Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

VERA CIRCULI dicta quantitas eodem etiam modo componitur ex ul-
timis ejus terminis convergentibus, qui æquales ſunt: ſit ultimus ille terminus x qui multiplicatus in {mae-mbe/ad-bd} & in m efficit xm & {xmae - xmbe/ad - bd}, quorum factorum ſumma nempe
{xmae - xmbe + xmad - xmbd/ad - bd} æquatur {maae - mbae + mbad - mbbd/ad - bd} & æquatio-
ne reducta invenitur x ſeu ſeriei terminatio {aae - bae + bad - bbd/ae - be + ad - bd},
quam invenire oportuit.

Ne minus exercitatis obſcurum videatur hoc problema,
illud in numeris illuſtrabimus: ſit c 7, d 2, e 3, a 28, b 42, erunt ſe-
cundi termini convergentes 32, 36, tertii 33 {1/7}, 34 {2/7}, & ejus ter-
minatio 33 {3/5}.

Neminem moveat, quod (etiamſi a ſit minor quam b )
{ca + bd - ad/c} poſſit eſſe major quam {bc - be + ae/c}, analyticè enim major
à minore poteſt ſubſtrahi, cnjus tamen exemplum non grava-
bimus exhibere, ſit c 7, d 5, e 4, a 28, b 42; erunt ſecundi termini
convergentes 38, 34, & tertii 35 {1/7}, 36 {2/7}, ejuſque terminatio
35 {7/9}.

Animadvertendum eſt hujus problematis ſolutionem eo-
dem modo ſe habere, etiamſi loco a ponatur cyphra ſeu me-
rum nihil, Ex. Gr; ſit c 8, d 3, e 4, a 0, b 24; erunt ſecundi ter-
mini convergentes 9, 12, & tertii 10 {1/8}, 10 {1/2}, & ſeriei termina-
tio 10 {2/7},

Harum etiam ſerierum terminationes poſſunt inveniri ex
Gregorii à S. Vincentio lib. de progreſſ. geometrica, etiamſi
methodo longe ab hac diverſa.

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