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# Title: [Observationes Diametrorum Solis Et Lunae Apparentium, Meridianarumque aliquot altitudinum Solis & paucarum fixarum] Observationes Diametrorum Solis Et Lunæ Apparentium, Meridianarúmque aliquot altitudinum Solis & paucarum fixarum (shelfmark Leibn. Marg. 130)
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IB. IFI. De nonnullis numerorum proprietaribus.
lRoBLeMa SECNduM.
Daris in eadem serie aliquot numeris, qui unà eademque ratione continl
procredientes, habeant terrias differentias aequales; quoslibet intermedios
numeros camdem prozressionis rationem servantes invenire.
Dacis numeris eliciendx sune differentixe primx, C primis secunda, rursu squa
Le lccundis cerrix, quae quia aequales lune ex chelis non dacur ulcerius proscedi.
Jam illae differentix incecea dabune differencias incermedias, ( dividaneur pet
numerum partium, quae in incerrallo diridendo requiruneur, hOC Cst, SI aNTUMATUIE
dirilor, qui sic semper un a unieare major numero cerminorum intermediorum, qui
dacis inserendi lune. Ieaque sunc primo dividenda differentix cerrix per astum-
Dcum dirilorem, qua, quia distane cribus seadibus a numeris provolicis, ideo
secundo diridendus est per cumdem divilorem Ouociens primxe dirisionis, e
cerrio Ouoriens secunda divisionis; cerrius aurem Ouoriens dabic differencias cer.
cias incermedias nec crescences, nec decrelcences, qua lunc collocandae in co-
dumna cerriarum differentiorum, non e regione cerminorum. led locis omnibus
intermediis.
Simili modo, quia differentiae secundx duobus distane sradibus a propositis
numeris, ideo duplici diritione ucendum est, ue supra, peract aque secunda divia
sione, Ouoriens dabie differeneias sccundas intermedias crescentes alcendendos
vel descendendo, quacum unaquae que locanda est cresione illius cermini, ad quem
incegra spectas differenria: reliquarum rerd iis inserendarum datur qualibecaddi-
rione, vel substractione differeneia certia intermedix.
Differencix primae incermedix paulo alicer investisaneur, nec camen minori cer-
cieudine, quam reliquae obcinentur: modus illas inquirendi calis est.
Sumantur e columna secundarum differenciarum mediarum, quae jaM nOEa
Habentur, omnes numeri incer dacos existentes cerminos, ita ue primo loco pona-
cur numerus primus (incipiendo a lupeciori, E differentix primx crelcune delcen-
dendo; due concra, incipiendo ab interiori, si differencixe primae crescune alcen-
dendo) sccundo loco aggregacum primi e secundinumeri: cerrio loco aG9rC82-
cum primi secundi de cerrii numeri: Ouarto loco aggresarum primi secundi cerrie
_ quarri numeri: e ica consequenter alin aggresata, si differentia cora in plures
subdiridatur differeneias: Flaec omnia aggresaca in unam conjice summam, quX I
incesra differencia primae aequalis fuerie, minima ex incermediis primis erie O. Si
rero ab eadem defecerit, defectum hunc, per divisorem in aliis differenciis jam
altumpeum, pareire; ericque numerus Quoriens difterencia minima ex incermediis
Primis alsumpei ince ralli: _ sic in reliquis incerrallis minima ex incermediis per-
mis, Cimili operati ne Cognoscetu. Reliquae vero iis incerlerendae BenE majores
acque majores per addirionem differenciarum secundarum mediarum: Ouibus
habicis, si daco numero addatur, vel suberaharue differentia prima media ricina,
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