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

[91.] Series nona.

Page: 333 (140)

[92.] Not.

Page: 333 (140)

[93.] Series decima.

Page: 334 (141)

[94.] Series undecima.

Page: 335 (142)

[95.] Not.

Page: 335 (142)

[96.] Series duodecima

Page: 336 (143)

[97.] Series decima tertia

Page: 336 (143)

[98.] Not.

Page: 336 (143)

[99.] Laus DEOO ptimo Maximo. FINIS.

Page: 340 (147)

[100.] ERRATA

Page: 341

[101.] Addenda Lectionibus Geometricis.

[102.] _Probl_. I.

[103.] _Probl_. II.

[104.] _Probl_. III.

[105.] Addenda Lectionibus Geometricis.

[106.] _Theor_. I.

[107.] _Theor_. II.

[108.] _Theor_. III.

[109.] _Theor_. IV.

[110.] _Theor_. V.

[111.] _Theor_. VI.

[112.] FINIS.

324131

Lect. XIII.

Æ _Quationum_ naturam è terminorum _analogia_ expoſuit _Vieta_;
illam ex eorum in ſe ductu dilucidiùs explicuit _Carteſius_. Eam
ego jam è linearum ſingulis appropriatarum deſcriptione conabor ali-
quatenus enucleatam dare; qui ſanè modus rem præſertim elucidare
videtur, ac ob oculos ponere, agedum.

_Notetur_, In ſequentibus perpetim ad eaſdem ſeries redigi æquatio-
nes, quæ _coefficientes_ habent eaſdem.

Æquationum Series prima.

_a_ + _b_ = _n_.

_aa_ + _ba_ = _nn_.

_a_3 + _baa_ = _n_3.

_a_4 + _ba_3 = _n_4, & c.

Sumatur recta BA æqualis coefficienti _b_, & hæc verſus H indefini-
11Fig. 206. tè protendatur; ſint anguli RAH, SBH ſemirecti, ſintque lineæ
ALL, AMM, ANN tales, ut rectâ GK ductâ ad AH utcunque
perpendiculari (quæ dictas lineas ordine ſecet punctis L, M, N; re-
ctaſque BS, AR punctis K, Z) ſit inter GZ, GK _media_ GL , 22Vid. pag. 90. _media_ GM, _trimedia_ GM; hæ lineæ propoſitarum æquationum
naturæ explicandæ inſervient. Nam ſi AG (vel GZ) dicatur _a_; erit
BG (vel GK) = _b_ + _a_; atque GLq = _aa_ + _ba_; & GM cub.
= _a_3 + _baa_; & GN_qq_ = _a_4 + _ba_3.

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