Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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xml:space
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">III. </
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</
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<
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xml:space
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">_ſpatium_ AC PX hoc eſt _Summa ſecamium ad arcum_ AM pertinen-
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tium, & </
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<
s
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xml:space
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">ad CB applicatarum) æquatur _duplo ſectori_ ACM.</
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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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">Nam _ſpatium_ AF MX _segmenti_ AFM _duplum_ eſt; </
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<
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xml:space
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">& </
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<
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xml:space
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<
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note-0289-01
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xml:space
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">Fig. 166.</
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XI.</
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_angulum_ FC PM _Trianguli_ FCM. </
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<
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xml:space
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">ergo _totum ſpatium_ ACPX
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totius _ſectoris_ ACM duplum eſt.</
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<
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<
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<
s
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">Etiam hoc è 16. </
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<
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<
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<
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xml:space
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<
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_ſpatium_ CVP (hoc eſt _ſumma tangentium ad arcum_ AM _pertinen-_
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<
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xml:space
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">Fig. 166.</
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_tium_, & </
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<
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xml:space
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">ad rectam CB applicatarum) æquale _ſemiſſi quadrati ex_
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_ſubtenſa_ AM.</
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</
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<
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<
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xml:space
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<
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<
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xml:space
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">ductâ QO ad CE parallelâ (quæ
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_byperbolæ_ LE occurrat in O) erit _ſpatium byperbolicum_ PL OQ du-
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ctum in _radium_ CB (ſeu _cylindricum ad_ bafin PLOQ, altitudine
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BC (duplum _ſummæ quadratorum_ ex rectis CS, ſeu PX ad _arcum_
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<
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xml:space
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">Fig. 166.</
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AM pertinentibus, & </
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<
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</
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<
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<
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<
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- CP. </
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tiones adjungendo) eſt PL + QO. </
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BC - CP + BC. </
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<
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2 BCq. </
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<
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<
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eſt PXq. </
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<
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<
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BCq:</
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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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xml:space
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QOxBC.</
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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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">quare PL x BC + QO x BC = 2PXq. </
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itaque BC in omnes PL + QO ducta adæquat omnia totidem PXq. </
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unde conſtat Propoſitum.</
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<
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<
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<
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ad αβ applicatarum) æquatur _ſubduple ſpatio byperbolico_ PLOQ.</
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<
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<
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ducatúrque recta NR ad AC parallela. </
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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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xml:space
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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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MN x PX x CA = MR x PXq. </
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<
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PXq. </
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<
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">atqui (ex præcedente) omnium MR x PXq ſumma ſpatii
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PL OQ in CA ducti ſubdupla eſt. </
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<
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in CA ducta eidem ſubduplo æquantur. </
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<
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