Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

DK eodem ordine media inter DL, DI, quo fuerat DF inter DG,
DE; erunt curvæ FBF, KBK analogæ, ſeu perpetuò DR. DK : :
DF. DE.

32.1.

Fig. 67.

Nam rurſus DS. * DR. * DI. \\ DL. * DK. * DI. \\ DG. *DF. * DE \\ DE. * DE. * DE. } ſunt {. ./. .}.

unde DR. DK : :
DF. DE.

Rurſus, pro circulis aliæ lineæ parallelæ, vel analogæ ſubſtitui
poſſent.

X. Sint denuò duæ lineæ quævis A GBG, EBE; & altera
FBF ſic ad iſtas relata, ut ductâ utcunque à deſignaro puncto D recta
DG, ſit perpetuò DF eodem ordine media proportionalis inter DG,
DE; tum adſumatur linea HEL lineæ AGB analoga (ſeu talis, ut
per D utcunque ductâ DLS, ſint perpetuò DS, DL in eadem ratio-
ne) ſit denuò linea KEK talis, ut ductâ utcunque DL, ſit perpetuò
DK eodem ordine media inter DL, DI, quo priùs DF inter DG,
DE; erit itidem linea FBF lineæ K EK analoga.

Rurſus enim DS. * DR* DI. \\ DL. * DK* DI. \\ DG. * DF* DE \\ DE. * DE* DE} ſunt {. ./. .}; }Et tam primi quàm ulti-
mi quatuor termini
ſunt proportionales. Unde liquet Propoſi-
tum.

XI. Sit Arithmeticè proportionalium Series A. B. C. D. E. F; in
qua ſumptis quibuſcunque duobus terminis D, F; ſit terminorum à
primo A (excluſivè) ad ipſum D numerus, N; & terminorum ab A
(itidem excluſivè) ad F, ſit numerus M; erit A -: D. A -: F : :
N. M.

Nam eſto differentia communis, X. eſt ergò D = A ± NX. & F = A ± MX. quare A -: D = NX. & A -: F = MX. unde A -: D. A -: F : : ( NX. MX: :) N. M.

XII. Hinc, ſi duæ fuerint ejuſmodi ſeries; & in utraque ſumantur

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