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Colored diff for /texts/archimedes/xml/carda_subti_016_la_1663.xml between version 1.28 and 1.29

version 1.28, 2007/04/23 17:15:14

version 1.29, 2007/04/24 11:51:09

Line 15869

<s id="s.010788">Viuimus enim tantum<lb/>modo dum contemplamur, quoniam vita <lb/>ea verè &longs;ola e&longs;t, quæ diuis conuenit &longs;em<lb/>piterno æuo, talis autem hæc &longs;ola in <lb/>nobis. <lb/><arrow.to.target n="marg1490"/></s>

<s id="s.010789"><margin.target id="marg1489"/>Sapiontis <lb/>tria munera.</s>

<s id="s.010789"><margin.target id="marg1489"/>Sapientis <lb/>tria munera.</s>

<s id="s.010790"><margin.target id="marg1490"/>Quomodo ex <lb/>&longs;criptis ad <lb/>pronuncia<lb/>tionem fiat <lb/>tran&longs;itus.</s>

<s id="s.010791">Quomodo autem ex &longs;criptis, ad vocem <lb/>verba transferantur, rur&longs;u&longs;que ad intelle<lb/>ctum, quanquam res leuis, ob frequen<lb/>tem v&longs;um videatur, & vnius modi, ardua <lb/>tamen e&longs;t etiam modorum diuer&longs;otum: igi<lb/>tur vt antea de &longs;ermone loquamur, &longs;uppo<lb/>nenda &longs;unt ea, quæ vel in nobis, vel in ani<lb/>malibus ip&longs;is experimur. </s>

<s id="s.010791">Quomodo autem ex &longs;criptis, ad vocem <lb/>verba transferantur, rur&longs;u&longs;que ad intelle<lb/>ctum, quanquam res leuis, ob frequen<lb/>tem v&longs;um videatur, & vnius modi, ardua <lb/>tamen e&longs;t etiam modorum diuer&longs;orum: igi<lb/>tur vt antea de &longs;ermone loquamur, &longs;uppo<lb/>nenda &longs;unt ea, quæ vel in nobis, vel in ani<lb/>malibus ip&longs;is experimur. </s>

<s id="s.010792">Sunt autem hæc <lb/>primùm, quòd cùm animalia &longs;en&longs;u vocem <lb/>emittunt, velut equi vi&longs;a f&oelig;mina, dum <lb/>hinniunt, primùm &longs;en&longs;u exteriore cogno&longs;<lb/>cunt obiectum, deinde vi&longs;ione, quæ e&longs;t ip<lb/>&longs;a cognitio interior &longs;ola, vel principalis. <lb/></s>

<s id="s.010793">Inde delectantur, atque ex delectatione ap<lb/>petunt, ac ge&longs;tiunt. </s>

<s id="s.010794">Inde ex appetitu <expan abbr="mot&utilde;">motum</expan>, <lb/>non &longs;olùm ad rem vi&longs;am, &longs;ed etiam lætitiæ <lb/>indicem ciunt medio habitus, ex motu au<lb/>tem vox ip&longs;a con&longs;equitur. </s>

Line 15903

<s id="s.010810"><margin.target id="marg1491"/>Quomodo <lb/>&longs;cripta intel<lb/>ligantur.</s>

<s id="s.010811">Quomodo autem ex &longs;criptis mens confi<lb/>ciatur, faciliùs e&longs;t digno&longs;cere: nam ex &longs;en<lb/>&longs;u vi&longs;io, ex vi&longs;ione iunctura, ex pluribus <lb/>iuncturis compræhen&longs;io generalis, ex ge<lb/>nerali comprehen&longs;ione propo&longs;itio vniuer<lb/>&longs;alis, ex vniuer&longs;ali propo&longs;itione: eo iun<lb/>cturæ genere quod vocatur ratio e&longs;tque <lb/>quartum in ordine, quum vnum ex alio in<lb/>fertur, mens fit: vnde &longs;implicium nullus <lb/>e&longs;t intellectus, veque mens: &longs;ed &longs;ic intelli<lb/>gere diuinum e&longs;t. </s>

<s id="s.010811">Quomodo autem ex &longs;criptis mens confi<lb/>ciatur, faciliùs e&longs;t digno&longs;cere: nam ex &longs;en<lb/>&longs;u vi&longs;io, ex vi&longs;ione iunctura, ex pluribus <lb/>iuncturis compræhen&longs;io generalis, ex ge<lb/>nerali comprehen&longs;ione propo&longs;itio vniuer<lb/>&longs;alis, ex vniuer&longs;ali propo&longs;itione: eo iun<lb/>cturæ genere quod vocatur ratio e&longs;tque <lb/>quartum in ordine, quum vnum ex alio in<lb/>fertur, mens fit: vnde &longs;implicium nullus <lb/>e&longs;t intellectus, neque mens: &longs;ed &longs;ic intelli<lb/>gere diuinum e&longs;t. </s>

<s id="s.010812">In re autem aliquibus <lb/>ardua, omnibus verò perquam vtili facil<lb/>limo exemplo vtar. </s>

<s id="s.010813">Videmus primùm om<lb/>nia animalia contrahi, atque id dum pun<lb/>guntur, ac cogno&longs;cimus: &longs;ed hoc e&longs;&longs;e ani<lb/>maduertit vis, quæ iungit: inde ex his tri<lb/>bus functionibus collecta, propo&longs;itione ani<lb/>mal &longs;en&longs;it, atque per memoriam repetita <lb/>&longs;it comprehen&longs;io generalis, quam et&longs;i La<lb/>tinè f&oelig;dum e&longs;t proferre, euidentis tamen <lb/>vtilitatis cau&longs;a proferam hoc & h<gap/>, & <lb/>qualecunque aliud animal &longs;entit, ex qua <lb/>rur&longs;us fit propo&longs;itio vniuer&longs;alis, omne ani<lb/>mal &longs;entit: atque hucu&longs;que mentis pro<lb/>prium, opus non e&longs;t, &longs;ed &longs;en&longs;iferæ ani<lb/>mæ quatenus menti iungitur, inde animal <lb/>&longs;entit, vniuer&longs;ale ac menti proprium. </s>

<s id="s.010814">Sunt <lb/>igitur & his &longs;eptem ordines &longs;en&longs;us: exte<lb/>rior phanta&longs;ia, iunctio, memoria, com<lb/>præhen&longs;io generalis, propo&longs;itio vniuer&longs;a<lb/>lis, & vniuer&longs;ale ip&longs;um, quod mentis pro<lb/>prium e&longs;t. </s>

Line 15928

<s id="s.010827"><arrow.to.target n="marg1493"/><lb/>cebimus. </s>

<s id="s.010828">Contracto verò calore, &longs;omnus <lb/>prohibetur, concoctio vitiatur, retitinen<lb/>tur excrementa, morbique creantur. </s>

<s id="s.010828">Contracto verò calore, &longs;omnus <lb/>prohibetur, concoctio vitiatur, retinen<lb/>tur excrementa, morbique creantur. </s>

<s id="s.010829">Di<lb/>cendum e&longs;t igitur nunc de paucis animi af<lb/>fectibus, vt eadem ratione alios a&longs;&longs;equa<lb/>mur. </s>

<s id="s.010830">Igitur in timore cogitur ilicò confer<lb/>timque &longs;anguis in interioribus partibus vn<lb/>de tremunt homines, vox tollitur, aut la<lb/>bat, pallet corpus. </s>

<s id="s.010831">Quod &longs;i per&longs;eueret, ac <lb/>ingens &longs;it, canitiem inducit, quibu&longs;dam <lb/>pili, nonnunquam etiam decidunt vngues, <lb/>contractóque intus &longs;anguine: aut tabe&longs;cit <lb/>homo, aut phlegmone excitato mortis &longs;ubit <lb/>periculum: quidam etiam &longs;ubitò extincti <lb/><arrow.to.target n="marg1494"/><lb/>&longs;unt. </s>

Line 15972

<s id="s.010851">Su&longs;picio ve<lb/><arrow.to.target n="marg1501"/><lb/>rò timor e&longs;t paruus, velut audacia &longs;pes ma<lb/>xima. </s>

<s id="s.010852">Differt à lætitia, quoniam in vtra<lb/>que e&longs;t firma &longs;pes, &longs;ed in audacia finis e&longs;t <lb/>mediocris in lætitia e&longs;t iucundus. </s>

<s id="s.010853">Memini&longs;<lb/>&longs;e autem horum inferius oportet, vt phæ<lb/>nomena intelligantur, adeò verò immu<lb/>tant hæc omnia corpus, vt &longs;i cum melancho<lb/>lico humore iungantur, ec&longs;ta&longs;im inducant: <lb/>quos &longs;i vras, aut nouacula incidas, nihil <lb/>&longs;entire comperies: alij iacent volentes, vt <lb/>mortui, alij etiam diuinant, hæcque pro ma<lb/>gnis miraculis apud imperitos habentur, <lb/>cum tamen dicat Hippocrates. </s>

<s id="s.010854">Si lingua <lb/><arrow.to.target n="marg1502"/><lb/>repentè incontinens fiat, aut aliqua pars <lb/>corporis ftupore elanguet, tale e&longs;t melan<lb/>cholicum. </s>

<s id="s.010854">Si lingua <lb/><arrow.to.target n="marg1502"/><lb/>repentè incontinens fiat, aut aliqua pars <lb/>corporis &longs;tupore elanguet, tale e&longs;t melan<lb/>cholicum. </s>

<s id="s.010855">Sed Galenus &longs;en&longs;um huius mini<lb/>mè e&longs;t a&longs;&longs;ecutus: ob hocque demiratur an<lb/>tiqui magi&longs;tri dicta. </s>

<s id="s.010856">Affectus igitur animi <lb/>corpora mutant, &longs;oni autem animi affectus. <lb/></s>

<s id="s.010857">Nece&longs;&longs;e e&longs;t igitur &longs;onos corpora mutare. <lb/></s>

<s id="s.010858">Omnium autem affectuum maximi, &longs;unt <lb/>timor & fortitudo: at hos mouere po&longs;&longs;unt <pb pagenum="586" xlink:href="016/01/233.jpg"/>&longs;oni, indicio &longs;unt tubæ, Laconicum inuen<lb/>tum tympana, barbarorum cornua & cla<lb/><arrow.to.target n="marg1503"/><lb/>mor Romanorum. </s>

<s id="s.010859">Nam Romani, &longs;ub pu<lb/>gnæ initio adeò magnis clamoribus ob&longs;tre<lb/>pebant, vt Io&longs;ephus coactus &longs;it Hebræorum <lb/>&longs;uorum militum aures ob&longs;truere, ne vel &longs;tre<lb/>pitu terrerentur, aut attoniti fierent. </s>

<s id="s.010860">Sæpè <lb/>contingit præteruolantes aues, ob cum cla<lb/>morem excidere. </s>

<s id="s.010861">Conftat igitur &longs;onos mul<lb/>tùm ad fortitudinem facere. </s>

<s id="s.010861">Con&longs;tat igitur &longs;onos mul<lb/>tùm ad fortitudinem facere. </s>

<s id="s.010862">Igitur ad alios <lb/>animi affectus. </s>

<s id="s.010863">Nunc pro clamoribus boant <lb/>machinæ igneæ non inani, &longs;ed exitiali &longs;tre<lb/>pitu. </s>

<s id="s.010864">Quantum verò corpora ex affectibus <lb/>animi patiuntur, indicant, qui dum cogi<lb/>tant intentius, neque vident, neque au<lb/>diunt. </s>

Line 16010

<s id="s.010889">Actiua verò, <lb/>atque præcipuè artificio&longs;æ vtrumque genus, <lb/>ab imaginatione maximè iuuatur. </s>

<s id="s.010890">Nec e&longs;t <lb/>fermè artificio&longs;a memoria aliud quicquam, <lb/>quàm tran&longs;latio rerum & verborum ad or<lb/>dinem, ac vim quæ imaginatur, ea tamen <lb/>tantùm affert commodi, verborum &longs;cilicet, <lb/>ac numerorum, vt faciliùs centum cum ea <lb/>quàm decem &longs;ine illa recitare po&longs;&longs;is. </s>

<s id="s.010891">Ratio <lb/>tamen omnium virtutum mortalium prin<lb/>ceps e&longs;t, hominique propria vt mortalis e&longs;t. <lb/></s>

<s id="s.010892">At verò vt intellectum po&longs;&longs;idet, artes & <lb/>&longs;cientias excolit, artificio&longs;áqe inuenta quæ<lb/>dam, quæ ad artes non pertinent, quoniam <lb/>vtilitate carent, aut incerti &longs;unt generis: om<lb/>nis autem ars, e&longs;t generis certi atque vtilis. <lb/></s>

<s id="s.010892">At verò vt intellectum po&longs;&longs;idet, artes & <lb/>&longs;cientias excolit, artificio&longs;áque inuenta quæ<lb/>dam, quæ ad artes non pertinent, quoniam <lb/>vtilitate carent, aut incerti &longs;unt generis: om<lb/>nis autem ars, e&longs;t generis certi atque vtilis. <lb/></s>

<s id="s.010893">De incertis igitur atque inutilibus, primò <lb/>dicendum. </s>

Line 16094

<s id="s.010937">Edetur autem hic liber. </s>

<s id="s.010938">Sed modum <lb/>nunc docere præ&longs;tat ex Arithmeticis arcanis <lb/>de&longs;umptum. </s>

<s id="s.010939">Quælibet ars quæ rebus non <lb/>placitis con&longs;tat, viginti &longs;implicibus regulis <lb/>contineri pote&longs;t. </s>

<s id="s.010940">Nam viginti propo&longs;itis ter<lb/>minis con&longs;tituuntur <expan abbr="cõiugationes">coniugationes</expan> 1048375. <lb/>Cuius numeri ratio ab&longs;oluti&longs;&longs;ima hæc e&longs;t: <lb/>&longs;ingularess viginti. </s>

<s id="s.010941">Pro 19. totidem. </s>

<s id="s.010942">Pro <lb/>18. & 2. duc 40. in 19. fit 760. diuide per <lb/>2. exit 380. Pro 17. & 3. duc 18. per 380. <lb/>& diuide per 3. exit 2280. Pro 16. & 4. <lb/>duc 2280. per 17. & diuide per 4. exit <lb/>9690. Pro 15. & 5. duc 9690. per 16. & <lb/>diuide per 5. atque ita &longs;emper ducendo ag<lb/>gregatum, procedens per numerum maio<lb/>rem præcedentem, & diuidendo produ<lb/>ctum per minorem numerum, ordine de<lb/>uenies ad 10. qui e&longs;t in medio: qui cùm <lb/>&longs;it ab&longs;que compari, duces præcedens ag<lb/>gregatum, quòd e&longs;t 325920. per 11. gene<lb/>rali ratione fit 3695120. diuide per 10. fit <lb/>369512, Sed quia hic numerus componi<lb/>tur ex &longs;imilibus, accipiemus &longs;olùm medie<lb/>tatem, &longs;cilicet 184756. Omnibus igitur <lb/>&longs;imul iunctis, additáque vnitate pro regu<lb/>la, quæ ex omnibus &longs;implicibus con&longs;tat, <lb/>fient ( vt dixi ) regulæ omnes, 1048575. <lb/>Cùm igitur libri omnes artis, Græci, Ara<lb/>bes, atque Latini, ne vige&longs;imam quidem <lb/>partem contineant, con&longs;tat &longs;implici&longs;&longs;imas <lb/>regulas, aut non tot e&longs;&longs;e, aut non expleri <lb/>omnes coniugationes. </s>

<s id="s.010943">Igitur cùm duabus <lb/>chartis, viginti regulæ tum modi coniuga<lb/>tionum contineri po&longs;&longs;int, tota etiam ars <lb/>continebitur. </s>

Line 16107

<s id="s.010948">Videntur enim mortalium chari&longs;<lb/>&longs;imam docere &longs;uppellectilem, tempus <emph type="italics"/>(<emph.end type="italics"/> in<lb/>quam) effundere. </s>

<s id="s.010949">Itaque meritò genus hoc <lb/>&longs;cribendi à Galeno in libris de Decretis Hip<lb/>pocratis, & Platonis damnatur, improba<lb/>tur, reiicitur. </s>

<s id="s.010950">Quid enim ab&longs;urdius, ne <lb/>&longs;tultius dicam: quàm in &longs;eriis rebus, & <lb/>quæ firmi&longs;&longs;ima indigerent demon&longs;tratione, <lb/>te&longs;timonium ab oraculis, & Poëtis petere, <lb/>quorum mens nihil minus cogitabat, quàm <lb/>quod &longs;criberent? </s>

<s id="s.010951">Id &longs;olùm quærentibus illis, <lb/>vt numerus impleretur, carmémque &longs;ona<lb/>ret. </s>

<s id="s.010951">Id &longs;olùm quærentibus illis, <lb/>vt numerus impleretur, carménque &longs;ona<lb/>ret. </s>

<s id="s.010952">In eodem genere collocantur Theolo<lb/>li naturalibus rationibus contra Philo&longs;o<lb/>phos di&longs;putantes, & hære&longs;ium omnium in<lb/>uentores, & qui de &longs;igillis &longs;ub certis c&oelig;<lb/>lorum con&longs;titutionibus faciendis loquuntur, <lb/>& qui de magia naturali à numerorum ra<lb/>tione &longs;umpta, vt Agrippa infelix: nam nu<lb/>meri <emph type="italics"/>(<emph.end type="italics"/> vt rectè Ari&longs;toteles dixit ) actionum, <lb/>& mutationum non po&longs;&longs;unt e&longs;&longs;e principia. <lb/><arrow.to.target n="marg1507"/><lb/>Ea enim quæ &longs;cribuntur, tria habere de<lb/>bent, vtilitatem præ&longs;entem, certum finem, <lb/>inexpugnabile fundamentum. </s>

<s id="s.010953">Quapropter <lb/>& Rhabani &longs;ubtilitas inter inutiles cen&longs;eri <lb/>debet, laboris immen&longs;i, & admodum curio<lb/>&longs;a. </s>

<s id="s.010954">Hic &longs;imul carminis & numerorum legem <lb/>&longs;eruat primò, tum imaginem figurarum &longs;itu <lb/>literarum explicat, literis in figura inclu&longs;is: <lb/>rur&longs;us &longs;en&longs;um, & hi&longs;toriam continet figu<lb/>ræ, atque his etiam carmina con&longs;truit. </s>

<s id="s.010955">To<lb/>ta verò &longs;erie carminum, omnem explicat <lb/>denuò &longs;en&longs;um figuræ contentæ. </s>

<s id="s.010956">Sic cru<lb/>ces, arbores, aue&longs;que, aliáque innumera, <lb/>hac arte depingit: cuius hoc vnum &longs;it exem<lb/>plum. <lb/><emph type="quote"/>Arbor odore potens, f r o ndo&longs;o vertice nata, <lb/>Qua &longs;umma verè &longs;acr o, u f luit ordine bertas, <lb/>Hortus ditatus, & pa r c u i nullus in orbe e&longs;t. <lb/></s>

<s id="s.010957">Floribus, & foliis, m i l leno germine diues, <lb/>Omnes excedens alt a s g rauitudine &longs;yluas, <lb/>Cumtotam piè magnu s u e &longs;tith onó&longs;que, decú&longs;que, <lb/>Ambit verus honor, l a e t vs loquitur ea voto, <lb/>Stans homo liuor ho c n a tioni denegat atræ. <lb/></s>

<s id="s.010957">Floribus, & foliis, milleno germine diues, <lb/>Omnes excedens altas rauitudine &longs;yluas, <lb/>Cum totam piè magnus ue&longs;tit honó&longs;que, decú&longs;que, <lb/>Ambit verus honor, laetvs loquitur ea voto, <lb/>Stans homo liuor hoc nationi denegat atræ. <lb/></s>

<s id="s.010958">Dæmonis horrendus r e m &longs;ciri laude moueri, <lb/>Arbor &longs;ola tenens u a r i os virtute colores: <lb/>Purpureo regis &longs;ub t a c tu ro&longs;cida fulgens, <lb/>Æterno es radio, &longs;t a n t in te nam piè vincta, <lb/>Ædes turritæ, ex ho c d u dum es nomine berta.<emph.end type="quote"/></s>

<s id="s.010959"><margin.target id="marg1507"/>Quæ &longs;cribun<lb/>tur tria ha<lb/>bere debent. <lb/></s>

<s id="s.010960">Rhabant <lb/>&longs;ubtilitas <lb/><gap/>ira.</s>

<s id="s.010960">Rhabani <lb/>&longs;ubtilitas <lb/><gap/>ira.</s>

<s id="s.010961">Si animaduertas, de&longs;cendendo legitur <lb/>carme<gap/> hoc: <lb/><emph type="quote"/><emph type="italics"/>Forma &longs;acrata crucis, venerando fulget amictu.<emph.end type="italics"/><emph.end type="quote"/></s>

Line 16237

<s id="s.011030"><margin.target id="marg1515"/><lb/>Demon&longs;tra<lb/>tio &longs;extæ pri<lb/>mi elemento<lb/>rum per ar<lb/>gumenti con<lb/>clu&longs;ionem, <lb/>&longs;eu ducens <lb/>ad neie&longs;&longs;a<lb/>rium. <lb/></s>

<s id="s.011031">7 37 <lb/>24 28 <lb/>25 29 <lb/>31 30 <lb/>32 31 <lb/>Prima 32 <lb/></s>

Line 16253

<s id="s.011036">Eadémque ratione totum &longs;ecundum <expan abbr="libr&utilde;">librum</expan>, <lb/>vltima dntaxat propo&longs;itione excepta. </s>

<s id="s.011036">Eadémque ratione totum &longs;ecundum <expan abbr="libr&utilde;">librum</expan>, <lb/>vltima dumtaxat propo&longs;itione excepta. </s>

<s id="s.011037">Primas <lb/><expan abbr="quoq;">quoque</expan> &longs;exdecim tertij libri, & partem <expan abbr="primã">primam</expan> <lb/>trige&longs;im&etail; primæ proportionis eiu&longs;dem, quam <lb/>trige&longs;imamquartam huius dicemus: nam du<lb/>cta linea ex centro, per &longs;ecundam harum, <lb/>con&longs;tat angulum &longs;upremum æqualem e&longs;&longs;e <lb/>duobus, qui &longs;unt &longs;upra ba&longs;im pariter acce<lb/>ptis: cùm verò tres ip&longs;i æquales &longs;int duobus <lb/>rectis ex trige&longs;imaprima, nece&longs;&longs;e erit fateri <lb/>&longs;upremum, qui in circuli dimidio con&longs;i&longs;tit <lb/>e&longs;&longs;e rectum. </s>

<s id="s.011038">Imò eodem modo quo ibi de<lb/>mon&longs;trantur, reliquæ huius propo&longs;itionis <lb/>partes patêre po&longs;&longs;unt. </s>

<s id="s.011039">Totus etiam quintus <lb/><arrow.to.target n="marg1518"/><lb/>liber, cùm ex aliis non pendeat, demon&longs;tra<lb/>bitur liberè ea ratione quæ ab Euclide: tum <lb/>verò & duodecim primi &longs;exti Elementorum <lb/>propo&longs;itiones, cùm demon&longs;tratis iam tantùm <lb/>indigeant. </s>

Line 16319

<s id="s.011083">Ex his patet demon&longs;tratas e&longs;&longs;e omnes <lb/>propo&longs;itiones quarti, ni&longs;i quòd non licebit <lb/>circulum circumducere, aut in&longs;cribere, &longs;ed <lb/>&longs;olùm inuenire centrum: ip&longs;á&longs;que figuras <lb/>æquilateras & æquiangulas con&longs;truere, to<lb/>tamque doctrina Euclidis, <expan abbr="v&longs;q;">v&longs;que</expan> ad finem 6. li<lb/>bri, &longs;eu 9. iam peracta e&longs;t. </s>

<s id="s.011084">Vt verò ad finem <lb/>reliquorum librorum perueniamus, demon<lb/>&longs;trabimus 44. quæ e&longs;t, ex quocunque puncto <lb/>in diametro propo&longs;ito perpendicularem eri<lb/>gere, quæ ad contactum periferiæ circuli <lb/>perueniat. </s>

<s id="s.011085">Nam per 35. inueniemus propor<lb/>tione mediam, & per &longs;extam educemus il<lb/>lam perpendicularem ad lineam propo&longs;itam <lb/>ex puncto dato, pertingéntque ad periferiæ <lb/>locum circuli, cuius propo&longs;ita linea e&longs;t dia<lb/>meter ex demon&longs;tratione decimætertiæ &longs;exti <lb/>Elementorum, qua Euclides vtitur. </s>

<s id="s.011086">Cùm ve<lb/>rò quadrage&longs;imam quintam demon&longs;trare <lb/>voluerimus, quæ talis e&longs;t: &longs;uper datam li<lb/>neam triangulum rectnm &longs;upremum ha<lb/>bentem, re&longs;picientémque datam lineam, <lb/>cuius latus vnum a&longs;&longs;ignatæ lineæ, quæ mi<lb/>nor &longs;it prima, con&longs;tituere, circulum de&longs;cri<lb/>bemus nobis iam conce&longs;&longs;um, ductáque dia<lb/>metro ex duodecima &longs;exti, lineam ei &longs;ubiun<lb/>gemus, ad quam diameter &longs;e habeat, vt pri<lb/>ma linea ad latus illud: erit igitur hæc li<lb/>nea minor diametro circuli conce&longs;&longs;i, quare <lb/>ex quadrage&longs;imaprima collocabimus eam <lb/>intra circulum, complebimú&longs;que trigonum: <lb/>igitur &longs;uper primam lineam angulum in ex<lb/>tremitate, angulo contento ex diametro, & <lb/>quarta linea æqualem per vige&longs;imamquin<lb/>tam faciemus, & lineam hanc productam <lb/>ex decimatertia faciemus æqualem a&longs;&longs;igna<lb/>tæ &longs;ecundæ: quare ex &longs;exta, &longs;exti Element. <lb/></s>

<s id="s.011086">Cùm ve<lb/>rò quadrage&longs;imam quintam demon&longs;trare <lb/>voluerimus, quæ talis e&longs;t: &longs;uper datam li<lb/>neam triangulum rectum &longs;upremum ha<lb/>bentem, re&longs;picientémque datam lineam, <lb/>cuius latus vnum a&longs;&longs;ignatæ lineæ, quæ mi<lb/>nor &longs;it prima, con&longs;tituere, circulum de&longs;cri<lb/>bemus nobis iam conce&longs;&longs;um, ductáque dia<lb/>metro ex duodecima &longs;exti, lineam ei &longs;ubiun<lb/>gemus, ad quam diameter &longs;e habeat, vt pri<lb/>ma linea ad latus illud: erit igitur hæc li<lb/>nea minor diametro circuli conce&longs;&longs;i, quare <lb/>ex quadrage&longs;imaprima collocabimus eam <lb/>intra circulum, complebimú&longs;que trigonum: <lb/>igitur &longs;uper primam lineam angulum in ex<lb/>tremitate, angulo contento ex diametro, & <lb/>quarta linea æqualem per vige&longs;imamquin<lb/>tam faciemus, & lineam hanc productam <lb/>ex decimatertia faciemus æqualem a&longs;&longs;igna<lb/>tæ &longs;ecundæ: quare ex &longs;exta, &longs;exti Element. <lb/></s>

<s id="s.011087">completo trigono, fiet &longs;imilis primo & or<lb/>thogonius. </s>

<s id="s.011088">Quo inuento, ad finem omnium <lb/>eorum, quæ ab Euclide &longs;cripta &longs;unt, tum ab <lb/>Hyp&longs;icle addita Alexandrino, ab&longs;que impe<lb/>dimento perueniemus. </s>

<s id="s.011089">Sed hæc (vt vbi) ac <lb/>&longs;imilia, ad o&longs;tentationem ingenij, vtilitatem <lb/>verò penè nullam, inuenta &longs;unt. </s>

Line 16359

<s id="s.011112">Pun<lb/>ctum habet in medio, à quo omnes lineæ, <lb/>v&longs;que ad circumferentiam ductæ, æquales <lb/>&longs;unt. </s>

<s id="s.011113">Si extra ip&longs;um punctus figatur, lineæ <lb/>quotquot ad aduer&longs;am circumferentiæ par<lb/>tem ducentur, ductæ in partem exteriorem <lb/>rectangulum efficient æquale quadrato con<lb/>tingentis ex eodem puncto. </s>

<s id="s.011114">Quod &longs;i diame<lb/>ter producatur extrà quantumlibet, alia ve<lb/>rò diametro in centro &longs;ecetur ad rectos, ex <lb/>huius fine diui&longs;a portione quarta circumfe<lb/>rentiæ in quotquot æquales partes, per ea<lb/>rum vltimam recta ducatur ad eam quæ ex<lb/>terius in directo diametri adiacet, erit ip&longs;a <lb/>diametro adiacens æqualis omnibus rectis <lb/>ex diui&longs;ionum periferiæ punctis ductis per<lb/>pendicularibus in &longs;ubiectam diametrum, v&longs;<lb/>que ad aduer&longs;am circumferentiæ partem, <lb/>quæ quidem lineæ omnes, vt palam e&longs;t dia<lb/>metro, quæ exterius e&longs;t productæ æquidi<lb/>&longs;tant. </s>

<s id="s.011115">Quod &longs;i ab eadem extremitate dime<lb/>tros lineæ quotquot, &longs;eu intrà, &longs;eu extrà, ad <lb/>adiacentem quidam extrà, ad circumferen<lb/>tiæ verò partem alteram intrà ducantur, <lb/>erunt in exterioribus rectangula ex tota li<lb/>nea in partem interclu&longs;am periferia circuli <lb/>& in interioribus ex tota in partem reliqua <lb/>diametro ad rectos &longs;tante interclu&longs;am qua<lb/>drato circulo in&longs;cripto &longs;emper æqualia. </s>

<s id="s.011115">Quod &longs;i ab eadem extremitate diame<lb/>tros lineæ quotquot, &longs;eu intrà, &longs;eu extrà, ad <lb/>adiacentem quidam extrà, ad circumferen<lb/>tiæ verò partem alteram intrà ducantur, <lb/>erunt in exterioribus rectangula ex tota li<lb/>nea in partem interclu&longs;am periferia circuli <lb/>& in interioribus ex tota in partem reliqua <lb/>diametro ad rectos &longs;tante interclu&longs;am qua<lb/>drato circulo in&longs;cripto &longs;emper æqualia. </s>

<s id="s.011116">Qu&etail; </s>

<s id="s.011117"><arrow.to.target n="marg1525"/><lb/>verò circulo, hyperboli, & defectioni com<lb/>munes &longs;unt, hæ &longs;unt. </s>

<s id="s.011118">Ducta ex contingente <lb/>perpendicularis &longs;uper diametrum iacentem <lb/>in directo puncti, ex quo contingens ducta <lb/>e&longs;t, partes diametros &longs;ub eadem proportione <lb/>diuidit, &longs;ub qua tota linea ex puncto è quo <lb/>contingens producta e&longs;t ad centrum circuli <lb/>veniens, v&longs;que ad alteram circumferentiæ <lb/>partem, ad partem exteriorem &longs;e habet. </s>

<s id="s.011119">Se<lb/>midiametros quoque proportione media e&longs;t, <lb/>inter eam quæ à centro ad punctum exte<lb/>rius, & eam qu&etail; à centro ad locum vbi cadit <lb/>perpendicularis ex loco contigentis &longs;uper <lb/>eandem diametrum. </s>

<s id="s.011120">Cùm verò à terminis <lb/>diametri duæ contingentes ducuntur, ab ei&longs;<lb/>dem verò punctis per idem punctum cir<lb/>cumferentiæ mutuò ad alteram contingen<lb/>tem, erit quod &longs;ub partibus contingentium <lb/>his po&longs;tremis lineis terminatarum rectan<lb/>gulum continetur æquale quadrato dia<lb/>metri. <lb/><arrow.to.target n="marg1526"/></s>

Line 16403

<s id="s.011142">Cum verò conus rectus (deinceps <expan abbr="aut&etilde;">autem</expan> bre</s>

<s id="s.011143"><arrow.to.target n="marg1527"/><lb/>æitatis cau&longs;a conum dixi&longs;&longs;e &longs;ufficiat, <expan abbr="quãdo-">quando-</expan><pb pagenum="594" xlink:href="016/01/241.jpg"/>quidem per conum rectum, conum &longs;olùm <lb/>intelligi volo) diuidetur plano &longs;uper tri<lb/>gonum A B C, ad perpendiculum &longs;tanti, <lb/>ita quòd tran&longs;eat per aliquem punctum con<lb/>&longs;titutum extra verticem, puta G, tunc vel <lb/>axis, &longs;eu dimetiens figuræ intra conum clau<lb/>&longs;æ æquidi&longs;tabit ba&longs;i &longs;ecans ambo latera <lb/>trianguli, & tunc figura illa erit nece&longs;&longs;ariò <lb/>circulus, vt in prima figura circulus GH. </s>

<s id="s.011143"><arrow.to.target n="marg1527"/><lb/>uitatis cau&longs;a conum dixi&longs;&longs;e &longs;ufficiat, <expan abbr="quãdo-">quando-</expan><pb pagenum="594" xlink:href="016/01/241.jpg"/>quidem per conum rectum, conum &longs;olùm <lb/>intelligi volo) diuidetur plano &longs;uper tri<lb/>gonum A B C, ad perpendiculum &longs;tanti, <lb/>ita quòd tran&longs;eat per aliquem punctum con<lb/>&longs;titutum extra verticem, puta G, tunc vel <lb/>axis, &longs;eu dimetiens figuræ intra conum clau<lb/>&longs;æ æquidi&longs;tabit ba&longs;i &longs;ecans ambo latera <lb/>trianguli, & tunc figura illa erit nece&longs;&longs;ariò <lb/>circulus, vt in prima figura circulus GH. </s>

<s id="s.011144">De<lb/>&longs;crip&longs;i autem tam ba&longs;im, quàm &longs;uperficiem <lb/>&longs;ecantem circulos perfectos in prima figura, <lb/>vt illos agno&longs;ceres. </s>

<s id="s.011145">In aliis autem &longs;equen<lb/>tibus figuris circuli longiores, quàm pro <lb/>latitudine &longs;cribentur, vt conus, & &longs;ectiones <lb/>ex plano ad &longs;olidi imaginem tran&longs;lati me<lb/>liùs reptæ&longs;entari po&longs;&longs;int. </s>

<s id="s.011146"><margin.target id="marg1527"/>Creatio <lb/>quinque fi<lb/>gurarum in <lb/>cono.</s>

Line 16421

<s id="s.011151">Veluti is tertia figura plano K <lb/>diuidente conum figura inclu&longs;a in cono, <lb/><figure id="id.016.01.241.2.jpg" xlink:href="016/01/241/2.jpg"/><lb/>quæ e&longs;t G H D F, habeat axem G æquidi<lb/>&longs;tantem AB, tertio lateri trigoni, tunc ve<lb/>cabitur figura illa Parabulæ, id e&longs;t, è regione, <lb/>quia quantumcunque cum cono ip&longs;o pro<lb/>ducatur, &longs;emper e&longs;t è regione alterius lateris. <lb/></s>

<s id="s.011152">Cùm igitur duæ præcedentes figuræ &longs;ecent <lb/>ambo latera trigoni ABC, hæc & &longs;equens <lb/>non &longs;ecant latus AB aduer&longs;um, vt vides. </s>

<s id="s.011153">Si <lb/>igitur planum ad perpendiculum &longs;tans &longs;uper <lb/>triangulum A E C, (quod &longs;emper intelligi <lb/>volo, &longs;icut etiam quòd tran&longs;eat per pun<lb/>ctum extra verticem (non &longs;ecuerit latus <lb/>illi contrapo&longs;itum, &longs;ecando conum, & ta<lb/>men illius figuræ, quæ intra conum clau<lb/>ditur axis, non æquidi&longs;tet tertio lateri, &longs;ic <lb/>enim e&longs;&longs;et Parabole, nec &longs;ecet latus, vt di<lb/>xi, contrapo&longs;itum intra conum, quia e&longs;&longs;et <lb/>Ellip&longs;is, vt dictum e&longs;t, &longs;ed illud latus con<lb/>trapo&longs;itum &longs;ecet extra conum, tunc dice<lb/>tur Hyperbole, id e&longs;t exce&longs;&longs;us: quià angu<lb/>lus axe figuræ, & latere trigoni conten<lb/>tus, in Hyperbole maior e&longs;t, quàm in Para<lb/>bule. </s>

<s id="s.011154">Sit igitur planum &longs;ecans conum bi<lb/>fariam, & ad perpendiculum &longs;tans &longs;upra <lb/>trigonum A B C, & fiat figura GHF, vt <lb/>in quarta de&longs;criptione, & huius figuræ di<lb/>mitiens GD, non &longs;ecet latus AB, intra co<lb/>num, nec ab illo æquidi&longs;tet, &longs;ed protra<lb/>ctum occurrat illi extra conum in E, quòd <lb/>nece&longs;&longs;arium e&longs;t, quandoquidem nec illi <lb/>æquidi&longs;tat, nec occurrit intra conum, tunc <lb/>hæc figura vocabitur Hyperbole, quia an<lb/>gulus AGD, in ea maior e&longs;t, quàm in Pa<lb/>rabole. </s>

<s id="s.011154">Sit igitur planum &longs;ecans conum bi<lb/>fariam, & ad perpendiculum &longs;tans &longs;upra <lb/>trigonum A B C, & fiat figura GHF, vt <lb/>in quarta de&longs;criptione, & huius figuræ di<lb/>mittens GD, non &longs;ecet latus AB, intra co<lb/>num, nec ab illo æquidi&longs;tet, &longs;ed protra<lb/>ctum occurrat illi extra conum in E, quòd <lb/>nece&longs;&longs;arium e&longs;t, quandoquidem nec illi <lb/>æquidi&longs;tat, nec occurrit intra conum, tunc <lb/>hæc figura vocabitur Hyperbole, quia an<lb/>gulus AGD, in ea maior e&longs;t, quàm in Pa<lb/>rabole. </s>

<s id="s.011155">Ex his iam patet in cono perfe<lb/>ctionem plani ad perpendiculum &longs;uper tti<lb/>gonum conum per axem diuidentis erecti, <lb/>& per datum punctum præter verticem <lb/><figure id="id.016.01.241.3.jpg" xlink:href="016/01/241/3.jpg"/><lb/>tran&longs;euntis, quatuor fieri figuras, &longs;eilicet <lb/>circulum, Ellip&longs;im, Parabolem, & Hyber<lb/>bolem, nec po&longs;&longs;e ex vno cono plura gene<lb/>ra inueniri: nam quintum habet plano <lb/>diuidente duos conos æquiangulos contra <lb/>&longs;e po&longs;itos ad verticem (in quinta figura <lb/><figure id="id.016.01.241.4.jpg" xlink:href="016/01/241/4.jpg"/><lb/>exemplum habes) & tunc fiunt nece&longs;&longs;a<lb/>riò duæ hyperboles: hæ duæ ab Apol<lb/>lonio vocantur contrapo&longs;itæ: vt &longs;i &longs;int <lb/>duo coni verticibus iuncti A B C, & <lb/>A D E, &longs;ic vt lineæ B A E, & C A D, <pb pagenum="595" xlink:href="016/01/242.jpg"/>&longs;int directæ, & &longs;int trigoni per axem in eo<lb/>dem plano ABC, & ADE, & puncta præ<lb/>ter verticem &longs;ignata in vno G, in altero H, <lb/>& planum K, per ambo puncta ad perpendi<lb/>culum &longs;uper ambos trigonos ductum, & <lb/>clarum e&longs;t quòd facit duas hyperboles, quia <lb/>axes figurarum occurrunt extra trigonum <lb/>lateri oppo&longs;ito: quia tales &longs;unt in ambobus <lb/>planis, videlicet duorum triangulorum & K, <lb/>igitur illæ figuræ erunt ambæ hyperbo<lb/>les, & vocantur ab Apollonio contra<lb/>po&longs;itæ. </s>

<s id="s.011155">Ex his iam patet in cono perfe<lb/>ctionem plani ad perpendiculum &longs;uper tri<lb/>gonum conum per axem diuidentis erecti, <lb/>& per datum punctum præter verticem <lb/><figure id="id.016.01.241.3.jpg" xlink:href="016/01/241/3.jpg"/><lb/>tran&longs;euntis, quatuor fieri figuras, &longs;cilicet <lb/>circulum, Ellip&longs;im, Parabolem, & Hyber<lb/>bolem, nec po&longs;&longs;e ex vno cono plura gene<lb/>ra inueniri: nam quintum habet plano <lb/>diuidente duos conos æquiangulos contra <lb/>&longs;e po&longs;itos ad verticem (in quinta figura <lb/><figure id="id.016.01.241.4.jpg" xlink:href="016/01/241/4.jpg"/><lb/>exemplum habes) & tunc fiunt nece&longs;&longs;a<lb/>riò duæ hyperboles: hæ duæ ab Apol<lb/>lonio vocantur contrapo&longs;itæ: vt &longs;i &longs;int <lb/>duo coni verticibus iuncti A B C, & <lb/>A D E, &longs;ic vt lineæ B A E, & C A D, <pb pagenum="595" xlink:href="016/01/242.jpg"/>&longs;int directæ, & &longs;int trigoni per axem in eo<lb/>dem plano ABC, & ADE, & puncta præ<lb/>ter verticem &longs;ignata in vno G, in altero H, <lb/>& planum K, per ambo puncta ad perpendi<lb/>culum &longs;uper ambos trigonos ductum, & <lb/>clarum e&longs;t quòd facit duas hyperboles, quia <lb/>axes figurarum occurrunt extra trigonum <lb/>lateri oppo&longs;ito: quia tales &longs;unt in ambobus <lb/>planis, videlicet duorum triangulorum & K, <lb/>igitur illæ figuræ erunt ambæ hyperbo<lb/>les, & vocantur ab Apollonio contra<lb/>po&longs;itæ. </s>

<s id="s.011156">Ex his patet igitur, quòd omnes hæ fi<lb/>guræ conueniunt in hoc, quòd generantur <lb/>ex &longs;ectione coni, aut conorum bifariam: per <lb/>planum ad perpendiculum erectum &longs;uper <lb/>&longs;uperficiem triangulorum, quòd non tran<lb/>&longs;eat per verticem coni: & quod latera ha<lb/>rum &longs;uperficierum &longs;unt lineæ obliquæ<gap/> & <lb/>quòd non po&longs;&longs;unt e&longs;&longs;e plures his quinque. <lb/></s>

Line 16507

<s id="s.011206">Spiralis autem lineæ priuilegia &longs;ex etiam <lb/>&longs;unt. </s>

<s id="s.011207">Primum quidem, quòd ducta contin<lb/><arrow.to.target n="marg1534"/><lb/>gens ex fine illius occurrit perpendiculari ex <lb/>initio, &longs;emper tantum ab&longs;cindens ex conti<lb/>genti, vt proportionem habeat ad circuli &longs;ub <lb/>eodem ordine periferiam, &longs;ecundum ordinem <lb/>&longs;eriei numerorum. </s>

<s id="s.011207">Primum quidem, quòd ducta contin<lb/><arrow.to.target n="marg1534"/><lb/>gens ex fine illius occurrit perpendiculari ex <lb/>initio, &longs;emper tantum ab&longs;cindens ex contin<lb/>genti, vt proportionem habeat ad circuli &longs;ub <lb/>eodem ordine periferiam, &longs;ecundum ordinem <lb/>&longs;eriei numerorum. </s>

<s id="s.011208">Vnde patet, quòd portio <lb/>primæ &longs;piralis ex perpendiculari, erit æqua<lb/>lis periferiæ primi circuli, & portio perpen<lb/>dicularis ex &longs;ecunda &longs;pirali dupla circuli &longs;e<lb/>cundi periferiæ, & portio ex tertia &longs;pirali <lb/>tripla circuli tertij periferiæ, atque ita dein<lb/>ceps. </s>

<s id="s.011209">Secundum, ex quocunque puncto pri<lb/>mæ &longs;piralis educta contingens, occurrit <lb/>perpendiculari ex initio eiu&longs;dem dimetien<lb/>tis ductæ, tantam ex illa ab&longs;cindens par<lb/>tem, quanta e&longs;t portio circumferentiæ cir<lb/>culi, cuius &longs;emidiameter e&longs;t linea ex initio <lb/>lineæ &longs;piralis, v&longs;que ad punctum contin<lb/>gentis, clau&longs;a inter primam lineam rectam <lb/>&longs;piralis, quæ moueri intelligitur, & locum <lb/>ad quem per motum peruenerit ip&longs;a &longs;pi<lb/>ralis è directo loci contingentis. </s>

<s id="s.011210">E&longs;tque <lb/>tertium priuilegium, quòd &longs;patia &longs;pira<lb/>lium ita &longs;e habent: primùm quidem vni<lb/>tatis, &longs;ecundum &longs;enarij, tertium duodena<lb/>rij, quartum decemocto, atque ita deinceps <lb/>additione perpetua per &longs;enarium facta. <lb/></s>

Line 16536

<s id="s.011221"><margin.target id="marg1537"/>Quadrati <lb/>proprietas.</s>

<s id="s.011222">Quadrati verò proprium e&longs;t, vt latus eius <lb/>inter aggregratum ex ip&longs;o dimetiente, ac <lb/>inter differentiam eorundem proportione </s>

<s id="s.011222">Quadrati verò proprium e&longs;t, vt latus eius <lb/>inter aggregatum ex ip&longs;o dimetiente, ac <lb/>inter differentiam eorundem proportione </s>

<s id="s.011223"><arrow.to.target n="marg1538"/><lb/>media con&longs;i&longs;tat. </s>

Line 16561

<s id="s.011236">Proportio partium corpo<lb/>rearum &longs;phæræ, quas planum vnum di&longs;tin<lb/>guit diametrum diuidens ei perpendicula<lb/>rem, e&longs;t veluti corporis producti ex quadra<lb/>to maioris portionis axis, in lineam con<lb/>&longs;tantem ex minore portione, & dimidio <lb/>axis, ad corpus, con&longs;tans ex quadrato mino<lb/>ris portionis in lineam con&longs;tantem ex dimi<lb/>dio, & maiore axis portione. </s>

<s id="s.011237"><margin.target id="marg1540"/>Sthara pri<lb/>uilegia 2.</s>

<s id="s.011237"><margin.target id="marg1540"/>Sphaera pri<lb/>uilegia 2.</s>

<s id="s.011238"><margin.target id="marg1541"/>Corporum <lb/>quinque <lb/>&longs;phæra con<lb/>tentorum <lb/>proprietas. <lb/></s>

Line 16587

<s id="s.011248">Sed <expan abbr="&longs;phæroidali&utilde;">&longs;phæroidalium</expan> priuilegia quatuor &longs;unt <lb/><arrow.to.target n="marg1545"/><lb/>cùm enim plano diuiditur, per centrum, per <lb/>æqualia diuiditur, eritque quælibet portio <lb/>dupla cono ba&longs;im, & axem æquales portioni <lb/>ip&longs;ius &longs;phæroidis habenti. </s>

<s id="s.011249">Si præter cen<lb/>&longs;phæroides &longs;ecetur, quomodolibet proportio <pb pagenum="598" xlink:href="016/01/245.jpg"/>partis eius ad corum eandem altitudinem <lb/>& ba&longs;im habentem, e&longs;t velut dimidij axis <lb/>cum reliquæ portionis axe, ad eandem re<lb/>liquam axis portionem alterius partis &longs;phæ<lb/>roidis. </s>

<s id="s.011249">Si præter cen<lb/>&longs;phæroides &longs;ecetur, quomodolibet proportio <pb pagenum="598" xlink:href="016/01/245.jpg"/>partis eius ad eorum eandem altitudinem <lb/>& ba&longs;im habentem, e&longs;t velut dimidij axis <lb/>cum reliquæ portionis axe, ad eandem re<lb/>liquam axis portionem alterius partis &longs;phæ<lb/>roidis. </s>

<s id="s.011250">Ex quo patet quartum, quod cùm <lb/>&longs;phæroides, & portio &longs;phæræ altitudinem <lb/>& ba&longs;im eandem, aut æquales retinuerint, <lb/>ip&longs;æ inuicem erunt æquales. <lb/><arrow.to.target n="marg1546"/></s>

Line 16600

<s id="s.011253">Inde cylindri priuilegia duo. </s>

<s id="s.011254">Cylindrus <lb/>cono triplus e&longs;t, altitudinem eandem ac <lb/>ba&longs;im habenti. </s>

<s id="s.011255">Sphæræ verò, cuius diameter <lb/>&longs;it æqualis altitudini &longs;uæ, & maior circulus <lb/>ba&longs;i Cylindri ip&longs;e cylindrus &longs;e&longs;quialter erit. <lb/></s>

<s id="s.011256">Hæ igitur &longs;unt &longs;exaginta proprietates, nobi<lb/>litate, & pulchritudine, & admiratione <lb/>præ&longs;tantiores, Geometricarum figurarum <lb/>tam &longs;uperficialium, quàm corporearum: <lb/>quandoquidem non me præterit eas penè <lb/>e&longs;&longs;e infinitas, &longs;ed cum his elegantia non <lb/>po&longs;&longs;unt conferri: vel quia nondum demon<lb/>&longs;tratio earum inuenta e&longs;t, vel quia non ex <lb/>&longs;ola nominum dignotione po&longs;&longs;unt intelli, <lb/>vel quia ad æqualitatem non referuntur, &longs;ed <lb/>qua&longs;i vagantur. </s>

<s id="s.011256">Hæ igitur &longs;unt &longs;exaginta proprietates, nobi<lb/>litate, & pulchritudine, & admiratione <lb/>præ&longs;tantiores, Geometricarum figurarum <lb/>tam &longs;uperficialium, quàm corporearum: <lb/>quandoquidem non me præterit eas penè <lb/>e&longs;&longs;e infinitas, &longs;ed cum his elegantia non <lb/>po&longs;&longs;unt conferri: vel quia nondum demon<lb/>&longs;tratio earum inuenta e&longs;t, vel quia non ex <lb/>&longs;ola nominum dignotione po&longs;&longs;unt intellegi, <lb/>vel quia ad æqualitatem non referuntur, &longs;ed <lb/>qua&longs;i vagantur. </s>

<s id="s.011257">Æqualitas enim Geometræ <lb/>quidam e&longs;t &longs;copus. </s>

Line 16669

<s id="s.011301">7/54 in <lb/>2 1/3 ( m 1/3. ex prima æ&longs;timatione. </s>

<s id="s.011302">Quibus <lb/>habitis, &longs;i ducatur ex B linea per centrum, <lb/>& vbi cadit in circuli periferia linea ad F <lb/><figure id="id.016.01.246.1.jpg" xlink:href="016/01/246/1.jpg"/><lb/>& ad A, habebis quadrilaterum cum duo<lb/>bus dimetientibus, cuius duo latera, & di<lb/>metientium vna erit cognita. </s>

<s id="s.011303">Duos in&longs;u<lb/>per trigonos orthogonios, quorum ba&longs;is <lb/>erit diameter cirouli: vnde po&longs;ita reliqua <lb/>dimetientium re, cùm dimetientibus re<lb/>ctangulum æquale &longs;it rectangulis duobus <lb/>quæ fiunt ex lateribus quadranguli inuicem <lb/>oppo&longs;itis per demon&longs;trata à Ptolomæo, erit <lb/>ex his, quæ docuimus in Arte magna, <lb/>compo&longs;itis minoribus capitulis ratio dia</s>

<s id="s.011303">Duos in&longs;u<lb/>per trigonos orthogonios, quorum ba&longs;is <lb/>erit diameter circuli: vnde po&longs;ita reliqua <lb/>dimetientium re, cùm dimetientibus re<lb/>ctangulum æquale &longs;it rectangulis duobus <lb/>quæ fiunt ex lateribus quadranguli inuicem <lb/>oppo&longs;itis per demon&longs;trata à Ptolomæo, erit <lb/>ex his, quæ docuimus in Arte magna, <lb/>compo&longs;itis minoribus capitulis ratio dia</s>

<s id="s.011304"><arrow.to.target n="marg1552"/><lb/>metri circuli ad A B latus heptagoni co<lb/>gnita. </s>

Line 16822

<s id="s.011431">Quo fit vt cùm nobili&longs;&longs;ima &longs;it, <lb/>præclaram etiam exigat cantatoris naturam, <lb/>& ingenium: quibus fit de&longs;tituatur, nulla <lb/>pror&longs;us euadit. </s>

<s id="s.011432"><margin.target id="marg1557"/>Chromatiei <lb/>Enarmoniei <lb/>Diate&longs;&longs;ari <lb/>inuentio.</s>

<s id="s.011432"><margin.target id="marg1557"/>Chromatici <lb/>Enarmonici <lb/>Diate&longs;&longs;ari <lb/>inuentio.</s>

<s id="s.011433"><margin.target id="marg1558"/>Altus vox <lb/>nobili&longs;&longs;ima.</s>

Line 16837

<s id="s.011440">Ter<lb/>tius omnium optimus e&longs;t, vt imaginatione, <lb/>& voce quidem notas, & vocum magnitu<lb/>dinem retineas, lingua verò &longs;yllabam &longs;ubie<lb/>ctam proferas: atque hic vt e&longs;t optimus, ita <lb/>difficillimus. </s>

<s id="s.011441">Igitur tribus modis rur&longs;us <lb/>hunc a&longs;&longs;equemur: vel longa con&longs;uetudine, <lb/>vt&longs;en&longs;im dimi&longs;&longs;a nota, proferas &longs;yllabam in <lb/>notis, primò longioris moræ, & vni&longs;onis: <lb/>deinde &longs;en&longs;im a&longs;cendentibus ac de&longs;cenden<lb/>tibus, mox in diapa&longs;on, & diapente, & <lb/>diate&longs;&longs;aron. </s>

<s id="s.011442"><expan abbr="It&etilde;">Item</expan> in con&longs;onantiis, quas vocant <lb/>cadentias, demùm in aliis vocibus, pò&longs;t ad <lb/>notas breuis moræ te transferas. </s>

<s id="s.011443">Alter mo<lb/>dus e&longs;t, vt linguam immobilem retinere <lb/>condi&longs;cas, atque ita vocem &longs;ine notis ac&longs;yl<lb/>labis proferas. </s>

<s id="s.011444">Pò&longs;t &longs;ub vna tantùm &longs;yllaba <lb/>&longs;emper, vt &longs;ub A, vel E. </s>

<s id="s.011445">Vltimò ad &longs;yllabas <lb/>proferendas accedas. </s>

<s id="s.011446">Hic modus varietatem <lb/>ex modo proferendi &longs;u&longs;cipit, vt primus ex <lb/>re ip&longs;a &longs;eu cantu. </s>

Line 16855

<s id="s.011453">Verùm hæc &longs;cientia optica media vide<lb/>tur inter Mathematicas, & pulcherrimam <lb/>naturalium rerum &longs;cientiam, quam voca<lb/>mus Philo&longs;ophiam, cuius ambitus lati&longs;&longs;imè <lb/>patet. </s>

<s id="s.011454">Scrip&longs;imus de dignioribus illius <lb/>partibus in libris de Æternitatis Arca<lb/>nis, animi immortalitate, rerúmque va<lb/>rietate. </s>

<s id="s.011455">Verùm nobili&longs;&longs;ima pars e&longs;t illius, <lb/>quæ temporum naturam præcogno&longs;cere do<lb/>cet, & aëris temperiem: vtilis nanque agri<lb/>colis, nautis, mercataribus, imperatori<lb/>bú&longs;que, denique omni humano generi tum <lb/>iucunda, tum &longs;alutaris. </s>

<s id="s.011455">Verùm nobili&longs;&longs;ima pars e&longs;t illius, <lb/>quæ temporum naturam præcogno&longs;cere do<lb/>cet, & aëris temperiem: vtilis nanque agri<lb/>colis, nautis, mercatoribus, imperatori<lb/>bú&longs;que, denique omni humano generi tum <lb/>iucunda, tum &longs;alutaris. </s>

<s id="s.011456">Aëris igitur con<lb/>&longs;titutiones duabus con&longs;tant differentiis, <lb/>quarum altera in frigido, & calido, reliqua <lb/>verò circa humidum, & &longs;iccum ver&longs;atur. <lb/></s>

<s id="s.011457">Hoc in genere quinque &longs;unt &longs;pecies: Sere<lb/>num, quòd & tranquillum &longs;it: vento&longs;um, <lb/>nubes, imbres, grando, &longs;eu horrida tempe<lb/>&longs;tas. </s>

<s id="s.011458">Niues imbrium loco habentur, cùm <lb/>hyems fuerit. </s>

Line 16874

<s id="s.011465">Tempe&longs;tatum &longs;igna melius, quàm <lb/>Poëta tuus explicare me po&longs;&longs;e non con<lb/>fido, tamet&longs;i mihi libera &longs;it oratio, Vir<lb/>gilij verò numeris veluti compedibus con<lb/>tineatur. </s>

<s id="s.011466">Primo igitur Georgicorum &longs;ic in<lb/>quit: <lb/><emph type="quote"/><emph type="italics"/>At Boreæ de parte trucis cùm fulminat, & cùm <lb/><arrow.to.target n="marg1562"/><lb/>Eurique, Zephyrique tonat domus, omnia plenis <lb/>Rura natant &longs;o&longs;&longs;is, <expan abbr="atq;">atque</expan> omnis nauitaponto <lb/>Humida vela legit. </s>

<s id="s.011466">Primo igitur Georgicorum &longs;ic in<lb/>quit: <lb/><emph type="quote"/><emph type="italics"/>At Boreæ de parte trucis cùm fulminat, & cùm <lb/><arrow.to.target n="marg1562"/><lb/>Eurique, Zephyrique tonat domus, omnia plenis <lb/>Rura natant fo&longs;&longs;is, <expan abbr="atq;">atque</expan> omnis nauitaponto <lb/>Humida vela legit. </s>

<s id="s.011467">Nunquam impruden, tibus imber <lb/>Obfuit, aut illum &longs;urgentem vallibus imis <lb/>Aëuiæ fugêre grues: aut bucula c&oelig;lum <lb/>Su&longs;piciens, patulis captauit naribus auras: <lb/>Autarguta lacus circumuolitauit hirundo: <lb/>Et veterem in limo ranæ cecinêre querelam: <lb/>Sæpiùs & tectis penetralibus extulit oua, <lb/>Angu&longs;tum formica terens iter: & bibit ingens <lb/>Arcus: & è pa&longs;tu decedens agmine magno. <lb/></s>

<s id="s.011467">Nunquam imprudentibus imber <lb/>Obfuit, aut illum &longs;urgentem vallibus imis <lb/>Aëuiæ fugêre grues: aut bucula c&oelig;lum <lb/>Su&longs;piciens, patulis captauit naribus auras: <lb/>Autarguta lacus circumuolitauit hirundo: <lb/>Et veterem in limo ranæ cecinêre querelam: <lb/>Sæpiùs & tectis penetralibus extulit oua, <lb/>Angu&longs;tum formica terens iter: & bibit ingens <lb/>Arcus: & è pa&longs;tu decedens agmine magno. <lb/></s>

<s id="s.011468">Coruorum increpuit den&longs;is exercitus alis. <lb/></s>

<s id="s.011469">Iam varias pelagi volucres, & quæ A&longs;ia circùm <lb/>Dulcibus in &longs;tagnis rimantur prata Cay&longs;tri, <lb/>Certatim largos humeris infundere rores: <lb/>Nunc caput obiectare fretis, nunc currere in vno <lb/>Et &longs;tudio in ca&longs;um videas ge&longs;tire leuandi. <lb/></s>

<s id="s.011470"><expan abbr="T&utilde;">Tum</expan> cornix plena <expan abbr="pluuiã">pluuiam</expan> vocat improba voce, <lb/>Et &longs;ola in &longs;icca &longs;ecum &longs;patiatur arena. <lb/></s>

Line 16889

<s id="s.011474">Illud etiam certo &longs;igno adiecit, quod ob<lb/>&longs;eruatione dignum e&longs;t? <lb/><emph type="quote"/><emph type="italics"/>Si nigrum ob&longs;curo <expan abbr="cõprehenderit">comprehenderit</expan> aëra cornu.<emph.end type="italics"/><emph.end type="quote"/></s>

<s id="s.011475"><emph type="center"/>Tum illa à Sole:<emph.end type="center"/><lb/><emph type="quote"/><emph type="italics"/>Ille vbi na&longs;centem maculis variauertt <expan abbr="ort&utilde;">ortum</expan> <lb/>Conditus in nubem, <expan abbr="medióq;">medióque</expan> refugerit orbe, <lb/>Su&longs;pecti tibi &longs;int imbres: <expan abbr="nãq;">nanque</expan> vrget ab alto, <lb/>Arboribú&longs;que &longs;ati&longs;que Notus, pecorique &longs;ini&longs;ter. <lb/></s>

<s id="s.011475"><emph type="center"/>Tum illa à Sole:<emph.end type="center"/><lb/><emph type="quote"/><emph type="italics"/>Ille vbi na&longs;centem maculis variauertit <expan abbr="ort&utilde;">ortum</expan> <lb/>Conditus in nubem, <expan abbr="medióq;">medióque</expan> refugerit orbe, <lb/>Su&longs;pecti tibi &longs;int imbres: <expan abbr="nãq;">nanque</expan> vrget ab alto, <lb/>Arboribú&longs;que &longs;ati&longs;que Notus, pecorique &longs;ini&longs;ter. <lb/></s>

<s id="s.011476">Aut vbi &longs;ub lucem den&longs;a inter nubila &longs;e&longs;e <lb/>Diuer &longs;i <expan abbr="er&utilde;pent">erumpent</expan> radij: aut vbi pallida &longs;urgit <lb/>Tithoni croceum linquens aurora cubile: <lb/>Heumalè <expan abbr="t&utilde;mites">tummites</expan> <expan abbr="def&etilde;det">defendet</expan> pampinus vuas: <pb pagenum="605" xlink:href="016/01/252.jpg"/>Tam multa in tectis crepitans &longs;alit horrida grando. <lb/></s>

<s id="s.011477">Hoc etiam, emen&longs;o cùm iam decedet Olympo, <lb/>Profuerit memini&longs;&longs;e magis: nam &longs;æpè videmus <lb/>Ip&longs;ius in vultu varios errare colores. <lb/></s>

<s id="s.011478">Cæruleus pluuiam denuntiat, igneus Euros. <lb/></s>

Line 16992

<s id="s.011547">Ab his <lb/>igitur cau&longs;is, quibus hi in rabiem aguntur, <lb/>corrumpuntur in hominibus humores, & <lb/>pe&longs;tis generatur. </s>

<s id="s.011548">Ob id etiam quandoque <lb/>contingit ante pe&longs;tem aues de&longs;erere oua at<lb/>que nidos, & imperfectos pullos: omnia <lb/>enim hæc &longs;igna &longs;unt prædominantis atræ <lb/>bilis, &longs;eu ob aërem, &longs;eu ob aquam corru<lb/>ptam. </s>

<s id="s.011549">Oues autem præcipuè ante id tempus <lb/>clade afficiuntur: imbecilliores enim ac &longs;i<lb/>miles hominibus natura, ab ei&longs;dem cau&longs;is, <lb/>quibus homines pe&longs;tem patiuntur: Rana<lb/>rum quoque multitudo, & blattarum in <lb/>muris ob &longs;uperfluum humidum pingue fit, <lb/>quod naturæ humanæ aduer&longs;atur, & illi <lb/>perniciem affert. </s>

<s id="s.011550">Cúmque vermes ac &longs;er<lb/>pentes apparent, tum talpæ, id contingit, <lb/>quoniam cubilia propria de&longs;erunt ob mole<lb/>&longs;tiam vapcris, qui &longs;ub terra continetur, qui<lb/>que a&longs;cendens aërem vitiat adeò infe&longs;to <lb/>affectu, vt perniciem &longs;erpentibus afferre po&longs;<lb/>&longs;it, ne dum hominibus. </s>

<s id="s.011550">Cúmque vermes ac &longs;er<lb/>pentes apparent, tum talpæ, id contingit, <lb/>quoniam cubilia propria de&longs;erunt ob mole<lb/>&longs;tiam vaporis, qui &longs;ub terra continetur, qui<lb/>que a&longs;cendens aërem vitiat adeò infe&longs;to <lb/>affectu, vt perniciem &longs;erpentibus afferre po&longs;<lb/>&longs;it, ne dum hominibus. </s>

<s id="s.011551">Nihil enim penitùs <lb/>&longs;ub terra &longs;alutare homini fermè e&longs;&longs;e pote&longs;t: <lb/>generaliter autem omninò e&longs;&longs;e non pote&longs;t. <lb/></s>

<s id="s.011552">Ob id oportet talia frequenter videri, & pa&longs;<lb/>&longs;im, & par&longs;euerare, & augeri: tunc enim <lb/>procul dubiò pe&longs;tem futuram prænunciant. <lb/></s>

<s id="s.011552">Ob id oportet talia frequenter videri, & pa&longs;<lb/>&longs;im, & per&longs;euerare, & augeri: tunc enim <lb/>procul dubiò pe&longs;tem futuram prænunciant. <lb/></s>

<s id="s.011553">Aues etiam &longs;i hunc morbum concipiant, in<lb/>gentis pe&longs;tis &longs;ignum &longs;unt. </s>

<s id="s.011554">Refert enim Ioa<lb/>chimus Schælerus, in illa graui&longs;&longs;ima pe&longs;te <lb/>Britannica aues &longs;ub arboribus mortuas in<lb/>ueniri &longs;olitas cum pu&longs;tulis &longs;ub alis. </s>

<s id="s.011555">Itaque <lb/>cùm &longs;iccius animalium genus atque liberius <lb/>eo morbo afficitur, multò magis etiam ho<lb/>mines. </s>

Line 17010

<s id="s.011565">Et &longs;i &longs;ub Caniculæ ortu <lb/>citò are&longs;cant. </s>

<s id="s.011566">Si enim vehemens hoc ma<lb/>lum fuerit, in plurimos annos protenditur: <lb/>velut de &longs;terilitate Io&longs;eph &longs;ub Pharaon<gap/>, <lb/>quæ &longs;eptem annis durauit. </s>

<s id="s.011567">Ob id etiam <lb/>qui &longs;erunt, meliora ex eo genere legunt &longs;e<lb/>mina. </s>

<s id="s.011568">Similiter & in fructibus, in quibus <lb/>perpetuum illud fermè manet, vt maximam <lb/>vbertatem maxima &longs;terilitas &longs;ub&longs;equatur, <lb/>&longs;eu exhau&longs;tis arborum viribus, &longs;eu quomo<lb/>cunque læ&longs;is germinibus, à quibus germina <lb/>prodeunt, vt etiam ex grandine contingit. <lb/></s>

<s id="s.011568">Similiter & in fructibus, in quibus <lb/>perpetuum illud fermè manet, vt maximam <lb/>vbertatem maxima &longs;terilitas &longs;ub&longs;equatur, <lb/>&longs;eu exhau&longs;tis arborum viribus, &longs;eu quomodo<lb/>cunque læ&longs;is germinibus, à quibus germina <lb/>prodeunt, vt etiam ex grandine contingit. <lb/></s>

<s id="s.011569">Ab accidentibus vero, & &longs;ignis: nam terræ<lb/>motus, & locu&longs;tæ, &longs;æpè pe&longs;tis, frequentiùs <lb/>&longs;terilitatis cau&longs;æ manife&longs;tæ, & efficaces fue<lb/>runt. </s>

<s id="s.011570">Et in&longs;ectorum ac pi&longs;cium abundantia <lb/>&longs;terilitatem nuntiat: ab humidi enim co<lb/>pia fiunt pi&longs;ces, triticum autem ab humido <lb/><expan abbr="t&etilde;peramento">temperamento</expan>, vnde (vt diximus) nec in in&longs;ula <pb pagenum="607" xlink:href="016/01/254.jpg"/>beati Thomæ prouenit. </s>

<s id="s.011571">Sic tritici vbertas <lb/>contraria ratione paucos pi&longs;ces facit. </s>

<s id="s.011572">Sed &longs;i <lb/>omnia attingere voluero, finem nunquam <lb/>&longs;um facturus: vituperabatur pictor ille quan<lb/>euam egregius ab Apelle, qui à tabula nun<lb/>quam &longs;ciret manus abducere, præcipuè cùm <lb/>homini nihil &longs;it difficilius &longs;cientia futuro<lb/><arrow.to.target n="marg1573"/><lb/>rum: hæc nanque adeò ob&longs;cura e&longs;t, vt ni<lb/>&longs;i diuino aliquo afflatu adiuuetur, vix lau<lb/>dem afferat. </s>

<s id="s.011572">Sed &longs;i <lb/>omnia attingere voluero, finem nunquam <lb/>&longs;um facturus: vituperabatur pictor ille quan<lb/>quam egregius ab Apelle, qui à tabula nun<lb/>quam &longs;ciret manus abducere, præcipuè cùm <lb/>homini nihil &longs;it difficilius &longs;cientia futuro<lb/><arrow.to.target n="marg1573"/><lb/>rum: hæc nanque adeò ob&longs;cura e&longs;t, vt ni<lb/>&longs;i diuino aliquo afflatu adiuuetur, vix lau<lb/>dem afferat. </s>

<s id="s.011573">Ob id qui in ea claruerunt, fue<lb/>runt autem admodum pauci, diuini meritò <lb/>vocati &longs;unt. </s>

<s id="s.011574">Claruerunt autem inter viros <lb/>Mu&longs;æus Athenien&longs;is, & ex eadem vrbe Ly<lb/><arrow.to.target n="marg1574"/><lb/>cus Pandionis filius & Bacchides B&oelig;otius, <lb/>tum Tire&longs;ias & ip&longs;e B&oelig;otius, tum Cyprius <lb/>Eucleus, & famo&longs;us Epimenides Creten&longs;is. <lb/></s>

<s id="s.011575">Sicut inter f&oelig;minas &longs;ibyllæ, à <foreign lang="greek">sibullia_|n</foreign>, <lb/>quod e&longs;t vaticinari, &longs;eu à <foreign lang="greek">siou\s</foreign>, quod e&longs;t deo<lb/>rum, & <foreign lang="greek">boule\</foreign> &longs;ententia, dictæ. </s>

Line 17053

<s id="s.011593">Archimedes primus &longs;it, non &longs;olùm ob mo<lb/>numenta illius nunc vulgata, &longs;ed ob mecha<lb/>nica, quibus vt Plutarchus auctor e&longs;t, vires <lb/>Romanorum &longs;æpius fregit. </s>

<s id="s.011594">Refert mira il<lb/><arrow.to.target n="marg1577"/><lb/>lius inuenta in M. </s>

<s id="s.011595">Marcelli vita, & nos alia <lb/>non minora, ex Galeni te&longs;timonio, in vtro<lb/>que genere non tam primus auctor, quàm <lb/>immitabilis. </s>

<s id="s.011595">Marcelli vita, & nos alia <lb/>non minora, ex Galeni te&longs;timonio, in vtro<lb/>que genere non tam primus auctor, quàm <lb/>immirabilis. </s>

<s id="s.011596">Nec qui Græculos <emph type="italics"/>(<emph.end type="italics"/> omne &longs;olet <lb/>appellare Cicero genus id hominum) laudare <lb/>ingenium, & inter vrbis ruinas Syracu&longs;iæ, ac <lb/><arrow.to.target n="marg1578"/><lb/>&longs;entes, &longs;epulchrum quærere dignatus e&longs;t. </s>

<s id="s.011597">Se<lb/>cundus e&longs;t Ari&longs;toteles Stagirita, Macedo <lb/>Magni Alexandri præceptor, qui res natura<lb/>les, ac diuinas, dialecticámque mirum in mo<lb/>dum excoluit: animaliúmque vitam, mores <lb/>ac &longs;tructuram incredibili &longs;agacitate per&longs;e<lb/>cutus e&longs;t. </s>

<s id="s.011598">Qui cùm in &longs;ingulis di&longs;ciplinis &longs;cri<lb/>p&longs;erit quod probaretur, error tamen con&longs;pi<lb/>cuus in tot &longs;eculis in illius &longs;criptis depræ<lb/>hendi non potuit. </s>

Line 17086

<s id="s.011611">Sextus locus Apollonio Pergeo debetur, <lb/><arrow.to.target n="marg1582"/><lb/>qui fermè &etail;tate &etail;qualis fuit Archimedi. </s>

<s id="s.011612">Scri<lb/>p&longs;it octo de Conicis elementis libros egre<lb/>gius: quorum ad hanc v&longs;que diem, primitan<lb/>tantùm quatuor editi &longs;unt, tam f&oelig;dè à trans<lb/>latore con&longs;purcati, vt ne illos etiam editos <lb/>meritò dicere po&longs;&longs;is. </s>

<s id="s.011612">Scri<lb/>p&longs;it octo de Conicis elementis libros egre<lb/>gius: quorum ad hanc v&longs;que diem, primi<lb/>tantùm quatuor editi &longs;unt, tam f&oelig;dè à trans<lb/>latore con&longs;purcati, vt ne illos etiam editos <lb/>meritò dicere po&longs;&longs;is. </s>

<s id="s.011613"><margin.target id="marg1582"/>Apollonij <lb/>laus.</s>

<s id="s.011614">Proximus autem huic, verùm longè anti<lb/><arrow.to.target n="marg1583"/><lb/>quior, Architas Tarentinus, vt etiam in<lb/>ter tam egregios viros &longs;edem aliquam Italus <lb/>vir obtineat, collocetur: qui præter ligneam <lb/>columbam volantem, quam con&longs;truxi&longs;&longs;e fer<lb/>tur, veram demon&longs;trationem duas lineas in<lb/>ter duas alias propo&longs;itas in continuo pro<lb/>portionem collocandi inuenit, quam inter <lb/>decem aliàs fal&longs;as Eutotius tradidit. </s>

<s id="s.011615">Huic <lb/>Mahometus Mo&longs;is filius Arabs, Algebrati<lb/>cæ (vt ita dicam) artis iuentor, &longs;uccedit. </s>

<s id="s.011615">Huic <lb/>Mahometus Mo&longs;is filius Arabs, Algebrati<lb/>cæ (vt ita dicam) artis inuentor, &longs;uccedit. </s>

<s id="s.011616">Ob id <lb/><arrow.to.target n="marg1584"/><lb/>inuentum ab artis nomine cognomen ade<lb/>ptus e&longs;t, Nonne Alchindus & ip&longs;e Arabs, <lb/>editorum librorum quorum Auerroës me<lb/>minit, exemplum e&longs;t, qui &longs;upere&longs;t libellus de <lb/>Ratione &longs;ex quantitatum, quem nos excu<lb/>dendum trademus, exhibet cùm nihil &longs;it in<lb/>genio&longs;ius. </s>

<s id="s.011617">Pò&longs;t &longs;equitur Heber Hi&longs;panus cla<lb/><arrow.to.target n="marg1585"/><lb/>ri&longs;&longs;imo inuento: cùm Ptolemæus ex quinque <lb/>quantitatibus maximo labore &longs;extam quæ<lb/>rat, hic in ei&longs;dem cum tribus quartam. </s>

<s id="s.011618">Mul<lb/>ta etiam in melius mutauit, quæ ad &longs;tatum <lb/>c&oelig;li pertinebant: vt facilè intelligas multo <lb/>minus æ&longs;tus maximos frigoribus gelidis ob<lb/>e&longs;&longs;e ingeniis. </s>

Line 17128

<s id="s.011634">A iudi<lb/>cio: vt Algebræ. </s>

<s id="s.011635">A &longs;en&longs;u atque experientia, <lb/>vt Vitruuij: cuius æmulus fuit Hero clari&longs;<lb/>&longs;imus inuentis, &longs;ed parum vtilib. </s>

<s id="s.011636">Præ&longs;tanti&longs;<lb/>&longs;imus in Vitruuio modus horologiorum, &longs;eu <lb/>per tympana & aquam, &longs;eu in anaporicis ex <lb/>&longs;ignifero, &longs;eu per analema quod cauis plan<lb/>tis, ac &longs;phæricis commune e&longs;t. </s>

<s id="s.011637">Atque hi om<lb/>nes ingenio præ&longs;titerunt, &longs;ed qui humanas <lb/>vires &longs;upergre&longs;&longs;i, propioré&longs;que diuinitati <lb/>cuipiam fui&longs;&longs;e videntur, tres &longs;unt: Ptolemæus <lb/>Alexandrinus, Hippocrates, Cous, & Ploti<lb/>nus. </s>

<s id="s.011637">Atque hi om<lb/>nes ingenio præ&longs;titerunt, &longs;ed qui humanas <lb/>vires &longs;upergre&longs;&longs;i, proprioré&longs;que diuinitati <lb/>cuipiam fui&longs;&longs;e videntur, tres &longs;unt: Ptolemæus <lb/>Alexandrinus, Hippocrates, Cous, & Ploti<lb/>nus. </s>

<s id="s.011638">Huic debeo, quòd intelligere multa po&longs;<lb/>&longs;e confidam, illi artis &longs;cientiam: primum ad<lb/>miror quod vix intelligam. </s>

<s id="s.011639">Coniector hanc <lb/>claritatem virorum, quòd reliquorum &longs;i per<lb/>ii&longs;&longs;ent monumenta, propo&longs;itis mihi tracta<lb/>tionibus <expan abbr="auxilii&longs;q;">auxilii&longs;que</expan>, quibus illi freti &longs;unt, cur <lb/>&longs;ingula re&longs;tituere non po&longs;&longs;em, & &longs;i non po&longs;<lb/>&longs;em, non intelligo: at vnius ex his, ne &longs;eptem <lb/>quidem lineas facturum me non po&longs;&longs;e toto <lb/>vitæ meæ tempore &longs;atis intelligo. </s>

<s id="s.011640">At qui <lb/>Hippocrati, Galenum parem e&longs;&longs;e putant, <lb/>neutrum eorum &longs;e intelligere ea confe&longs;&longs;io<lb/>ne fatentur. </s>

Line 17148

<s id="s.011648">Vt verò ab&longs;olutorum librorum rationem <lb/>qui&longs;que intelligat, & quónam modo ars vna<lb/>quæque doceri po&longs;&longs;it, neminem inuenio qui <lb/>id exactius me tradiderit, præter vnum Ga<lb/>lenum: quam &longs;i nos tempe&longs;tiuè tenui&longs;&longs;emus, <lb/>à multis &longs;anè laboribus excu&longs;a&longs;&longs;et. </s>

<s id="s.011649">Ea e&longs;t ra<lb/>io, qua &longs;æpius eadem ad hanc v&longs;que diem <lb/>no&longs;tra immutare coactus &longs;im, quæ prius aliis <lb/>placere c&oelig;perunt quàm mihi. </s>

<s id="s.011649">Ea e&longs;t rat<lb/>io, qua &longs;æpius eadem ad hanc v&longs;que diem <lb/>no&longs;tra immutare coactus &longs;im, quæ prius aliis <lb/>placere c&oelig;perunt quàm mihi. </s>

<s id="s.011650">Nunc verò <lb/>quæ edentur, percepta con&longs;cribendi ratione, <lb/>non minus nobis quàm aliis (vt exi&longs;timo) &longs;a<lb/>tisfaciens. </s>

<s id="s.011651">Mihi quidem præter Deum, ad <lb/>hanc v&longs;que diem nullus auxiliator ad com<lb/>ponendos libros fuit, vtinam non magis im<lb/>pedimento qui&longs;quam fui&longs;&longs;et. </s>

<s id="s.011652">Itaque inita ra<lb/>tione mecum, vt cogitarem aliquem e&longs;&longs;e, & <lb/>huius rei modum, ca&longs;us qui non &longs;ine numine <lb/>fuit, oblatus e&longs;t, quo Galeni &longs;ententiam de <lb/>hoc intelligerem. </s>

Line 17231

<s id="s.011695">Quæ verò &longs;olùm iuuantur, et&longs;i non illu<lb/>&longs;trentur, artes &longs;unt, Militaris, magia, chymi<lb/>&longs;tica, machinatoria, quæ &longs;ub architectura <lb/>continetur. </s>

<s id="s.011696">Pictura non &longs;olùm iuuatur, &longs;ed <lb/>etîam illu&longs;tratur. </s>

<s id="s.011697">E&longs;t enim pictura, mecha<lb/>nicarum omnium &longs;ubtili&longs;&longs;ima eadem verò <lb/>& nobili&longs;&longs;ima. </s>

<s id="s.011698">Nam quicquid pla&longs;tices, aut <lb/>&longs;cultura conatur, mirabilius pictura fingit, <lb/>addit vmbras, & colores, & opticen &longs;ibi <lb/>iungit, nouis etiam additis quibu&longs;dam in<lb/>uentionibus: nam pictorem omnia nece&longs;&longs;e <lb/>e&longs;t &longs;cire, quoniam omnia imitatur. </s>

<s id="s.011698">Nam quicquid pla&longs;tices, aut <lb/>&longs;culptura conatur, mirabilius pictura fingit, <lb/>addit vmbras, & colores, & opticen &longs;ibi <lb/>iungit, nouis etiam additis quibu&longs;dam in<lb/>uentionibus: nam pictorem omnia nece&longs;&longs;e <lb/>e&longs;t &longs;cire, quoniam omnia imitatur. </s>

<s id="s.011699">Et philo&longs;ophus pictor, architectus, & di&longs;<lb/>&longs;ectionis artifex. </s>

Line 17243

<s id="s.011703">In fa<lb/>cie &longs;umptum e&longs;t exemplum, quia homines <lb/>belluis, vt belluæ plantis, & plantæ regio<lb/>nibus, earumque partibus difficilius fun<lb/>guntur. </s>

<s id="s.011704">Facies autem ex hominis partibus, <lb/>& ex modis illius tota difficillimè exprimi<lb/>tur. </s>

<s id="s.011705">Primùm quidem, quia generaliter <lb/>duplus e&longs;t labor: inde comparatione, &longs;i <lb/>quid artifex delituit in magnitudine, nume<lb/>ro, forma, colore, lituris, rugis, cauitatibus, <lb/>alii&longs;que innumeris, quæ in vnius medietatis <lb/>figura latebant, manife&longs;ta facta, operis tur-<pb pagenum="610" xlink:href="016/01/257.jpg"/>pitudinem declarant. </s>

<s id="s.011706">Qui igitur fingere ali<lb/><arrow.to.target n="marg1596"/><lb/>quid volunt, formam eius primùm vi&longs;am <lb/>mente, qua&longs;i memoria concipere debent, in<lb/>de typum quendam &longs;eor&longs;um delineare &longs;ub<lb/>tiliu, pò&longs;t præ&longs;ente eo quod fingis &longs;ingula <lb/>animaduertendo ad amu&longs;&longs;im perficere: latet <lb/>enim in vnoquoque partium quædam &longs;ym<lb/>metria, quam &longs;i non mente comceperis, <lb/>oculorum verò præ&longs;idio tantum innixus <lb/>tentes exprimere, operam lu&longs;eris. </s>

<s id="s.011706">Qui igitur fingere ali<lb/><arrow.to.target n="marg1596"/><lb/>quid volunt, formam eius primùm vi&longs;am <lb/>mente, qua&longs;i memoria concipere debent, in<lb/>de typum quendam &longs;eor&longs;um delineare &longs;ub<lb/>tilius, pò&longs;t præ&longs;ente eo quod fingis &longs;ingula <lb/>animaduertendo ad amu&longs;&longs;im perficere: latet <lb/>enim in vnoquoque partium quædam &longs;ym<lb/>metria, quam &longs;i non mente comceperis, <lb/>oculorum verò præ&longs;idio tantum innixus <lb/>tentes exprimere, operam lu&longs;eris. </s>

<s id="s.011707">Neque <lb/>dimidium velut latus quoddam finges ne<lb/>mo enim &longs;ic in&longs;picit hominem, &longs;ed paulu<lb/>lum deflexo capite inter vtrunque &longs;itum. <lb/></s>

<s id="s.011708">Vnde etiam fit, vt ob hoc media facies <lb/>facilius, quàm tota repræ&longs;entetur: nam <lb/>quum media plures ( quemadmodum di<lb/>ctum e&longs;t <emph type="italics"/>)<emph.end type="italics"/> habeat &longs;itus, ideo illius forma in <lb/>quadam latitudine con&longs;i&longs;tit: tota verò in <lb/>vno qua&longs;i puncto po&longs;ita e&longs;&longs;et &longs;umma qua<lb/>dam perfectione repræ&longs;entationis. </s>

<s id="s.011709">Facilius <lb/>autem multò quod quantitatem habet a&longs;<lb/>&longs;equi, quàm rem diui&longs;ionis expertem, & <lb/><arrow.to.target n="marg1597"/><lb/>quæ &longs;olùm fermè cogitatione concipi po&longs;<lb/>&longs;it. </s>

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