22

Mulliplicando primam, quarlam, septimam per S'y" — S"y'? secundam, quintam,octauam per y a "— y"ct? terliam, sextam, nonain per ct'S" — a"S\ summan-doque aequationum inde profluenlium, deinceps per [l], [4], [7] 5 [2], [5], [g], [3],[6], [9] denotandarum, ternas ita, vt colligatur summa ex [l], [2], [3] 5 summaex [4], [5], [6] et summa ex [7], [g], [9], denique repetendo insuper bis com-putationem istam adliibitis loco S'y" — S"y'? y'ct" — y"ct -,> aS "— a'S' alteravice multiplicatoribus S"y — Sy"? y"et — ya"? ct"S — ctS" ? ac tertia vice multi-plicatoribus Sy' — S'y, yct' — y'ct, ctS' — ci'S , exorientur nouem aequationes,quas, desijjnata vti supra quantitate ctS'y"-\- Sy’a"-\- ya'S" — yS'a" — cty’S" — Sct'y”per /;, factisque reductionibus debitis, ita exliibcamus

(35)

f k[A] = L (6'y"—6" r ')-\-M'X 7 ' a "~y"u') + M'{a'6"—a6'),k[B] = M'Xß'y"—ß"y') + L' (/<*"—yV)-f M («'6"'— a"ß'),k[C] = M’ (6 "y"—ey) + M (y'a"-y"a) + L"( a 'ß"- a"ß'),k[A'] = L (6 '"y — ßy"} + M'Xy"a—yu") + M'(a"ß — a.ß"),k[B'] = M"(6‘"y — Gy") -f L' (/'’« — y a") -f 31 («"6” — « ß"),k[C’ ] = M' ( 6"y — 6 y") + M (y"a — y a") -f £"(a"ß — « 6”),k[A"]= L ( ßy' — ß'y ) + 31" {y «' — /«) + 31 (« 6' — aß ),k[B"] = 3I"(ßy'-ß'y ) + L'(ya'—y’a )+J I (aß' — a'ß ),k [C"] = 3I’ (ß y' — ß'y )+Jf (yu' — y'a )+ U’(a ß' — aß .).

Per algoritlimum *) eundem, quo ex aequationibus (34) aequationes (35) deriuataesunt, ex ipsis (35) nouem aliae deducuntur, quas eodem iure, quo ex (34) aequa-tiones (32) possunt restitui, in sequentes sex contrabcre licebit

kkA = L (ß'y"—ß"y'f + lJ(y'a''—y"a) 2 -\-E'(aß'

'ß’y

+ 23l(y'a-y"aXaß"-a"ß')+23l'(aß"-a"ß'Xß'y"-ß"y')+23I"(ß'y"-ß"y)(y'a"-y"a),kkA = L [ß"y — ß y"f -f B(y"a — y a") 2 + L"{a"6 — a ß") 2

+ 2 M(y"a-y u){u,"ß-aß")+2M(a"ß-uß"Xß"y - ß y")+23I"(ß" y- ß y")(y"a - y a"),kkA"— L (ßy' — ß'y ) 2 -}- L’(y «' — /« f + L"(a ß' — aß ) 2

+ 2 3l(ya—ya ){aß' — aß )-\-23l'(a 6" - aß ){ßy' —ß'y )-\-23I"(ßy' — ß'y )(ya —y'a ),

*) Toti computo, quippe quem cl. Seeher fusius exposuit in opere Untersuchungen über die Eigen-schaften der positiven ternären quadratischen Formen 1831 (pag. 37 sqq.) hic amplius immorarisuperfluum duximus.

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