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

Nam ob HL. LG: : PD. DH: : PD x DH. DHq; erit HL x
DHq = LG x PD x DH. hoc eſt HL x HOq = DC x Dψ x
DH. Similíque diſcurſu, LK x LYq = CB x CZ x CG. & KI
x KYq = BA x BZ x BF, & c. Verùm HL x HOq + LK x
LYq + KI x KYq, & c. adæquant trientem cubi ex DH; itaque
liquet Propoſitum.

III. Simili ratione conſtabit ſummam AZ x AEq + BZ x BFq
+ CZ x CGq, & c. æquari τῶ{DH_qq_; /4} & eſſe ſummam AZ x
AE cub. + BZ x BE cub. + CZ x CG cub & c. = {DH {5/ }/5}; ac
eodem in continuum tenore.

IV. Exhinc conſectantur haud aſpernanda _Theoremata_: Sit
VDψφ ſpatium quodlibet, cujus axis VD, ut dictum, æquiſectus;
22Fig. 122. ſi concipiantur ſingula ſpatia VAZφ, VBZφ, VCZφ, & c. in
ſuas ordinatas AZ, BZ, CZ, & c. reſpectivè ſingulas duci, quæ pro-
veniet ſumma adæquabitur ipſius ſpatii VDψφ ſemiquadrato.

Nam (utì priùs oſtenſum) figuræ VDψ φ adaptari poteſt ſpatium
VDH; tale nimirum ut ductà quâvis ad curvam VH perpendiculari,
ceu EP, ſit AP ſibireſpondenti applicatæ AZ æqualis; unde 33_Præced_. Lect. X.441 _hujus_.55Fig. 122. ſpatium VAZ φ = {AE_q_/2}; & VBZ φ = {BF_q_; /2} & VCZ φ = {CG_q_/2}
& c. quapropter omnia VAZφ x AZ + VBZφ x BZ + VCZφ
x CZ, & c. æquabuntur omnibus {AE_q_ x AZ + BF_q_ x BZ + CG_q_ x CZ/2}
hoc eſt τῶ {DH_qq_/4 x 2}; hoc eſt τῶ {VDψφ x VDψφ/2. }

663 _hujus_.

V. Quòd ſi ducantur omnia √ VAZφ, √ VBZφ, √ VCZφ,
& c. in ſuas applicatas AZ, BZ, CZ, & c. reſpectivè proveniet ag-
gregatum æquale duabus tertiis radicis quadratæ facti ex ipſo ſpatio
VDψφ cubato (τῶ {2/3} √ VDψφ {3/ })

Nam adaptatâ curvâ VH, eſt √ VAZ φ = AE√ {1/2}; & √ VBZφ
= BF √ {1/2}, & VCZφ = √ CG √ {1/2}, & c. Cùm itaque

Table of contents

Text layer

Text normalization

Search