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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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Numerus aequalis suis divisoribus. DiviCoE namq. var EFoxl ta-
lis, Sive pcresor numeri cujusdam nihit aliud. quam ejusdem.
parcem aliqrotam, imporeat; feri qridem incerdum Polet, ut de
aliqranta divisoris racionem subeac, cum V. 8. 9. Sic per 7. diri-
deridus, exacti camen calis minime.
5. XX.
Forma iphus loco, quae ulcimam veluri Numero Pertecto ra.
tionem superaddi, funsitur aequalitas; relatio nimirrim ipsa hoc
loco inter ipsum Perfectum Mumerum _ partes ejuldem omnes
simul simpeas, gratenus neqi tia illum excedane, neqre ab illo
eriam excedaritur. Dicitur Y. B. A. primus pertectos incer nu
merus, cujus
B. 1.
R. 6. C, 2. 26. F.
D
divisor eA B. secundum axioma s. L. VII. Fucl Unicas omnem n-
morum per Unitates, qua in ipso sunt, h. c. per ipsummet numerum me-
ricur. Meciuntur dein cundem C. _c D. juxta EHCl. Axiom. 8. L.
VII. Si numerus numorum meciatur s ille, per quem metirur, eundem
mecietur per eas, quae in metiente sunt unitates, h. c. per ipsum nume-
rum merientem. Ve adeo omnes partes sinE B. C. D. in unam
collecx summam producenies F. ip Si R. cujus dirilores antea ex-
cicerune, equalem, cum nec L. Superorediatur A. nec rice verla A.
Superxrediatur P. Verus ipitur Perfectus erit Numenus A. juxta defi.
nitionem Fuclidis hactenus proposicatm.
5. X.
Ex qrâ lCer Perteai Numeri natura Patis ininocuerie, clario.
rem camen adHuc, Impertectuum ubi quoq; consideraverimus; e
valuram, eritus ile Philosoptiorum Canon: Oppotita juXta se POMa
masis elACesCUNE; cesatUr. Imperfecti quidem desimtionem
apud Pielidem ipsum deprehendimus nullam, suppectitatur ramen
ab ejusdem Commentatoribus. Nosinaselius Arith. lib. L. Aphor. 20.
hanc habet: Numerus impersectus, Grace a rekis; est, qui suis ipsous
parcibus ost inaequalis. Cum qu a P. Rami loc. cIc. plane coincidit;
imperfectus est, cujus divisores funt inaequales cori. Watur v. 8. 14.
Cujus