Liber. i.

Iſcis iſta oīa ad plenitudinē: noſti locoꝝ ſegregationē. Nā ꝗ ignorāt regulā huiꝰ artismulta opponūt falſa ꝓ veris.DQuomō īuenta eſt geometria.M Inuentā eē geometriā aegiptii dicūt ꝓ neceſſitate termīoꝝ terre: quos nullꝰ iundatiōis tempore īfundebat.DUnde vocata ſit geometria.M Geometria nominata ē a dimē̓ſiōe terre: ꝑ quāvniuſcuiuſqꝫ terre termini declarari ſolent.DQuid ſit geometria.M Geometria ē diſciplina magnitudinis ⁊ figure:que ẜm magnitudinem contemplatur.D Que ſit intentio.M Intentio euclidis duplex ē ad diſcipulū reſpitiēs⁊ ad naturas reꝝ ad diſcipulū reſpiciēs: qꝛ oꝫ eūab his vti iſagogicis īciꝑe ꝓ facilitate ꝓ breuitate: ⁊ eo qd̓ ī qōibꝰ ob hoc nulla ſit difficultas. ꝓreꝝ naͣ eo qd̓ phiſice ſcīe: ⁊ timei ſiue platōis doctrina plurima geometrice demōſtrare noſcūt̉.DQue vtilitas.M Utilita ( (vt ſupra p̄fati ſumꝰ) geometrie triplexē ad facultatē: ad ſanitatē ad aīam: ⁊ facultatē:vt mechāici ad ſāitatē: vt medici ad aīaꝫ vt ph̓i.D Qui ordo ē geometrie in diſciplinis.M Aliqͣtenꝰ poſt arithmeticā ẜuus ē: aliqͣtenꝰ tertiꝰDTituli inſcriptio quomō intelligatur.M Eſt enī tituli p̄ſcriptio elemētoꝝ: q̄ figure ſimpliciores ſtͣ: ⁊ ex his alie ꝯponūt̉: q̄ ī hiſ ēt reſoluūt̉D Si proprius codex.M Codex iſte ẜm diſpōnē euclidis eē dr̄: ẜm demōſtrationē vel īuentionē alioꝝ plerūqꝫ eē diciturDIn quot partes diuiditur.M Diuidit̉ codex iſte ī qͣtuor ꝑtes ī epipediſ: ī arithmeticis: in rōalibꝰ ⁊ irratiōalibꝰ līeis: ⁊ ī ſolidis.D Que ſunt in demonſtratiōe geometrica.M Propoſitio diſpō: diſtributio deſcriptio demōſtr o. ⁊ concluſio.ati Eſtat aūt nobis ꝓ fūdiſſimā quādā tradere diſciplinā: q̄ ad oīuꝫ nature: tū reꝝ ītegritatē maxime rōne ꝑtineat. Magnꝰ ꝗppe ī hac ſcīa fructꝰ ē: ſi ꝗs nō neſciat: qd̓bonitas diffinita ⁊ ſub ſcīa cadēs aīoqꝫ ſiimitabil̓ ⁊ perceptibilis prīa natura eſt: ⁊ ſue ſubſtātie decore ꝑpetua: īfinitū vero malitie dedecꝰ nullis ꝓpriis prīcipijs nixū: ſꝫ naͣ ſꝑ errās ab oī definitiōe pricipli tāqͣꝫ aliqͣ ſigno optīe figure īpreſſa cōponit̉: ⁊ exillo erroris fluctu retinet̉. Nā nimiā cupiditatē ireqꝫīmodicā effrenationē qͣſi ꝗdā rector aīus pura intelligētia roboratꝰ aſtringit. Nos tn̄ q̄ de nūeris a nichomaco diffuſiꝰ diſputata ſūt vel a varrōe de mēſurisoſiſa ſūt moderata breuitate collegimꝰ. Et que tranſcurſa velociꝰ anguſtiorē ītelligētie p̄ſtabāt aditū: mediocri adiectiōe reẜauimꝰ: vt aliqn̄ ad euidentiā reꝝnr̄is etiā formul̓ ac deſcriptionibꝰ vteremur. qd̓ nobis qͣꝫtis vigiliis ac ſudore ꝯſtiterit: facile ſobrius lector agnoſcit. Et has quodāmō īeqͣlitatis formas tēperata bonitate laborando collegimꝰ: ipſe lector ꝓbabit: que nos ex grecaꝝ opulētia lr̄aꝝ in romanū orationis theſaurū ꝯtrahimus: Si q̄ ex ſapīe doctrinisemicuerūt ſapientiſſimi iudicio ꝑ nos cōprobent̉: vides igit̉: vt tā magni laboris effectꝰ tuū tm̄ lector expectet examen. Nec ī aures prodire publicas niſi docte ſnīe adſtipulatiōe nitat̉. qd̓ nihil mirū videri debet cū id opꝰ qd̓ ſapīe īuēta ꝑſeꝗt̉. nō auctoris. Sed

alieno incūbat arbitrio. eſt .n. Sapīa nū̓eroꝝ cās ⁊ diuiſiones earum: que vera eſt cognitio ⁊ integra comprehenſio. quod hec ꝗ ſꝑnit .i. ſemitam ſapīe: ei denūtio nō recte philoſophandū. Hec aūt ē arithmetica: hec .n. cūctis prior ē: nō mō quod hāc ille huiꝰ mūdane molis ꝯditor deꝰ primā ſue habuit rōcinatiōisexēplar. ⁊ ad hāc cūcta ꝯſtituit: quecūqꝫ fabricata ratione ꝑ numerū aſſignati ordinis inuenere cōcordiā.ſꝫ hoc quoqꝫ prior arithmetica declarat̉. qd̓ quecūqꝫna priora ſūt: his ſublatis ſimul poſteriora tolluntur.qd̓ ſi poſteriora pereant nihil de ſtatu prioris ſubſtātie ꝑmutat: vt aīal prius ē hoīe. Nā ſi tollas aīal ſtatꝭquoqꝫ hoīs natura d̓leta ſit. ſi hominē ſuſtuleris aīanō ꝑibit ꝓpe tn̄ ipſa numeroꝝ natura cūcta p̄ceſſit.oīa quecūqꝫ a primeua reꝝ natura conſtructa ſūt: vident̉ numeroꝝ rōne formata. Hoc .n. fuit principaleī aīo ꝯditoris exēplar. Hīc .n. qͣttuor elemētoꝝ multitudo mutuata ē. Hic tꝑoꝝ vices. hic motꝰ aſtroꝝ: celiqꝫ cōuerſio. Proprie tn̄ ipſa numeroꝝ natura oēsaſtrorū curſus. oīſqꝫ aſtronomica rō ꝯſtituta ē. Sic.n. ortꝰ occaſuſqꝫ colligimꝰ. ſic tarditates velocitateſqꝫ errantiū fiderū cuſtodimꝰ. ſic defectus ⁊ multiplices lune variatiōes agnoſcimꝰ: qꝛ̄ qm̄ p̄ior: vt claruitarithmetice vſus ē. huic diſputatōis ſumamꝰ exordiūhoc idē ī geometria vel in arithmetica vr̄ incurrere.Si .n. nūeros tollas: vnde triāgulū vel qͣdratū cōprehēdere poſſumꝰ vel ꝗcꝗd ī geometria v̓ſat̉: q̄ oīa numeroꝝ denominatiua ſunt. hoc aūt erit ꝑſpicuū ſi intelligamꝰ omnes inequalitates creuiſſe primordijs: vtipſa quodammodo equitas matris ⁊ radicis obtinens vim ipſa omnes inequalitatis ſpēs ordineſqꝫprofundauit. Sint .n. nobis tres bini vel tres ternivel tres quaterni vel quantos vltra libet ponere. qd̓.n. in his tribus terminis euenit idem contingit inceteris. ex his igitur ẜm precepti noſtri ordinem videas primū naſci multiplices ſi conuertant̉. ⁊ in hisduplices priꝰ. de hinc triplos inde qͣdruplos ⁊ ad eūdem ordinē ꝯſequentes. Rurſus multiplices ſi ꝯuertant̉: ex his ſuꝑparticulares orientur. Ex duplicibusꝗdem ſeſqualteri. Ex triplicibꝰ ſeſꝗtertii ex qͣdruplisſeſꝗquarti ⁊ ceteri ī hūc modū. Ex ſuꝑparticularibꝰv̓o ꝯuerſis ſuꝑpartiētes naſci neceſſe eſt ita vt ex ſeſqͣltero naſcat̉ ſuꝑbi partiens ſuꝑtripartiētē ſeſꝗtertius gignat vt ex ſeſꝗqͣrto. ſuperqͣdri partiēs. Rectisaūt poſitis neqꝫ ꝯuerſis prioribus ſuꝑparticularibꝰmultiplices ſuꝑparticulares oriunt̉. Rectis v̓o ſuperpartientibus multiplices ſuꝑpartientes efficiūt. precepta aūt tria hec ſūt. vt primū numeꝝ primo faciasparem. Secundo vero primū ⁊ ſcd̓o tertiū: prīo duobus ſecūdis ⁊ tertio. cū .n. cū in terminis eqͣlibus feceris ex his qui naſcent̉ duplices erūt. De ꝗbꝰ duplicibus ſi idē feceris: triplices ꝓcreant̉. Et de his quadruplices atqꝫ in infinitum oēs formas numeri multiplices explicabis. Illi ꝗdē quorū ꝑtes vltra quā ſatisē ſeſeꝑexerint: ſuꝑflui nominātur: vt ſūt. xii. vel. cxiiiiHi enim ſuis ꝑtibꝰ cōparati maiorē partiū ſūmamtoto corpore ſortiuntur. ē enī duodenarii medietas.vi. pars tertia. iiii. ꝑs quarta. iii. pars ſexta. ii. parsduodecima .i. Omniſqꝫ hic cumulus redūdat in. xvi.⁊ totius corporis ſui multitudinem vincunt. Rurſusxxiiii. numeri medietas eſt. xii. tertia. viii. quarta. viSexta. iiii. Octaua. iii. Duodecima. ii. vigeſimaqͣrta.i. Qui omnes: xxxvi. rependūt in qua re manifeſtumeſt qd̓ ſūma partium maior ē: ⁊ ſupra propriū corpusexundat. Atqꝫ hic quidē cuiꝰ ꝯpoſite partes totiꝰ termini