ</reg>
                inter
                  <var>.f.</var>
                et
                  <var>.c.</var>
                non ſolum non erunt delata anteà, ſed potius à primo ſitu retrorſum
                  <lb/>
                erunt repulſa. </s>
                <s xml:id="echoid-s1987" xml:space="preserve">Vnde non eſt, quòd in tantam admirationem ducamur ſi dum reuol
                  <lb/>
                uitur circulus maior, arcus
                  <var>.g.b.</var>
                circuli minoris, totam lineam
                  <var>.g.K.</var>
                tranſire videtur,
                  <lb/>
                & dum reuoluitur minor, apparet arcum
                  <var>.f.c</var>
                : maius iter quam ab
                  <var>.f.</var>
                ad
                  <var>.e.</var>
                non facere,
                  <lb/>
                cum maiore ſeſe in orbem ferente, quodlibet punctum arcus
                  <var>.g.b.</var>
                ad vnam
                  <reg norm="eandemque" type="context simple">eandẽq;</reg>
                  <lb/>
                partem duos motus obtineat. </s>
                <s xml:id="echoid-s1988" xml:space="preserve">vt exempli gratia punctum
                  <var>.b.</var>
                non ſolum mouetur ver
                  <lb/>
                ſus
                  <var>.m.</var>
                quòd circa centrum
                  <var>.a.</var>
                feratur, cum ipſum etiam centrum moueatur verſus
                  <var>.m.</var>
                  <lb/>
                ſed quia pręter hoc deferantur quoque à circulo maiori verſus
                  <var>.m.</var>
                vſque ad lineam
                  <var>.
                    <lb/>
                  k.l</var>
                . </s>
                <s xml:id="echoid-s1989" xml:space="preserve">Dum verò minor circulus in girum ducitur, habet quodlibet punctum arcus
                  <var>.f.c.</var>
                  <lb/>
                duos motus contrarios, quorum alter verſus
                  <var>.i.</var>
                virtute reuolutionis circuli minoris,
                  <lb/>
                & alter ex eo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                dictus circulus maior circa centrum
                  <var>.a.</var>
                voluatur, vnde omne
                  <reg norm="punctum" type="context">punctũ</reg>
                  <lb/>
                contactus circuli maioris cum recta
                  <var>.f.i.</var>
                tetrorſum pellitur verſus
                  <var>.x</var>
                .</s>
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