## 77._Notetur autem_,

1. Ducta AD ad BH perpendiculari, ſi in hac capiatur AE = _n_; ducatúrque EF ad AH parallela; hujus cum lineis expoſitis interſe-
ctiones æquationum propoſitarum radices exhibebunt reſpectivè; erit
utique EK, vel EI, vel EM, vel EN æqualis ipſi _a_; hoc eſt ipſis AG, concipiendo à ſingula interſectione deduci ad AH
perpendiculares, quæ puncta G determinet.

### 77.1.

Fig. 206.

2. Quò punctum G magîs à termino A removetur (& quidem poteſt
GA deſumi quavis deſignatâ major) eò ordinatæ GK, GL, GM, GN
magìs increſcunt; adeo ut quantacunque ponatur AE, parallela EF
curvis occurſura ſit; & proinde ſemper habetur vera radix iſtarum
æquationum cuilibet conveniens; & ea tantùm una, quoniam EF
curvas iſtas unico puncto interſecat.

3. _Curva_ ALL eſt _hyperbola æquilatera_, cujus _axis_ AB, reliquæ
AMM, ANN ſunt _hiperboliformes_.

4. Si AO ſit {1/2} AB; & AP = {1/3} AB, & AQ = {1/4} AB, du-
cantúrque OT, PV, QX ad BS parallelæ, erunt hæ curvarum ALL,
AMM, ANN _aſymptoti_.

5. Hinc conſtat in ſecundo gradu fore _a_ & gt; _n_ - {_b_/2}; in tertio _a_& gt; _n_ - {_b_/3}; in quarto _a_& gt; _n_ - {_b_/4}; quæ tamen inæqualitates, ſi AE
benemagna ſit, exiguæ erunt.

6. Æquationibus iſtis nulla competit _maxima, vel minima_.

## 78.Series ſecunda.

_a_ - _b_ = _n_.

_aa_ - _ba_ = _nn_.

_a_ 3 - _baa_ = _n_ 3 .

_a_ 4 - _ba_ 3 = _n_ 4 , & c.

Sit rurſus AB = _b_; & indefinitè protrahatur AB verſus I, & ſint anguli RAI, SBI ſemirecti; tum concipiantur curvæ BLL,
BMM, BNN tales, ut ſi utcunque ducatur GZ ad AI perpendicu-
laris (dictas lineas ſecans, utì cernis, punctis K, L, M, N, Z) ſit inter

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