Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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pus per NG, vt BG ad NG, & ad tempus per GF, vt BG ad 24951. &
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ad tempus per BGF, vt BG id eſt, 100000. ad 124951. porrò tempus
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per B 3. eſt BG; </
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<
s
id
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">ergo vt quadratum temporis per BG ad quadratum
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temporis per BGF, ſcilicet vt 10000000000. ad 1561475241. ita B 3.
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ſcilicet 81655. ad aliam, hæc erit 123496. igitur in BF, quæ eſt partium
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141422. percurruntur partes 123496. eo tempore, quo percurruntur
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BGF; </
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<
s
id
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">at verò eo tempore, quo percurruntur BHF; </
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<
s
id
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N23510
">percurruntur in
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BF 122702. igitur pauciores; </
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<
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id
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N23516
">igitur minore tempore; igitur duæ BHF
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percurruntur minore tempore, quàm duæ BGF, quod erat demon
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ſtrandum. </
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<
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">Similiter deſcendet citiùs per duas BHF, quàm per duas BZF: </
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">immò
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quod mirabile eſt, patetque ex analytica, citiùs per duas BGF, quàm per
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duas BZF; </
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<
s
id
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">(ſuppono enim BZ eſſe arcum grad. 45.) ſit enim Z
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per
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pendicularis, itemque Z
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B eſt æqualis BR. igitur 70711. Z
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eſt
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29289. igitur
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1223. igitur B
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71924. igitur B
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51858. iam tempus
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per BZ eſt ad tempus per YZ vt BZ ad YZ. id eſt, vt 76536. ad 184777.
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ſit autem vt AYF 261313. ad aliam 219737.ita hæc ad YZ; </
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<
s
id
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N23552
">certè tem
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pus per BZ eſt ad tempus per BZF, vt BZ ad 111496. igitur B
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fit
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tempore BZ; ergo vt quadratum BZ ad quadratum 111496. id eſt, vt
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4857759296. ad 12431358016. ita ſit B
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, id eſt 51858.ad 132708.igitur
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eo tempore, quo percurruntur BZF, percurruntur in BF 132708.earum
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partium, quarum BF eſt 141422. ſed pauciores percurruntur eo tempo
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re, quo fit deſcenſus per BHF, vel BGF. </
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Lemma
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16.
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Citiùs percurruntur duæ inferiores.v.g. </
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; </
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<
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id
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">eſt enim
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PF ſubdupla ſecantis NF; </
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<
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id
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">igitur 193185. FG eſt 51764. GP 141421.
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ſit autem PG ad 165285.vt hæc ad PF; </
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<
s
id
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">certè tempus per HG eſt ad
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tempus per PG, vt HG ad PG; </
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>
<
s
id
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">igitur tempus per HG eſt ad tempus
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per HGF, vt 51764. ad 75628. ſed BX eſt æqualis, eiuſdemque incli
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nationis cum HG; </
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<
s
id
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">igitur tempus, quo percurritur BX eſt BX. vel HG; </
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ſit autem vt BX ad 75628. ita hæc ad aliam 111092. igitur eo tempore,
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quo percurruntur HGF, percurruntur in BF 111092. minor BF; igitur
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citiùs percurruntur HGF quàm BHF, vel BZF, &c. </
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<
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id
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">igitur duæ infe
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riores citiùs, quàm duæ ſuperiores. </
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<
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">Ex his manifeſtum eſt, quænam ſint quaſi termini progreſſionis in aſ
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ſumptis duabus chordis; ſi enim diuidatur arcus BF in 6.arcus æquales,
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BF tardiſſimè, BHF velociſſimè, &c. </
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<
s
id
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">poſt BHF, BGF, tùm ſingulæ ab
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H verſus Z & verſus V reſpondent ſingulæ immediatè AG verſus Z, &
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verſus
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Lemma
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17.
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Si ſint duo pendula inæqualia, tempora deſcenſuum per chordas ſimiles,
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ſunt in ratione ſubduplicat a earumdem; </
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<
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; </
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<
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drans A
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, cuius radius A
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ſit ſubquadruplus radij AB; </
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<
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id
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ſimiles
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, BF; </
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<
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">hæc eſt quadrupla illius; </
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<
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id
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">igitur cum ſit eadem vtriuſ-</
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