Monantheuil, Henri de
,
Aristotelis Mechanica
,
1599
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42
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& angulus E H I ad centrum conſtitutus in æqualibus circulis ex
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fab. ſunt æquales prop. 27. lib. 3. quia æquales ſunt peripheriæ A M,
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D E ablatæ ſcilicet ab æqualibus ſemißibus M N & E I ex
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fab. prop. 3. & 29. lib. 3. </
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>& ſic reliquum latus N H æquale eſt re
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liquo I H. </
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<
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id
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id.000765
">Ergo cum tota A N æqualis D I ſit maior A K
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parte ſua ax. 9. erit & D I maior ipſa A K.
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Ergo perpendiculares à peripherijs in ſemidiametros &
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ct. </
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>quod fuit demonſtrandum. </
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<
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id
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id.000769
">Hoc autem theorema videtur
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abbr
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quodãmodo
">quo
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dammodo</
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<
foreign
lang
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el
">para/docon. </
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Erat enim veriſimilius in maiore circulo
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abbr
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ſegmentũ
">ſeg
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mentum</
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ſemidiametri eſſe maius, & in minore minus: at non ita eſt vt
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patuit. </
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id
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id.000770
">Cauſa autem hæc reddi poteſt, quod eadem recta, ſi fiat arcus
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minoris circuli plus incuruetur oportet: quam ſi fiat arcus maioris,
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atque his omnibus eo tendit Ariſtoteles, vt oſtendat maiorem circu
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lum mobiliorem, & ideo etiam mouentiorem eſſe minori: rationem
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autem mobilitatum eſſe, vt ſemidiametrorum.
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id
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">In quanto vero.]
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Concluſio eſt qua concluditur, vbi motus
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ſecundum naturam in vtriſque circulis æquales eſſent: ibi motum
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præter naturam in maiori circulo minorem, & in minori maiorem
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reperiri. </
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id
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id.000772
">Antea dixerat duas lationes illas eſſe in nulla ratione, in
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tellige igitur quæ rectis lineis exactè exprimi poßit. </
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id
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id.000773
">Nam ſinus tam
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rectus quam verſus, quibus rationis harum lationum termini expri
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muntur, vt ſint rectæ lineæ: hæ tamen non ad vnguem arcus ſuos
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metiuntur. </
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id
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">Et ſic in nulla ſunt ratione ad vnguem expreſſa: ſunt ta
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men vt hic quodammodo, & vt aiunt ferè.
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<
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lang
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">dei= de\ a)na/logon ei)=nai,
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w(s to\ kata\ fu/sin pro\s to\ kata\ fu/sin, to\ para\ fu/sin
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pro\s to\ para\ fu/sin.</
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<
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lang
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">mei/zona a)/ra perife/reian dielh/luqe
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th\n *h*b th=s *w*b.</
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<
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lang
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el
">a)na/gkh de\ th\n *h*b e)n tou/tw| tw=| xro/nw|
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dielhluqe/nai: e)ntau=qa ga\r e)/stai, o(/tan a)na/logon a)mfote/rws
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sumbai/nh| to\ para\ fu/sin, pro\s to\ kata\ fu/sin.</
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>
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<
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lang
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">ei) dh\
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mei=zo/n e)sti to\ kata\ fu/sin e)n th=| mei/zoni ku/klw|, kai\ to\ para\ fu/sin
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mei=zon, a)\n e)ntau=qa sumpi/ptoi monaxw=s, w(/ste to\ *b, e)nhne/xqai
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a)\n th\n *b*h e)n tw=| e)f' ou(= *x shmei=on. </
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>
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<
foreign
lang
="
el
">e)ntau=qa ga\r
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kata\ fu/sin me\n gi/netai tw=| *b shmei/w| h( *k *b. </
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>
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<
foreign
lang
="
el
">e)/sti ga\r
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au)th\ a)po\ tou= *h ka/qetos, para\ fu/sin de\ e)s th\n *k*b.</
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<
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lang
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">e)/sti
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de\ w(s th\n *h*k pro\s th\n *k*b, h( *q*z pro\s th\n *z*x. </
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<
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lang
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">fanero\n
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de\ e)a\n e)pizeuxqw=sin, a)po\ tw=n *b, *x e)pi\ ta\ *h, *q.</
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<
foreign
lang
="
el
">ei) de\
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e)la/ttwn h)\ mei/zwn th=s *h*b e)/stai, h)ne/xqh to\ *b, ou)x o(moi/ws
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e)/stai ou)de\ a)na/logon e)n a)mfoi=n to\ kata\ fu/sin pro\s to\
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para\ fu/sin.</
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<
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lang
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">di' h(\n me\n toi/nun ai)ti/an a)po\ th=s au)th=s
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i)sxu/os fe/retai qa=tton to\ ple/on a)pe/xon tou= ke/ntrou shmei=on [1kai\ m gra/fei h( mei/zwn]1
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dh=lon dia\ tw=n ei)rhme/nwn.</
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<
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id
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vt id quod
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abbr
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ſecundũ
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<
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abbr
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naturã
">naturam</
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,
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ad id quod
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ſecũdum
">ſecundum</
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natu
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ram: ſic quod præter natu
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ram, ad id quod præter
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expan
abbr
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naturã
">na
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turam</
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. </
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<
s
id
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id.000777
">Igitur maiorem quam
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<
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lang
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el
">b w</
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>
<
expan
abbr
="
peripheriã
">peripheriam</
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>
, vt
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lang
="
el
">b h</
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>
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abbr
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pertrãſijt
">per
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tranſijt</
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>
. </
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<
s
id
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id.000778
">Neceſſe igitur in eo
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tempore
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lang
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tranſijſſe. </
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<
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id
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id.000779
">Ibi
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enim erit, vbi proportiona
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les
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cõtingẽt
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<
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vtrinq;
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motus </
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