Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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a
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quatur ipſi R x RM, vel R x QP. </
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<
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">itaque totum ſpatium ADE
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quod ab ejuſmodi ſectoribus minimè differt adæquatur toti R x DK.
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</
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<
s
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">quod erat Propoſitum.</
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<
s
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">XXIII. </
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<
s
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<
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<
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">Fig. 128.</
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ad KT, & </
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<
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">& </
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<
s
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xml:space
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">concipiatur jam curva
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AE naturâ talis, ut ſit DE = √ DK x DH; </
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<
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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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">DF = √ DM x
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DI; </
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<
s
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">ac ità perpetuò; </
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<
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">erit ſpatium ADE quadrati ex DK ſubqua-
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druplum.</
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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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">: DK. </
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<
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<
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">: DKq. </
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<
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<
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xml:space
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">: DKq.
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</
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<
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<
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<
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<
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EX. </
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<
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<
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xml:space
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">: DKq x DE. </
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<
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">DEq x EX. </
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<
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<
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hoc eſt DK PK:</
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<
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xml:space
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<
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">DE x EX. </
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<
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">vel DKq. </
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<
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<
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xml:space
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<
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DE x EX. </
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<
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">unde DK x PK = DE x EX. </
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<
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">Simili ratione DM x MR
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(vel DP x PQ) = DF x FY. </
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<
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">Verúm omnia DK x PK, DP x
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PQ, &</
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<
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">c æquantur ſemiſſi quadrati ex DK; </
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<
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DF x FY, &</
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">c æquantur _duplo ſpatio_ EDA; </
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<
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ſequitur Propoſitum.</
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<
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">Sit curva quæpiam DOK, in qua punctum D; </
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">cuique
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<
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ſubtendatur recta DK; </
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DOK puncto quopiam M, connexâque DM; </
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<
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perpendiculari, & </
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<
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<
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DP = DM, & </
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<
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">ductâ PZ ad DK perpendiculari, ſit PZ = DS;
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</
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<
s
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">erit _ſpatium_ DKI æquale _duplo ſpatio_ DKOD.</
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<
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<
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">Nam recta KP concipiatur indefinitè parva; </
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<
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<
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pendicularis ſit, & </
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<
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<
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arcu MP) rurſus KP. </
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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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">unde KP x
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KI = PM x KD. </
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<
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Q ducatur arcus QN, quem ſecet ſubtenſa DM in R; </
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<
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ſus MR. </
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<
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<
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re PQ x PZ = RN x MD; </
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<
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<
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omnia ſimul rectangula KP x KI, PQ x PZ, &</
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<
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<
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to omnium PM x KD, RN x MD, &</
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<
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<
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duplo ſpatio DKOD æquari.</
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</
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<
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<
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">Iiſdem quoad cætera poſitis atque paratis, ordinatæ PZ jam
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æquales concipiantur ipſis MS reſpectivis; </
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<
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">& </
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<
s
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">ad rectam aſſumptam
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<
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X_k_, diſtantiáſque X_k_, X_m_, X_n_, &</
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<
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">c, æquales ipſis curvæ partibus
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DOK, DOM, DON, &</
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<
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<
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