Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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eodem ſemper ordine media inter QL, QI (eodem inquam illo, quo
<
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PF media fuerat inter PG, PE) : </
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<
s
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xml:space
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">dico lineas FBF, KEK analo-
<
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note-0236-01
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">Fig. 65.</
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gas eſſe; </
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<
s
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echoid-s10694
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xml:space
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">hoc eſt ordinatas (quales QR, QK) eandem perpetuò in-
<
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ter ſe rationem habere; </
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<
s
xml:id
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echoid-s10695
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xml:space
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">eandem ſcilicet illi quam habet PF ad PE.</
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<
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</
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<
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<
s
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xml:space
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">Hoc è Lemmate proximè præmiſſo conſectatur, utì patebit, ad ſub-
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jectum Schema mentem advertendo.</
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<
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</
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<
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<
s
xml:id
="
echoid-s10699
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xml:space
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">QS* QR* QI. </
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<
s
xml:id
="
echoid-s10700
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xml:space
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">\\ QL* QK* QI. </
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>
<
s
xml:id
="
echoid-s10701
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xml:space
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">\\ PG* PF* PE. </
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<
s
xml:id
="
echoid-s10702
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xml:space
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">\\ PE* PE* PE.</
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<
s
xml:id
="
echoid-s10703
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xml:space
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">} Sunt {.</
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<
s
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="
echoid-s10704
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xml:space
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">./.</
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<
s
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xml:space
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">.}. </
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<
s
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xml:space
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">unde QR. </
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<
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="
echoid-s10707
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xml:space
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">QK:</
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<
s
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="
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xml:space
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">:
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PF. </
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<
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xml:space
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">PE.</
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<
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="
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</
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<
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xml:space
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">Not. </
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xml:space
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">Pro lineis rectis AB, HE, CD ſubſtitui poſſent quælibet,
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etiam curvæ, parallelæ.</
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<
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xml:space
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">VIII. </
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">Sint rurſus, in A concurrentes duæ rectæ AB, AD, rectaq;
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</
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xlink:label
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note-0236-02
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xml:space
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">Fig. 66.</
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BD poſitione data; </
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<
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xml:space
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">item duæ curvæ EBE, FBF ſic relatæ, ut ductâ
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utcunque PG ad DB parallelâ, ſit ſemper PF eodem ordine media
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proportionalis inter PG, PE; </
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<
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xml:space
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">tum connexâ AE, ſit alia cu
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rva
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KEK talis, ut ductâ quâpiam rectâ QLI ad DB parallelâ ſit ſemper
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QK eodem ordine media inter QL, QI, quo fuit PF inter P G, PE;
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</
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<
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xml:space
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">erit rurſus linea FEF ipſi KBK analoga; </
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<
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PF. </
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<
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">PE.</
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</
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<
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<
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xml:space
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">Nam QS* QR* QI. </
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xml:space
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">\\ QL* QK* QI. </
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<
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xml:space
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">\\ PG* PF* PE. </
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xml:space
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">\\ PE* PE* PE.</
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<
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xml:space
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<
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<
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">PE.</
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<
s
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">}ergò QR.
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</
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<
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<
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PF. </
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<
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">PE.</
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<
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</
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<
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<
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xml:space
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">Pro rectis AB, AH, AD ſubſtitui poſſent tres quævis lineæ
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analogæ.</
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<
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<
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">aliæque duæ curvæ
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EBE, FBF tales, utper D ductâ quâcunque rectâ DG, ſit perpe-
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<
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position
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xlink:label
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tuò DF eodem ordine media propor
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ionalis inter DG, DE; </
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<
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centro D per E deſ@ribatur circulus H E; </
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<
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xml:space
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talis, ut ductâ per D quâpiam (ad circulum HE) rectâ DL, ſit </
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