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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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Cap. XXXVIII.
Demon- Demonttratio praxeos haec erir. Ouoniam, ex hypocheti, ponitur rectangu
srasio. lum primi in secundum, aquale rectangulo cerrii in quarcum; hoc est AxB =
axB, Sre AB = a B; erie urinque diridendo per a = =B.
guaestio. Quactiones per hanc regulam Solvendx, ab iis gux Solvendx suNE Per PERCC.
nes per dencem; sic distinguant TITOneS. Si, ex natura quaestionis, quo major lic ter-
hancre- minus terrius, eo major requiratur quarcus; regulae directx opus elt: Sin, quo
culam
MajOT TETTIIS EO MINOE REGUIVIEE quaEEUS, Sire quO MINOE TEETUS, eO major quar-
solvenda. rs; inversae regulae opus exit.
Verbi oratia; Si quis x2 boris conficiat milliaria 20;
12, 20:: 6. =20. idem horis 6, quot conficiet. Ouoniam, Hic maniteltum
12) F20(20 =O
est, longiori tempore plura conticienda milliaria; quo
major elt terminus cerrius (numerus horarum) eo na-
jor crit e quartus, numerus milliarium quaelits. FF
Propterea, per auream regulam directam, inrenitur terminus quartus quaelicus, 10.
12, 20:6. 9= 40
6) 240 (40 =0.
Contra vero; Opus a viris 12, diebus 20 perficiendum:
Si acerediantur viri 6, quot illi diebus boc persiient 
Ouoniam liquer, ex qualtionis natura, pauctores viros
nonnili pluribus dicbus idem opus contecturos; adeoque
quo minor est cerminus tertius, (rirorum numerus;) co
major Fucurus SIc cerminuS quartUS, (numerus dierum requisituS;) Per regulan
icaque invertam, quarendus CAE FERMINUS QuarEUIS, 40.
Eodem modo: Sit tapeti lato pedes 9, loneo 20, ob ducendus pannus vilior, qui
9. 20: 3. 9= 60.
3) 180(60=0.
tocum reeat, latus pedes 3; quaeritur quot pedes loneus esse
debeat, ut necotio sufficiat? Duoniam hic manilestum lic,
quo minorem habeat lacitudinem pannus hic, eo majorem
requiri lonsicudinem, qua lacicudinis defectus luppleacur:
per regulam inverlam, reperietur lonsicudo quaelica, De.
dum 60. Atque in aliis pariter.
Ded. Dux aurem operationum compendia, de Regula directa, in Capite praeccdente
rationum ostendimus, (sive quoad ordinem operarionum perticiendarum, lire etiam ter-
comper minorum praecedaneam reductionem,) etiam hic, mutatis mucandis, locum ha-
BenE. Nec opus est ut ea ligillatim hic repetam; sed porius ut lectoris lagacitati
comous Permittatur, quxe illie dicta sune hrie aptare. Ouod d de Probationibus illic tra-
ditis, incellectum relim; quas, qui canti esse puter, etiam huc, mutatis mutandis,
non disticulter cransterat
Reductio Norandum denique, Proportionem Reciprocam in Directam conversum iris si
lae ad
qui in reciproca est terminus certius, statuatur in directa primus. Nempe si lit
In proportione reciproca 9. 20: 3. 9 = 60.
Eric in proportione directa 3. 20: : 9.  =60.
Reciproce.
9. 20: 3. 9 = 60.
3) 280(60 =0.
Directe.
3. 20::9. =60.
3) 180(60 =9.
Acque hactenus de Aurea Regula simplici; sire Regula Trium; cam directa
quam Reciproca. Sequitur ut de Mulciplici rerba laciam; ubi nempe plures
quam tres occurrum termini, iplaque Proportionis Regula Eapius reperenda. FA-
que ea, vel, qua rocatur Aurea Recula composita; ret quae Resula Societatis
dicitur. De quibus in sequentibus Capicibus dicetur.
DE REOULA
204
diis; e
proba
Bujus Re
directam.