Fvndamenta Nova Investigationis Orbitae Verae Qvam Lvna Perlvstrat, Qvibvs Annexa Est Solvtio Problematis Qvatvor Corporvm Breviter Exposita

Cover Fvndamenta Nova Investigationis Orbitae Verae Qvam Lvna Perlvstrat, Qvibvs Annexa Est Solvtio Problematis Qvatvor Corporvm Breviter Exposita

Peter Andreas Hansen

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Secundum hypothesin statutam ponere licet — iGz=2Fcos(at4-|5) , |^^H=2;W^8in (a^-f^) u)ide 24 Digitized by Google 186 r = A — I e€? 4- 2 Slr^ «(«> cos [xy4- «f-f fl ubi in SDinmatione efiam valor x= o excludendus est, quia termini omnes, i(i quibus x = e est, extra summationis signum appositi sunt, et ubi *(x) pj^4.fr»iiw Positis deinceps in hac aequatione et x-|-l, et — «, et — x — 1 ioco x, elicitur „(-x) _ yj^_jf^^m) de a' .(-'«-I) r^t!l_fF(^+i)B(x4..) ubi F et n^ ubique eaedem quantitates s...unt, quoniam e tc non pendent.
Eliminatis (jleinceps V ei fV ope primae et tertiae harum quatuor aequa- tioQum, nanciscimur F = W = a(x) _ ^(-x) 2xjR(;) q«ae in seeunda et quarta aequatione substitutae subministrant ubi X absolute, hoc est sine respectu signi sui algebraici sumenda est, et ubi M ^ | L de J (x-4-1) JJ(x-+i) K^') x-S»» r =i- Habemus igitor hoc IV de J (x-»-l) J2(''+'>l ^de J *m Digitized by Google 18?
Theorema.
Quotiea F est functid huius farmae r — Zr 4- G ^ cos 9 4- H ^ sin 9 ubi Ly G atque H indolis supra designatae sunt: ope aequationum (^)^ quarum prior ad terminos ipsius JT, m quihus % positiuus^ pBsterior vero ad terminos^ m quibus x negatitms, adhibenda esty termini, in quibus x sine respectu signi sui algebraici maior est quam 1 , ex iis^ m quibus x=l rfx= — 1, faciWma opera computantur, unde in evolutione ipsius r ceteroquin instituenda non nisi ad terminos, in quibus x = o , % = 1 e* X = — 1 est^ respicere opus est Facile quoque reperitur theorema idem locum habere, quoties G for- mae Vsin J^at^P) et H formae W cos (a* + ^) sunt.

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