Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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DE x HO ergò DH x BF + DH x KO = DE x HO; </
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<
s
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xml:space
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">hoc eſt
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DH x BF + DH x HO - DH x BL = DE x HO; </
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<
s
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xml:space
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nendo igitur eſt DH x HO - DE x HO = DH x BL - DH x
<
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">Fig. 39.</
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BF. </
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<
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">hoc eſt EH x HO = DH x FL; </
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<
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xml:space
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">vel EH x GO + EH x
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HG = DE x FL + EH x FL; </
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<
s
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echoid-s9844
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xml:space
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">quare, demptis æqualibus, eſt EH
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x GO = DE x FL; </
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<
s
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xml:space
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">vel ZG x GO = DE x FL; </
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<
s
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xml:space
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">cum itaque
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DE x FL ſit quid determinatum, conſtat lineam OBO effe hy-
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perbolam, cujus aſymptoti ZR, ZS.</
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<
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<
s
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">V. </
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<
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">Si MO capiatur ad alteras rectæ BC partes, etiam DE.
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</
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<
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">BF ad alteras punctorum D, B partes accipi debent; </
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<
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">uti Schema
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monſtrat; </
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<
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<
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<
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que punctum D ducantur utcunque duæ rectæ MN, XY rectam
<
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<
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">Fig. 41.</
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BQ interſecantes punctis OP (quorum utique ſit O propius ip-
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ſi B) erit MN. </
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<
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<
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<
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xml:space
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cipiatur _hyperbola_ VOB (qualem jam mox attigimus, ſic ut inter-
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ceptæ rationem habeant illam quam MN ad MO) erit igitur
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MN. </
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<
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<
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<
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<
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</
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<
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<
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<
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</
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<
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<
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& </
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<
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interſecant ut vides; </
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NE. </
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<
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gitur ex æquo eſt NE. </
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<
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<
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<
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<
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<
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duci poſſe; </
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<
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">ità ut è D eductarum partes ab illa rectáque BC ad
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interceptas à rectis BA, BC rationem habeant minorem quâpi-
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am datâ.</
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<
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<
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<
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BO tangit; </
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<
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<
s
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">liquet à rectis BQ, BC interceptas ad intercep-
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tas à BC, BA minorem rationem habere, quàm habent inter-
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ceptæ ab hyperbolâ OBO & </
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<
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<
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norem datâ quâpiam.</
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<
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<
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