Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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24855 item PO ad TE parallela. Eſtque EFq = EOq (CPq) + OFq
+ 2 EO x OF (+ 2 CP x OF). Verùm ob CP. CA : : OP.
OF : : CE. OF; eſt CP x OF = CA x CE; ergò EFq =
CPq + OFq + 2 CA x CE. item eſt AEq = CEq +
CAq - 2 CA x CE; quapropter eſt EFq + AEq = CPq +
CAq + OFq + CEq. hoc eſt EGq = (APq + PFq = )
CVq + PFq. vel EGq - PFq = CVq. Verùm eſt CE.
(PO). PF : : CP. AP : : CP. CV; unde EGq - {CVq/CPq} CEq
= CVq; adeóque linea GVG eſt _hyperbola_, cujus centrum C; ſe-
miaxes CV, CP.

Not. Ductà rectâ FQ ad TH perpendiculari, ſumptáque QR =
AE; & connexâ GR; erit GR _hyperbolæ_ VGG perpendicularis;
mihi præſta sîs ſidem; aut ipſe rem ad Calculum exige; eò verba
non proſundam.

XXVI. Poſitione datæ ſint rectæ AC, BD (ſe interſecantes in X)
11Fig. 59. qnas decuſſet recta A B; tum ductâ utcunque rectâ PKL ad AB
parallelâ, (quæ rectas AC, BD ſecet punctis P, K) ſit PL æqua-
lis ipſi BK; erit linea ALL recta.

Nam, (ductâ XQ ad BA parallelâ, eſt AQ. AP : : (BX.
BK : : ) QX. PL: ergo linea ALL eſt recta.

XXVII. Poſitione data ſit recta A X, & punctum D; neque non
linea DNN talis; ut per D ductâ quâcunque rectâ MN (quæ re-
22Fig. 60. ctam AX ſecet in M, & lineam DNN in N) ſit perpetim rectangu-
lum ex DM, DN æquale dato (puta quadrato ex Z); erit linea
DNN circularis.

Nam ducatur DB ad AX perpendicularis; ſitque DB. Z : : Z.
DE; & connectatur NE; Eſt jam DM x DN = Zq = DB x
DE; quare DM. DB : : DE. DN. ergò triangula DBM, DNE
ſimilia ſunt; quapropter angulus DNE rectus eſt; itaque linea DNN
eſt circularis: (ad circulum pertinens, _c@jus Diameter_ DE).

Vides nedum rectam & _hyperbolam_; ſed & ſuo modo rectam ac
_circulum_ ſibi lineas eſſe reciprocas. Verùm hîc, etſi præludiis no-
ſtris nondum abſolutis, paulùm ſubſiſtamus.

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