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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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scere hauet licent, sevant id quidem aligromodo Repulae apud
Stranchium cum generales ex Euclide Apt. 57. tum Speciales ABh.
58. de Numor. Doctrina, quae videri ibidem queune, citaex; peni
cus camen haud colUnE.
S. XIII.
Specialius est, quoad Primos hoc in negotio Numeros,
Obserratum: grod omnis Primus (qui Scilicet ex mumerorum
duplae progrestionis collectione resulcat) sit ABBrePatuM ex
cerminorum ab unitate in dupla proportiono deinceps posito-
rum numero, E is Primus existat, emersens; adeoqre, grodcun
que AGCresatum ex numero cerminorum Compolito emergie,,
nOn EF NumeruS PrimuS. Sic postquam hi numeri 1. 24. 8. 16.
32. 64. 128. 256. in unam collecti fuerine summam, oppido colsi-
Bitur Agcresatum hoc: su. gria exnovemterminis, ceu Numero
Composico. fuit progenicum, Cimilicer Numerum esse Compoli-
cum ac menturam, cum novenarium meciatur cernarius, aeno-
Ecere sextenarium, ipsum nimirum Asgresacum erium termino-
rum L. 2. 4. Nocandum camen, in reciproconhaud valere sentu,
nec, omne Agresatum ex numero terminorum Primo reultans
esle Numerum Primum, concludendum esse: fiori namquo inter-
dum, qramvis admodum raro, solet, ut ipsum ejusmodi Ag-
cresatum Compolitus sic Numerus atque ab alio, numero scili-
cet terminorum duplaco ac unitate aucto, aliquando mensuretur,
secus ac vere Primorum natura requirit. Sic propositus 2047.
Acoresatum eqridem undecim terminorum, qui NumeruS PRIIUS
est, deprehenditur; ast, cum duplacus undenarius addica sirnul
unitate, nempe 23 ejus sit mensura, Primis haud accensendus:
Qvod idem in 8; 88607. _ 2199023255551. Aseresatis 23. d 4 r. termi-
norum (quorum illud 47. hoc vero 83. meticur) videre est.
5. XIV.
Modum Pertectos generandi Numeros talem nobis extibee
Enclides 36. Prop. IX. Si ab unicate quoteunque numeri deinceps expo-
nancur in dupla proporiione; quoad totus composius fac primus; s
rotus hic in uleimum mulciplicatus faciat aliquem; Faltus erit perse-
Ao. SIEC. B. ab umIEatE A. qrorcunqrenumeri B. C. D. F. P. Hd
et a