Pagina:Johannes Kepler - Harmonices Mundi Libri V.pdf/329

E Wikisource
Haec pagina nondum emendata est

Harmonicis Lib. V.

251 CAP. IX.

edron efi Cuho cognatum y ttqualemhahens orhium proportionem ; lcojiedronverb Dodecaedro : quodigitur Luhus habet dcperfetiione injcriptionis , idem if fkiedro debebatur :

qucd Dodecaedron , idem

&

Icojiedro.

EJi 0$ conjtmilis

Iktedri (itus)Jitui Cubii lcojiedriverb ,Jitui Dodecaedri : quia vrt

tenet terminum adextcriora

fic

0-

O-

Cuhus alterum

Ocluedron tenet reliquum extremum adinte-

ricraMundi,Dodecae'dronverb(j Icojiedronmediant': Convenit igitur etiam (imilis injcriptio ,illic penelrativaOrbis planetmij interioris , hic dejciens ah

Echinus verb, qui fummitdtibus an ^ulorum rcpr<efentat Icojiedron, hajic bus Dodeca'e'dron } utramtfe eiiam regionem, tntn inter Martem Z$ fellurem, Dodecaedro } qudm "mter Tellurcm d) l^enerem , Icofaedro tributas implere_j, complectijeu difyonere dehuit. ^Utrum autem oppojitorum , utrijbcietati conveniat, jixiomapr&miftum clarum facit. Tetraedron enim,habens infcriptum orbem effkbilem, medium fortita eji locum inter Primarias Jiipata utrin^,Jiguris incommenfurabdium Orbium, quarumexterior Cuhus,imerior Dodecaedron,per cap.I huius. Hacverbqua/itas Geometrica, Effabilitzis infcripti, reprcefntztt inNatura injcriptionem flaneturij Orbis perfeSktm^ Cuhus igitur cumjbcid hahent int iilo.

ex dimidio (dltefn effabiles , id eji ,Jolapoteniia ; debent igiturJemiper; ubi licct non ipfa Orbis planetarij Extremiinterius a/iquid, if) nominatim Medietas inter Orbcs,aphe/ium £$ tas, atja/tem

fcriptos ,

fbcTzim reprdjenture injcriptionem

perihe/ium Jiper alias rationesferipojfit,attingatur a centris p/anorumfgura.

Dodecaedron contrdcu njocia hahent infcriptos p/ane inejfabi/es d) /ongitudineradij t$ potentia : debent igitur plane imperjetktm repr&Jentztre infcriptionem , £$ ptnitusnihil de Orhe planeUrio attingeniem ,hoc eji',deficientem,&

ufque adapheliump/anetce orhem nonp/anepertingentemjuorump/dnorum cen-

Echinus &tfi Dodecacdro z$ fbci& cognatut ejl shah&t tzimen a/iquidjimile Tetraedro. f^am radius infcripti laterihus ejus inverfis, eji quidem incom-

tris.

menfurahi/is circumjcriptitadio

,

at commenfurabilis

eji

interim /ongitudir.e

,

dijkmtict hinorum angutorum vicinorum. Itztcj,perfbBio commenjurationis ra-

diorumfere tztnta , quankt Tetraedro imperfeBio altrinfecus tztntzt, quantzt Do decaedro tf Jocice. ConJenUneum igitur eji, eiiamphyficam injcriptionem ei competere , necplane Tetracdricam , necplane Dodecaedricam ,Jedgeneris in-

vt quia Tetraedronplanispertingere debuit adjummum Orbu , Dodecaedron non attingere certojpacio ;jam hcec aculeatajigura iaterihus inverfs interj^acium IcoJi'e'dricum,$ inter orhis injcriptifummujiet.jpxime hancftimmitatem attingem : Jitnmen etiam ifkif^ura in fbcietzttem reliquarum quinque ter?nedij ;

,

'

adfcifcenda fuit , leges^ ifi*, fkxntibus legihus illarum , toleraripotuerunt.

lmb

qUiddico toleraripotuerunil quihus ilU carere nonpotuerunt, 'Afamji Dodecae-

dro competebat inJcriptiolaxa,necattingens;quidaliudindefinita7n illam laxi-

tatem intra certce quantitatis^ metas coercere potuitiquam h<ecfubjidiariajiguraa Dodecaedro £? Icojiedro cognatzii injcriptioneJuaproxime attingente , ecplus deficiente

(Jitamen

dejicit3 )

quam

Tetraedron excedit

& penetrat ? de qua

quantiktte jam infequenti agemusi

Valdeverifimilem reddichahc caufam Echini afTociati duabus cognacisfiguris(utfcilicecdecerminarecur proporcio Orbium Marcis &Veneris,quamilla; indefinicam reliqueranc) quod invenicur Semidiamecer Orbis Telluris iooo.propeadmodu medio loco proporcio-

Gg

3

nalis