Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of Notes

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          <pb file="0027" n="27" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
        </div>
        <div xml:id="echoid-div13" type="section" level="1" n="9">
          <head xml:id="echoid-head11" xml:space="preserve">Appendix primi huius pronunciati.</head>
          <p>
            <s xml:id="echoid-s664" xml:space="preserve">P Oſtquam abunde diſſertum eſt ſuper præparatione, qua quis ſupputando Primum
              <lb/>
            Mobile per ſinus aſſequatur, ſubinde non uanũ iudicauimus, ſi & </s>
            <s xml:id="echoid-s665" xml:space="preserve">eoſdem Mobilis
              <lb/>
            primi uſus per inſtrumentum cõſequi tradamus, eo´ potiſſimum, quod maior ferè pars
              <lb/>
            huc incumbentium, ſphæricæ ſupputationis ignara indocta´ ſit, licet interim diffiteri
              <lb/>
            non audemus per calculos quæcun prædictorum commoda plura´ alia cõſummati-
              <lb/>
            us haberi poſſe longe quàm per inſtrumenta. </s>
            <s xml:id="echoid-s666" xml:space="preserve">Attamen ne pleri retroacti rationum
              <lb/>
            oneribus opus deſerant, idcirco inſtrumentum quo rem inuenire quàm promptiſsime
              <lb/>
            poſſunt adijcere coacti ſumus. </s>
            <s xml:id="echoid-s667" xml:space="preserve">In eo enim non ſecus at per numeros omnia efficiun-
              <lb/>
            tur, qua muis non adeo exacte & </s>
            <s xml:id="echoid-s668" xml:space="preserve">minutim uſ, niſi inſtrumentum quantitate præſter.
              <lb/>
            </s>
            <s xml:id="echoid-s669" xml:space="preserve">quanto nan inſtrumentum eſt capacius tanto certius, & </s>
            <s xml:id="echoid-s670" xml:space="preserve">computo uicinius reſpondet. </s>
            <s xml:id="echoid-s671" xml:space="preserve">
              <lb/>
            Compoſitionem igitur nunc trademus eiuſmodi, ut qualecun inſtrumentum libeat fa
              <lb/>
              <note position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">
                <emph style="it">Compoſitiò</emph>
                <lb/>
                <emph style="it">Quaàrãtis</emph>
              </note>
            bricare (quale in poſterum uocabitur Primi mobilis Quadrans) non ægre liceat. </s>
            <s xml:id="echoid-s672" xml:space="preserve">Pri-
              <lb/>
            mum ergo ſemicirculus in ſuperficie plana, quæ, uel lignea, uel papyracea, uel metallica
              <lb/>
            ſit, fiat, cuius diametro KC inſcribantur, cẽtro litera A circuli KC mediũ quæratur,
              <lb/>
            & </s>
            <s xml:id="echoid-s673" xml:space="preserve">cum B litera ſignetur, A & </s>
            <s xml:id="echoid-s674" xml:space="preserve">B iungantur cũ linea recta, quæ diuidet ſemicirculi pla
              <lb/>
            num in quadrantes duos, quorŭ alter KB, alter BC uocabitur, ſingu!os in 90. </s>
            <s xml:id="echoid-s675" xml:space="preserve">partes
              <lb/>
            more aſtronomico ſectus. </s>
            <s xml:id="echoid-s676" xml:space="preserve">Puncta item uicina literis K & </s>
            <s xml:id="echoid-s677" xml:space="preserve">C cõnectantur recta, quæ pa
              <lb/>
            rallela lineæ K C erit. </s>
            <s xml:id="echoid-s678" xml:space="preserve">Iam proxima ſequentia duo quadrantum puncta iunge linea re-
              <lb/>
            cta, item tertia, item quarta, donec omnia connexueris quadrantum amborum, ſicut
              <lb/>
            perpetuò in eadẽ diſtantia ſint à K & </s>
            <s xml:id="echoid-s679" xml:space="preserve">C, quo ad in B uſ perueniatur. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Sciendum tamẽ
              <lb/>
            lineas has in quadrãte A B C, dũtaxat ꝓduci ſic, ut manifeſtè ſint, oportere, in quadran
              <lb/>
            te A B K minime, ſed occultè, poſterior enim ille quadrans abijciendus omnino erit, cũ
              <lb/>
            nihil uſui reliq̊ cõferat. </s>
            <s xml:id="echoid-s681" xml:space="preserve">Iam inchoando à C uerſus B limbi numera quin, ea´ ſigna
              <lb/>
            cum cyffra 5. </s>
            <s xml:id="echoid-s682" xml:space="preserve">Poſtea alia quin numera, & </s>
            <s xml:id="echoid-s683" xml:space="preserve">ea cum 10. </s>
            <s xml:id="echoid-s684" xml:space="preserve">inſcribe, & </s>
            <s xml:id="echoid-s685" xml:space="preserve">ſic conſequenter qua
              <lb/>
            drantem integrũ per quinarios, donec in 90. </s>
            <s xml:id="echoid-s686" xml:space="preserve">peruenias, inſigni, ſimiliter ab A uerſus B
              <lb/>
            fiat, & </s>
            <s xml:id="echoid-s687" xml:space="preserve">quadrantem perfectum habebis, dempto quod filum adhuc unà cum margarica
              <lb/>
            centro A porrectum deſideretur, quod ſi addis, omnia habes, ueluti etiam prima illa ſe
              <lb/>
            quens docet figura.</s>
            <s xml:id="echoid-s688" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div15" type="section" level="1" n="10">
          <head xml:id="echoid-head12" xml:space="preserve">VSVS QVADRANTIS.</head>
          <p>
            <s xml:id="echoid-s689" xml:space="preserve">Duplex uſus eſt inſtrumenti, quem aliàs ingreſſum appellaueris, ſcilicet Lateralis
              <lb/>
            & </s>
            <s xml:id="echoid-s690" xml:space="preserve">Arealis. </s>
            <s xml:id="echoid-s691" xml:space="preserve">Lateralis eſt, quando duo numeri noti quæruntur, hic in diametro AB, il-
              <lb/>
              <note position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve">
                <emph style="it">Latcralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
                <lb/>
                <emph style="it">quid.</emph>
              </note>
            le in limbo BC. </s>
            <s xml:id="echoid-s692" xml:space="preserve">Arealis, quando unus ſaltem & </s>
            <s xml:id="echoid-s693" xml:space="preserve">is notus in area quadrantis requiritur
              <lb/>
            altero uero in diametro uel limbo. </s>
            <s xml:id="echoid-s694" xml:space="preserve">Lateralis uſus bifariam patet. </s>
            <s xml:id="echoid-s695" xml:space="preserve">Verum numeri duo
              <lb/>
            quibus latera ingredi paras diſsimiles eſſe debẽt, ueluti, hic maior, ille minor, uel contra,
              <lb/>
            nunquam uero pares. </s>
            <s xml:id="echoid-s696" xml:space="preserve">Primus introeundi modus ſic perficitur. </s>
            <s xml:id="echoid-s697" xml:space="preserve">Numerum minorem in
              <lb/>
              <note position="right" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus ꝗd.</emph>
              </note>
            dia metro AB accipis, cui filum cum margarita adducis, maiorempoſtea in limbo
              <lb/>
            BC requiris, filum´ per eundem extendis, ſic enim agenti unio numerum oſtendit quæ
              <lb/>
              <note position="right" xlink:label="note-0027-04" xlink:href="note-0027-04a" xml:space="preserve">
                <emph style="it">Prima uia</emph>
                <lb/>
                <emph style="it">lateralis in</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            ſitum, Arealem ſcilicet in quadrantis area, Linea autem graduum cui margarita inci-
              <lb/>
            dit, numerum ſuum in diametro AB, nec non in limbo BC ſignatum obtinet, cuius rei
              <lb/>
            exemplum eſto. </s>
            <s xml:id="echoid-s698" xml:space="preserve">Vt ſi ponatur lateralis numerus minor 30. </s>
            <s xml:id="echoid-s699" xml:space="preserve">ſcilicet graduum, maior ue
              <lb/>
            ro 43. </s>
            <s xml:id="echoid-s700" xml:space="preserve">graduum & </s>
            <s xml:id="echoid-s701" xml:space="preserve">10. </s>
            <s xml:id="echoid-s702" xml:space="preserve">minutorum. </s>
            <s xml:id="echoid-s703" xml:space="preserve">Minor uero 30. </s>
            <s xml:id="echoid-s704" xml:space="preserve">in diametro AB quæratur (id quod
              <lb/>
            eſt in figura per E literam expreſſum) filum´ ſuper inducatur margarita adiuncta, de
              <lb/>
            inde idem filum maiori numero, qui eſt graduũ 43. </s>
            <s xml:id="echoid-s705" xml:space="preserve">minut. </s>
            <s xml:id="echoid-s706" xml:space="preserve">10. </s>
            <s xml:id="echoid-s707" xml:space="preserve">admoueatur, & </s>
            <s xml:id="echoid-s708" xml:space="preserve">hoc in lim
              <lb/>
            bo, tũ margarita cõperitur in area oſtendere gradũ 20. </s>
            <s xml:id="echoid-s709" xml:space="preserve">in puncto H, numerũ hactenus
              <lb/>
            ignotum. </s>
            <s xml:id="echoid-s710" xml:space="preserve">Nec ignorandum eſt, quod numeri Arealis non ſignentur tantum in area, ſed
              <lb/>
            etiã reperiam iuxta lineæ & </s>
            <s xml:id="echoid-s711" xml:space="preserve">diametri AB arcus, itidem BC contactus. </s>
            <s xml:id="echoid-s712" xml:space="preserve">Inuertemus nũc
              <lb/>
              <note position="right" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve">
                <emph style="it">Sccũda uia</emph>
                <lb/>
                <emph style="it">lateralis in</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            exemplum hoc modo, quæ & </s>
            <s xml:id="echoid-s713" xml:space="preserve">ſecunda lateraliter operandi uia eſt. </s>
            <s xml:id="echoid-s714" xml:space="preserve">Numerum maiorem
              <lb/>
            qui eſt graduũ 43. </s>
            <s xml:id="echoid-s715" xml:space="preserve">minut. </s>
            <s xml:id="echoid-s716" xml:space="preserve">10. </s>
            <s xml:id="echoid-s717" xml:space="preserve">in diametro AB ſumemus. </s>
            <s xml:id="echoid-s718" xml:space="preserve">quem locũ unione@ſignabimus
              <lb/>
            (id q̊d in tertia figura per literã D clarũ fit) iam ſi filum gradibus 30. </s>
            <s xml:id="echoid-s719" xml:space="preserve">qui numerus mi-
              <lb/>
            nor eſt, inferimus margaritam, non ſecus at antea gradum 20. </s>
            <s xml:id="echoid-s720" xml:space="preserve">demonſtrare in area </s>
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