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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 359, page id 826603459:0405
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C AP. 39.
De Recula Aurea Compr Aia.
Exlempli graria. Si 36 = a, librae panis, sufficiant militibus
B = B, in dies 6 = C; librae 180 = a, mililibus 9 =-B, in
quor dies sufficient? puca in dies y.
EA quidem hic analogiarum alcera directa, nempe Si librae
36 = R, sufficiant in dies 6  C: librae 280, susficient in dies
quor: Duca 4  30. Ac altera est Reciproca, nempe Si militi-
bus 6 = B sufficiant in dies 30 =9; milicibus 9 =B, sufficient
in dies quot: Cerre non nili in dies pauciores, propter plures mi
lices, nempe, in dies 20. Adcoque illic, regula directa cA
adhibenda; hic, recipPTOCA.
Nepe 36. 6: :180 36. 6:: 180. 9 = ,5X 180 =30.
3
: 9. Q. 3. 4: 9. Q = 3X9= 3X30 = 20
Icem A. C:: a
B: B. V.
A. C:: a. 9.
B. 9: B. V.
B
Adeogue q = A C. FFY L B + 4 = BA C.
Si aurem libeat pro duabus his operationibus, unam compo.
sicam substicuere: Factus ex duabus divisoribus (puca cermino
primoanalogix directae, de terrio reciproca) erit composius di
visor; (adeoque in analoera directa, terminus Primus:) factusque ex
multiplicatoribus, composius mulriplicator: CAdeoque, in eadem ana-
locia terminus verrius, in secundum ducendus.) Hloc eH, (in expolica
a
B
quaettione,) AB, C:: a B. 7 = AB C. ucprius.
Ba
lB
v i DBC
Ec quiem uose e altatla Coone, e Repula Peru
Directae icem, Ere reciprocae, id universalicer dicendum: FX omni. rats.
bus Divisoribus (nempe cerminis primis analogiarum directari, e
tertiis reciprocarum,) consinue ductis, fiat Divisor; ex religuis om-
mibM