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# Title: Disputatione Mathematica Numerum Perfectum Perfectissimi Favente Gratia Nec non Benevole Inclyta Facultate Philosophica Indulgente A.C. MDCLXXVIII. ad d. XXI. Sept. P.P. M. Johann Wilhelmus Pauli, Lipsiens. Philiater, Responsuro Johann-Luca Rhiem/ Coburgo-Franco, Medicinae Studioso (shelfmarks Leibn. Marg. 88, Stück 2; Leibn. Marg. 88)
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quoque perfecti, ne senario quidem excepco, in sud serio Forene
conspicui.
5. XIX.
Perfecti tandem Numeri Adiundis, quae non propria qui
dem. sed Pallem communia, pariter concemplanda rectant, non
immerito eorum iplorum accensetur paucitas, quae, cestante §. 17.
tanta est, ut 10, inter _ 100, 100. X 1000. unus unice existat, nec,
obterrance quogre Ramo loc. alles. Singulis gractibus plures uno
perfecti, imo Bracibus nonnullis nuIII inVeNIANCUT. AC OIMMINO
ab unitate ad 140000000000000000. ulqre plures gram septem
Pertecti numerari negreune Numeri, secus, ac seneire videtur Dn.
Clarsdorserns; qui citance Scranchio de Numer. Doctr. Aph. 16. ab
Wnicatensquead 40000000. tancum, septem dari obserravic: (sed
a duobus perfectis spuriis, nempe, 130815. _ 2096128. abundanci-
bus pocius, numeris circumvencus. Dein omnium Pertectorum
Numerorum noca inicialis auc senarius est, aut octonarius; ica qui-
dem ut alternacim modo, modo secus se inricem segrancur.
5. XX.
Accedic denique omnem Numerum Pertectum esse SimuI
Numerum Frisonalem; cujns Radix est ipse Primus, a cujus cum
combinaco seu ancecedence ancea mulciplicatione fuit progenitus.
Sumamus probandi eaula perlectum: 1374 38691328 qui num Tri
eonus tuerie, Radix Trigonalis manifectum reddet; hac uc inve-
niatur, ex dupio ipso numero proposico RadiX (J. extrahenda eAt
cui Residuum ubi tuerie aegrale, iptam Radicem esse vere Triso:
nolem, evidencissime patebit. Sit