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Notes Du Mont Royal ← Notes du mont Royal www.notesdumontroyal.com 쐰 Cette œuvre est hébergée sur « No- tes du mont Royal » dans le cadre d’un exposé gratuit sur la littérature. SOURCE DES IMAGES Google Livres EUCLIDIS’ ELEMENTA GRAEICEjET LATINE. l COMMENTARÏIS INSTRUCTA EDIDERUNT flIlOANN’ES GUILELMUS CAMERER CABOLUS FBIDERICUS HAUBEÈ. BEROLINI SUMTIBUS G. REIMERI a x MDcccxxv.u . l. à VEU’CLIDIS g ELEMENTOBUM LIBRI SEX PRIORES I h GRAECE ET LATINE COMMENTARIO E SCRÎPTIS VETERUM AC RECEN- IIÔRUM MATHÉMATICORUM ET PFLEIDERERI MAXIME ILLUSIRATI. EDIDIT æ IOANNES. GUILELMUS CAMEBEÏ: GYMNASI! STUTTGARDIANI RECTOB. TOM. Il. COMPLECTENS LIBR. IV-VI. CUMx V1. TABULIS. BlE R O L I N I SUMTIBUS ,0. REIMERI lubcccxxv. ,Mcfih Z751 .31. (JE) (a); ï... HAPVARD UNlN ERSITY LI BRARY "EUCLJDIS ELEMENTÔBUM . LIBRI SEX PRIORES. s l Euclid. nouent.l r. n. ’ A ETKJÉIJOÏ 2 T 0 I x E AI sa N, ’ BIBLIjONÏTEçFARTON’. Ï’OPOI. d. 217mo» sûâîiygamt-ov si; axfipa’æfiôüygappov 37- yçdçpaôdi 16,787.14, 51ml indou; un mot? êyygaçzo- Iuévov ovipares yœvwîv indu-tr; nÂazigcïg c017 si; 3 êyygéçpezat ânïqtrm. 13’ . 217mm 3è Jpolœg au); agriffiez nsgiygolrpsaâw klystron; ,ô’waf ÉZOËOTI] filmerai un? mgiygwpom’vov indou]; ywvlœc un? rugi il nepzyga’qiermz &n’l’mal. h 7’. 2177,40; ôè eüâüygappoy sis minbar êyyqé- (pauma léyervcu, 610w indou] ywau’a un? ëyygatpops’alov anima; mie ne? minÂO’U’ nsglqleçeiag. d’4. ’Zzfipa 6è eüôtiygappow negiil 3:15»le nain-l 79quth lignerai, 570w ézcloæq agença! mon"! ingr- 7eaçoyévov êtpdnmma mais me? minou neptçapst’ag 1). é. Kclulog d’à si; 0172m» circulais 1578105; ingé- rpeaâm, 5mn! 97’106 miniez; negupæ’gem’éuolmojg alev- gâg mû sic a êyygolrparmt flamme 2]. Un: rectius’om’nino cum Coûts. le ît Peyrgrdua. Fric. tu editiones habebant: 31ml 5115017 «lança de 1001153100 m- çchspu’uc tu; nepzypaqzopëvov êqmîmfinou. a) Si van saut, quae e Rob. Simson. .a 1H. Def. 2.110- tuimlu, hic legendum fuel-i; igame». W EUCLIDIS ELEMENTOEUM LÎBER QUARTUS. .. DEFINITIONES..i .1.Figura rectilinea in figura rectilinea inscribi dici. tut, quando sunusquisque inscriptae figurao angullu tangît unumquodque lama eîus, in qua inscribitur. 2. Figura amena, similiter cires figuram circum- 1 scribi dicitur, quando unumquodque latins circum’scri- ptae mugit unumquemque angulum eius, cira quarra drcumscribitur. * L ’, 3. Figur’a vero rectilinea in cîrculo inscribî dîcîa par, quando unuSquisque angulus circmnàçriptae tangitl circuli circumferentiam. Il. Figura autem rectilinea citez cirçulum circum- scribî dicitur, quando unumquodque’latus circumScrio pue contingit circulî circumferentiam. i L 5. Circulus vero in figura similiter dicîtur inserîbî, quando circuli circumferentia unumquodque lams eiusi in qua inscribimr contingit. tDEFINfl 0585 Ôampanns’ baba: tantum dans primas bains libri- .ûcfinitiones. , A: mac ipsaox maquant ndhibenmr. Kim; dur 4 ILIIINTORUK ,g’. Ktlulog Je rugi (mafflu negtygdrpwôm Mywaz, forma! 1j 101i minicar "relaieriez êxtioufi ywî’t’uÇJO’Ü r rugi J nsgzypdtpemz chiqua. Ç’. Eæiâeîa sic aduloit ëvrcçluôçwâuc léyswt, 316w frai nëçaïu min]: Mi iojç simiesque; 106 minima ’ i - - r - ’ IIPOTAZ’ISoE. El; nia! (hâlant; minium! ryj’ôoüu’oy tamia. fui ,ualÇow 0570?; 17]; un? 311332.61; ÜIU[lé’TQO’(’, l’ail-v 61;196Îu’l’ nuancent."Etna 6 863.52g «fado; ô 4113T, ’ a;, d’à , (bâchiez I aimiez 511,9 .pslçnw 17;; 101711721011 diapawov 7j 11’ * titi 69j ciguës! ABI’ minimal 7,] d mimait; 1’ch ul- ’ 05mm! drageonna - ’ ’ 4 L "1114940 1013 ABF mixiez! (bégaya; 1; Br. Fi ph! 657 i011 émir â Br Tfi A, fermais à! si?) 16 [attrazâè-y’ êwjppomm gag dg ni)! ABF lutiniez! 1,5 bium vidai posait, mon. serins adiectae funin: ad analogiam neguntium. ’ . l ’ ’ .PROPOSITIO I. s lObl. r Quum l - punctum « P in circumferentia pro lubitu. uni quant, palet, innumerin media problemn lsolvi poste, niai nova adhnc daterminatio aoccdat. Eiusmodi determinatio en que patent, si punctum F flntum essc sumac velis. Ve- mm, adam hoc aumto, duplex tamen, quod et Commcndi- nua monuil, solutio locum habçbit: aequo enim dupa recta F Z 1d punctum Z, in quo circuli inrum sibi occultant, pro- .I biomati satisfaciet, ac recta 1M. Ah’a determinario haec eue 1 pelait, ut mon circula inscribend; vel ipsa , vol producu, par daçnm’punctum trament, quod non si: in circuli circulo- formât; vel ut flic palud. ait recru position dune. Et, N Luna courras. ’ 5’ 6. Circulus autem circa figuram circumscribi di-I citûr, Iquando ’circuli .circum’l’erentia unumquemque an- gulum ipsius , circa quam circumscribitur, (angle. 7. Berna in circula aptari dicitür, quando termini dus in circumferentia sur)! circuli. ànorosx’rro 1. (Fig.283.) e In dito circula datae rèctac, quad non mnior ait diametro circuli, aequalçm rectam. agnate; Sit dams circulas ABI’; ’data amerri recta il non . major circuli diametro, oportet igitur in circula 418F rectae A aequalem rectam apure. r Ducatur circuli ABF dîameter Br. Si guident igitur Br aequalis est J,. factum erît propositum. Aptata est enim in circula ABF, BI’ rectae A ae- si quidam illud. postnletur, ut recta circula data inactibendn par datura punctum translan, problema unum 0x ü: est, qu" Pappo restante in Pnefar. ad libr. VIL Collect. Math. Apol- lonius in libris ne?! vsôaswvftnctaviyt. (Cf. Apollonii Pargaei Inclinat. Libri duo cd. Horsl’oy Oxon. 1170. et: Dia Biiclnr (des Apolloniul van Perga de Inclixiationibus van Diutervveg Berlin. 1823 ).’ Et particulare illud problema facile IOlvetuf quuentem-inA1111. Put: fadant, etm-odum. Fig. 284. recta 4B,. i glue ne- qudil si: renne dans A diametro non maieu’, inscripn si: circula data ABZ, caque ipsa auz producta par datum pun- luni 1’ trumeau, quad non lit in cimuli dati circumferemiu Et 1) quidam,1 si raca data si: aequalis diametro circuli, mon circula inscribendu cri: diameter par dnfum punctum duca- Si autan: non fouit diamant, en. a: hyp. minot diamanta, l p.46 «303:2; surannronufl a»; 1; BI’. El 63”01), peigna: écala 1; ’BP , Ï tuf; A, ami «61’001» 1) cg" A l’ai; 17’ TE, ml «évada: ph 14,5 Il, ÛlWfl’WIL d’à un? TE Midas yeygëqiûw à AEZ, nul 571555610!» a]? TA.  , ’ ’Enei mit! c6 P amadou m’auront! 3012 coti AEZ miaulai), ion Sofia! fi TA ni TE, 241.102 rugi A a; k TE êtnlaf î’mr Mal ,41 02’904 1?? TA émiai l’on. E29 aigu 1:67 600ème: «6;.on wôvIABI’, agi do- ûet’oy aidait; 2), a?) pet’ÇO’w 0470?] mais coti minima d’mps’cgov, 5’01] êwjçpoarwc ri T11. ,"Oflee au flonflon. 11.220 T4212 fifi -.EÏQ 156v (barème; minicar 5:95 doôe’wa coagulai? tao-- yniwov cgiywwov êyypa’tpw. t "Etna; ci 6064929 5:67:10; 0’. JET, ad 03604933411951 www, a; AEZ’ dei d’1) sis Œôv JET ululai agi AEZ ægzyuivgo iooyw’mow aglywww ëyyçdtpaz. i 1) Peyrardus cum Cod. l legit: si dé (caton: En)! fi B!” 1776 a, minât». Nos restituimus lectioncm cd. Oxan. 2) Poyrardus cum Cod. a. ’omittit verbn ln) peignai; anion C179 coi; adula» (harpé-mou et corum loco parait ci; J: nos isn verba, quae nccessariam omnino dicterminntionem continent, restituirnus. ’ «icaque extra centrant E transibit (HI. 15.). Demi"; igitur in nm a centra perpendicularis E9 cant bisecabit (HI. 5.), - adeoquc, ab datant JE, data cri: dimidia .49, adeoque’ du: agit, val inveniti poterit in triangulo ad a rectangulo 49E, in Qquo etiam E4 datur, recta E9 (1. 47. Cor. 20.) vol di. ’stnntia, qua recta A3 a centro E abesr, val , ut aliter dica- Ir’mujsi, notum orit, in qua distantia a oentro E situai esse de- bau:Nn.- punctum 9, poulpe in circula centra E, radio E9 de- scripto. (Quod ipsum brevîul e HI. 15. Cor. derivari po- tout.) Qui circulus si describatur, cantingct auna recta dB a c . un" cannas. I 7 qualis. Sin minus, maior est BF ipsa A,iet pOnatur ipsi A aequalîs TE (I. 3.), et centra P, intervallo veto TE, circulas describatur AEZ :(Post. 3.), et itmgatur TA. Quoniam igitur punctum F centrurntest circuli MEZ, aequalis est F11 ipsi Flic Sed TEipsi .1 i est aequalis; et A igitur ipsi F)! est aequalis. In data igitur circula ABF, datae rectae, quae mon maier’est diametro.circuli, aequ’alis aptata est TA. Quod apartebat facere. PROPOSITIO Intrigue) In data circula inscribere triangulum aequiangulum dataSit datas triangulo: circulus ABÏ’ , datum . vero triangulum AEZ; aportet in circula ART trianguloiAEZ acqui- angulum triangulum Iinscriberen - in 9 (HI. 16.), adeoque tata extra eum pasira erit. Unde, lut recta dB transite posait. pet [panctum detum If, neicesse est, ut punctum 1’ non cit intra circulum eentro E, radia E9, descriptum. Quadsi non fuerit, problema reductum est Id hoc: e puncto data T, quad non ait inti-n circulant datant, ducere cd [une circulum rectam, quae eum continent, i. a. Compotitio grabIematisîithue hue redit. Si recta data A aequaliead si: HI.diametro circuli 11. (inti, ducatur . par punctum datum T disante! circuli. (Puucturn nempe Î acentro Ediversum eue lumitur, quodei non foret, quaevis diameter pliablemati entichant.) Sin autant recta dm miner si: diametro circuli dati ,v lumatur in cireumferentia circuli punctum quodcnnque Il, et ex W. 1. circula inscribatur recta 11K:d, et, domino in HK perpendiculo El, centra E, radio El, describatur cir- culus. Quodli hm punctum datum F lit intn hune circu- 3 t , cnnmcuronvm "H100; coti ART mixiez; ëmuntope’m] H9 nard :76 A, mil CUVEO’FOCITŒ, nçôç plat! agi A9 569.959: un! ce? n96; au??? amicale) 756 A agi tînô AEZ grandet 5’01] ai 6nd GAP M269 (là et? HA 5150612; nul 193 mais «Un; GliflôI-Ilp Il,» A T?!" and ZAE moula un; 1; 6nd iHAB, ’ anda xëneçetilûw a N tî BI’. ’ ’Eml mit! minot! mû ABP épincetai ces 611,19’GÎŒ , 9; 9A, ’ual (inti tifs and ni A Ënarprfç si; tôt! mî- ’u2.ov chinoit EÜÛ’GÏŒ 7j AI” a; (2’904 6nd GAP fin; Sud tu)? à! on; éveillai un? mixiez; rythmai yœw’ç, ,Œ’Iîî’Üflô ABF.
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