Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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    <echo version="1.0RC">
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        <div xml:id="echoid-div80" type="section" level="1" n="54">
          <pb o="39" file="0059" n="63" rhead="Liber Quartus."/>
          <p>
            <s xml:id="echoid-s3803" xml:space="preserve">illuminatum M R N. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">verſus Solem: </s>
            <s xml:id="echoid-s3805" xml:space="preserve">linea E F. </s>
            <s xml:id="echoid-s3806" xml:space="preserve">ſit diametro paralella, claudatq; </s>
            <s xml:id="echoid-s3807" xml:space="preserve">portionem terræ N E F M.
              <lb/>
            </s>
            <s xml:id="echoid-s3808" xml:space="preserve">quam vltra hemiſphærium Sol illuſtrat; </s>
            <s xml:id="echoid-s3809" xml:space="preserve">hæc autem terræ portio eſt inſtar faſciolæ cuiuſdam terræ præcin-
              <lb/>
            gentis, cuius latitudo erit arcus N E. </s>
            <s xml:id="echoid-s3810" xml:space="preserve">vel M F. </s>
            <s xml:id="echoid-s3811" xml:space="preserve">quæritur nunc quantus ſit hic arcus, hic enim eſt quantitas por
              <lb/>
            tionis illius. </s>
            <s xml:id="echoid-s3812" xml:space="preserve">pars autem terræ E F. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">vmbroſa eri
              <unsure/>
            t, vmbraq; </s>
            <s xml:id="echoid-s3814" xml:space="preserve">terræ erit E F C. </s>
            <s xml:id="echoid-s3815" xml:space="preserve">lam dico angulum vmbræ C. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">tot
              <lb/>
            gradus aut minuta continere, quotſunt in duobus arcubus ſimul N E. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">M F. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">ideſt, eund m arcum angulo C. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">
              <lb/>
            ſubtendi: </s>
            <s xml:id="echoid-s3820" xml:space="preserve">hoc autem eſt nihil aliud quam angulum C. </s>
            <s xml:id="echoid-s3821" xml:space="preserve">quantitatem illam continere: </s>
            <s xml:id="echoid-s3822" xml:space="preserve">quod ſic patebit; </s>
            <s xml:id="echoid-s3823" xml:space="preserve">conſi-
              <lb/>
            deretur quadrilaterum I E C F. </s>
            <s xml:id="echoid-s3824" xml:space="preserve">in quo duo anguli ad E. </s>
            <s xml:id="echoid-s3825" xml:space="preserve">& </s>
            <s xml:id="echoid-s3826" xml:space="preserve">F. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">ſunt recti per 18. </s>
            <s xml:id="echoid-s3828" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3830" xml:space="preserve">ergo reliqui duo an-
              <lb/>
            guli ad I. </s>
            <s xml:id="echoid-s3831" xml:space="preserve">& </s>
            <s xml:id="echoid-s3832" xml:space="preserve">C. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">ſunt ſimul æquales duobus rectis, quia quodlibet quadrilaterum habet ſuos 4. </s>
            <s xml:id="echoid-s3834" xml:space="preserve">angulos ſimul
              <lb/>
            æquales quatuor rectis, ex ſchol. </s>
            <s xml:id="echoid-s3835" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s3836" xml:space="preserve">32. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">primi Elem. </s>
            <s xml:id="echoid-s3838" xml:space="preserve">quare angulus I. </s>
            <s xml:id="echoid-s3839" xml:space="preserve">tãto minor erit duobus rectis, quan-
              <lb/>
            tus fuerit angulus C. </s>
            <s xml:id="echoid-s3840" xml:space="preserve">ſiue minor erit duobus rectis, quantitate anguli C. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">quare arcus E F. </s>
            <s xml:id="echoid-s3842" xml:space="preserve">qui angulo I. </s>
            <s xml:id="echoid-s3843" xml:space="preserve">ſubten-
              <lb/>
            ditur ex centro, ac propterea eius quantitatem indicat, tanto minor erit duobus angulis rectis, hoc eſt tanto
              <lb/>
            minor erit gr. </s>
            <s xml:id="echoid-s3844" xml:space="preserve">180. </s>
            <s xml:id="echoid-s3845" xml:space="preserve">ſiue ſemicirculo N E F M. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">quantus fuerit angulus C. </s>
            <s xml:id="echoid-s3847" xml:space="preserve">ſiue dixer s, tanti erunt duo arcus ſi-
              <lb/>
            mul N E. </s>
            <s xml:id="echoid-s3848" xml:space="preserve">M F. </s>
            <s xml:id="echoid-s3849" xml:space="preserve">qui conflant exceſſum vltra dimidium illuſtratũ. </s>
            <s xml:id="echoid-s3850" xml:space="preserve">qui exceſſus duplus ex aſtronomicis demon-
              <lb/>
            ſtrationibus, & </s>
            <s xml:id="echoid-s3851" xml:space="preserve">calculis reperitur eſſe minuta 28. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">quaretotus arcus E R F. </s>
            <s xml:id="echoid-s3853" xml:space="preserve">illuſtratus, erit gr. </s>
            <s xml:id="echoid-s3854" xml:space="preserve">180. </s>
            <s xml:id="echoid-s3855" xml:space="preserve">28′. </s>
            <s xml:id="echoid-s3856" xml:space="preserve">arcus ve
              <lb/>
            rò N E. </s>
            <s xml:id="echoid-s3857" xml:space="preserve">& </s>
            <s xml:id="echoid-s3858" xml:space="preserve">M F. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">ſinguli e unt 14′. </s>
            <s xml:id="echoid-s3860" xml:space="preserve">min. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">quare Zonula illa N E F M. </s>
            <s xml:id="echoid-s3862" xml:space="preserve">lata erit tantummodo min. </s>
            <s xml:id="echoid-s3863" xml:space="preserve">14′. </s>
            <s xml:id="echoid-s3864" xml:space="preserve">ideſt, quar
              <lb/>
            ta ferè pars gradus, quæ erunt milliaria aſtronomica 15. </s>
            <s xml:id="echoid-s3865" xml:space="preserve">Sol igitur vltra terræ hemiſphærium illuminat hinc
              <lb/>
            in gyrum milliaria 15. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">aſtr
              <unsure/>
            onomica, quæ omnia probari poſſunt etiam oracticè, vt in apparatu docui; </s>
            <s xml:id="echoid-s3867" xml:space="preserve">cõſtru-
              <lb/>
            cta enim qualibet figura in qua corpus @uminans ſit vtcumq; </s>
            <s xml:id="echoid-s3868" xml:space="preserve">maius illuminato, & </s>
            <s xml:id="echoid-s3869" xml:space="preserve">ductis reliquis lineis, & </s>
            <s xml:id="echoid-s3870" xml:space="preserve">
              <lb/>
            vmbra etiam delineata, ſemper reperies (ſi per circinum rectè acuminatum diligenter operatus fueris) an-
              <lb/>
            gulum vmbræ, tot gradus, vel min. </s>
            <s xml:id="echoid-s3871" xml:space="preserve">compræhendere, quot fuerint in exce
              <unsure/>
            ſſu, vltra hemiſphærium illuſtrato. </s>
            <s xml:id="echoid-s3872" xml:space="preserve">
              <lb/>
            6 Quantitatem vmbræ terreſtris, ſeu longitudinem explorare oportet. </s>
            <s xml:id="echoid-s3873" xml:space="preserve">huius rei gratia duo ſupponere
              <lb/>
            oportet, quæ inferius ſuo loco erunt demonſtranda. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">quorum primum eſt, Solis centrum a centro terræ di-
              <lb/>
            ſtare, in mediocri diſtantia, ſemidiametris terræ 1142. </s>
            <s xml:id="echoid-s3875" xml:space="preserve">alterum eſt ſemidiametrum Solis ad ſemidiametrum
              <lb/>
            terræ habere proportionem quam habet 5 {1/2}. </s>
            <s xml:id="echoid-s3876" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s3877" xml:space="preserve">ſi igitur accuratè figura deſcribatur, quæ haſce habeat ra-
              <lb/>
            tiones, qualis eſt præſens ad ſiniſtrã, ſlatim apparebit vmbræ longitudo exploranda; </s>
            <s xml:id="echoid-s3878" xml:space="preserve">ibi enim vmbra in acu-
              <lb/>
            tum deſinet, vbi radij Solis extremi terram contingentes concurrent, reperieſq; </s>
            <s xml:id="echoid-s3879" xml:space="preserve">vmbram elongari per ter-
              <lb/>
            ræ ſemidiametros ferè 254. </s>
            <s xml:id="echoid-s3880" xml:space="preserve">✠</s>
          </p>
          <p>
            <s xml:id="echoid-s3881" xml:space="preserve">Idem autem Geometricè ijſdem ſuppoſitis aſſequeris in hunc modum, in figura ſuperiori, qua vſi ſumus
              <lb/>
            ad illuminationem terræ inueſtigandam, ducatur linea O I. </s>
            <s xml:id="echoid-s3882" xml:space="preserve">paraleila ipſi B E. </s>
            <s xml:id="echoid-s3883" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s3884" xml:space="preserve">paralellogranũ B E I O.
              <lb/>
            </s>
            <s xml:id="echoid-s3885" xml:space="preserve">nam etiam duæ O B. </s>
            <s xml:id="echoid-s3886" xml:space="preserve">I E. </s>
            <s xml:id="echoid-s3887" xml:space="preserve">ſunt paralellæ, quia perpendiculares ſunt eidem B E. </s>
            <s xml:id="echoid-s3888" xml:space="preserve">per 18. </s>
            <s xml:id="echoid-s3889" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3890" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3891" xml:space="preserve">conſiderentur
              <lb/>
            præterea duo trianguia A B C. </s>
            <s xml:id="echoid-s3892" xml:space="preserve">& </s>
            <s xml:id="echoid-s3893" xml:space="preserve">A O I. </s>
            <s xml:id="echoid-s3894" xml:space="preserve">quæ ſimilia ſunt, per coroll. </s>
            <s xml:id="echoid-s3895" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3896" xml:space="preserve">ſexti
              <unsure/>
            ; </s>
            <s xml:id="echoid-s3897" xml:space="preserve">igitur perquartam ſexti, eſt vt
              <lb/>
            A C. </s>
            <s xml:id="echoid-s3898" xml:space="preserve">ad I C. </s>
            <s xml:id="echoid-s3899" xml:space="preserve">i
              <unsure/>
            ta A B. </s>
            <s xml:id="echoid-s3900" xml:space="preserve">ad O B. </s>
            <s xml:id="echoid-s3901" xml:space="preserve">ſiue ad ipſi æqualem I E. </s>
            <s xml:id="echoid-s3902" xml:space="preserve">& </s>
            <s xml:id="echoid-s3903" xml:space="preserve">diuidendo vt A I. </s>
            <s xml:id="echoid-s3904" xml:space="preserve">ad I C. </s>
            <s xml:id="echoid-s3905" xml:space="preserve">ita A O. </s>
            <s xml:id="echoid-s3906" xml:space="preserve">ad O B. </s>
            <s xml:id="echoid-s3907" xml:space="preserve">ſiue I E. </s>
            <s xml:id="echoid-s3908" xml:space="preserve">eſt
              <lb/>
            autem ex ſuppoſitione A B. </s>
            <s xml:id="echoid-s3909" xml:space="preserve">5 {1/2}. </s>
            <s xml:id="echoid-s3910" xml:space="preserve">partium, qualium I E. </s>
            <s xml:id="echoid-s3911" xml:space="preserve">eſt vna; </s>
            <s xml:id="echoid-s3912" xml:space="preserve">quare A O. </s>
            <s xml:id="echoid-s3913" xml:space="preserve">erit 4 {1/2}. </s>
            <s xml:id="echoid-s3914" xml:space="preserve">eſt igitur eadem ratio 4 {1/2}. </s>
            <s xml:id="echoid-s3915" xml:space="preserve">
              <lb/>
            ad 1. </s>
            <s xml:id="echoid-s3916" xml:space="preserve">quæ lineæ A I. </s>
            <s xml:id="echoid-s3917" xml:space="preserve">quæ continet ſemidiametros trrræ 1142. </s>
            <s xml:id="echoid-s3918" xml:space="preserve">ad alium numerum, qui explicet quantitatem
              <lb/>
            vmbræ terreſtris, qui per regulam auream reperitur eſſe quaſi 254. </s>
            <s xml:id="echoid-s3919" xml:space="preserve">ſcili
              <unsure/>
            cet ſemid. </s>
            <s xml:id="echoid-s3920" xml:space="preserve">terræ tanta igitur eſt ter-
              <lb/>
            reſtris vmbrę a terra proceritas, cum igitur inueſtiganda eſt a@icui
              <unsure/>
            us aſtri vmbra, fiat vt exceſlus diametri So-
              <lb/>
            lis ab aſtro ad aliud per auream regulam, illud enim erit vmbræ longitudo. </s>
            <s xml:id="echoid-s3921" xml:space="preserve">vide infra in cap. </s>
            <s xml:id="echoid-s3922" xml:space="preserve">de Lunæ ma-
              <lb/>
            gnitudine; </s>
            <s xml:id="echoid-s3923" xml:space="preserve">necnon in cap. </s>
            <s xml:id="echoid-s3924" xml:space="preserve">de loco Solis; </s>
            <s xml:id="echoid-s3925" xml:space="preserve">vbi plura de hac vmbra, & </s>
            <s xml:id="echoid-s3926" xml:space="preserve">modo eam deſcribendi traduntur. </s>
            <s xml:id="echoid-s3927" xml:space="preserve">Tan-
              <lb/>
            dem conſiderandus eſt huius vmbrę motus; </s>
            <s xml:id="echoid-s3928" xml:space="preserve">cum enim ea ſit penitus Soliauerſa, erit ſemper eius apex in gra-
              <lb/>
            du Eclypticæ Solis oppoſito, progredieturq; </s>
            <s xml:id="echoid-s3929" xml:space="preserve">conſequenter ad motum Solis ſecundum ſignorum ordinem,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s3930" xml:space="preserve">hæc ad hanc vmbram colluſtrandam ſufficiant.</s>
            <s xml:id="echoid-s3931" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div81" type="section" level="1" n="55">
          <head xml:id="echoid-head58" style="it" xml:space="preserve">De Terræ figura. Cap. IV.</head>
          <p>
            <s xml:id="echoid-s3932" xml:space="preserve">PVeri, atq; </s>
            <s xml:id="echoid-s3933" xml:space="preserve">imperitum vulgus, ſenſus æſtimatione perſuaſi, terram eſſe planum quoddam ad cælum vn-
              <lb/>
            diq; </s>
            <s xml:id="echoid-s3934" xml:space="preserve">attinens, falsò exiſtimant: </s>
            <s xml:id="echoid-s3935" xml:space="preserve">quorum mundi fabricam habes in ſecunda gura cap. </s>
            <s xml:id="echoid-s3936" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3937" xml:space="preserve">de S
              <unsure/>
            phæra.
              <lb/>
            </s>
            <s xml:id="echoid-s3938" xml:space="preserve">Elementari, in qua terra ſecundum eos eſſet planum A C. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">cælum vero efſet circulus A B C. </s>
            <s xml:id="echoid-s3940" xml:space="preserve">&</s>
            <s xml:id="echoid-s3941" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3942" xml:space="preserve">ſi enim id
              <lb/>
            eſſet; </s>
            <s xml:id="echoid-s3943" xml:space="preserve">primo ſequeretur magnum inconueniens, neminem ſcilicet (præter vnum) in tali terræ planitie ha-
              <lb/>
            bitare, aut conſiſtere poſſe (quod prima facie mirum videbitur) nam ſi terra eſſet tale planum, in medio eius
              <lb/>
            medio eſſet centrum mundi, quia huiuſmodi planum ſecat cælum, ac mundum bifariam. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">atqui omnia gra-
              <lb/>
            uia deſcendunt ad centrum mundi niſi impediantur: </s>
            <s xml:id="echoid-s3945" xml:space="preserve">igitur quoduis graue poſitum in illa planitie extra cen
              <lb/>
            trum illud, ad illud delaberetur, quia nihil obſtaret. </s>
            <s xml:id="echoid-s3946" xml:space="preserve">quare ſolus ille habitator, qui in medio terræ, atq; </s>
            <s xml:id="echoid-s3947" xml:space="preserve">adeo
              <lb/>
            in centro eſſet, ibi manere, accon ſtere poſiet, isenim centro mundi hæreret. </s>
            <s xml:id="echoid-s3948" xml:space="preserve">cæteri vero in plano illo non
              <lb/>
            poſſent erecti inſiſtere, quia vt erecti inſiſtamus, neceſſe eſt noſtri corporis longitudinem eſſe in linea per-
              <lb/>
            pendiculari, quæ directionis dicitur, ita vt pedes centrum aſpiciant, caput vero ſurſum ad cælum. </s>
            <s xml:id="echoid-s3949" xml:space="preserve">Secundo
              <lb/>
            ſequeretur eodem temporis momento Solem, ac cætera ſydera omnibus tam orientalibus, quam occidenta-
              <lb/>
            libus oriri atq; </s>
            <s xml:id="echoid-s3950" xml:space="preserve">occidere, omnes enim vnicum haberent horizontem, planum illud videlicet terræ: </s>
            <s xml:id="echoid-s3951" xml:space="preserve">quod ta-
              <lb/>
            men aliter contingit; </s>
            <s xml:id="echoid-s3952" xml:space="preserve">nam primo orientalibus, deinde alijs locis ſucceſſiuè, & </s>
            <s xml:id="echoid-s3953" xml:space="preserve">poſtremo occidentalibus ap-
              <lb/>
            paret, & </s>
            <s xml:id="echoid-s3954" xml:space="preserve">occultatur vt manifeſtè
              <unsure/>
            in Eclypſibus cernitur; </s>
            <s xml:id="echoid-s3955" xml:space="preserve">nam ſi nobis, v. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3957" xml:space="preserve">in meridie Sol eclypſetur, orien-
              <lb/>
            talibus eadem, ecly@ſis poſt meridiem accider, & </s>
            <s xml:id="echoid-s3958" xml:space="preserve">tanto poſt meridiem tardius, quantoij fuerin
              <unsure/>
            t orientalio-
              <lb/>
            res. </s>
            <s xml:id="echoid-s3959" xml:space="preserve">idem et@ã accidit in Lunæ defectibus. </s>
            <s xml:id="echoid-s3960" xml:space="preserve">conſtat autem ex cercis relationibus tardius eas apparere ad orien
              <lb/>
            tem, quam ad occidentem, tardius, ideſt, plur
              <unsure/>
            ibus horis ſecundum horologium, illius loci orientalioris: </s>
            <s xml:id="echoid-s3961" xml:space="preserve">ab-
              <lb/>
            ſoluto
              <unsure/>
            enim omnibus eodem temporis momento fiunt. </s>
            <s xml:id="echoid-s3962" xml:space="preserve">imo Aſtronomi prædicunt quot horis prius vni </s>
          </p>
        </div>
      </text>
    </echo>
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