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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 351, page id 826603459:0397
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De Recula Aurea.
quarcum, cum decundo in cerrium, s utrobique idem pro
ducum emergat, indicio cA rem probe peractam cAe. (Puta
Ei proposicis 3. 5:: 9. Q. prodeac quartuis  = 15. Facto cx
amine, reperietur 3 n 15 (=- 45) = - 5 n 9. adcogue 3. 5:3
9. 25. Proporcionaleselle, acque opcracionem recte institu
Cam.) Nam (i, quacuor cerminorum, Factum ex mediis aequerur
facto ab excremis, lunc illi guatuor termini proporcionaless
Cujus Demonstracio luperius aliguories adducta cH.
Vel sc. Si terminus quarcus, modo invencus, jam Hat primmue,
acq: operacio inverle insticuacur: Nempe uc qui quarius erac ad
cerciu, ita qui sccundus erat, ad quaesicus Factaq; opcracione pro-
deac qui tuerar primus, recte procestic operacio; sin minus. ali-
cubierracum est. Puca, AI uE PriUS, exPOFICIS 3. 53:9. Q, de
prodeacguartus 9 =- 45. adcogue 3. 5 :: 9. 45. Examen
instiruo invercendo proportionem 45. 9:: 5. . CNam 1
quancicaces sinc proporcionaler, erune e inverle provortiona
les; ut fupra ostensum eAt. )Ec quoniam, c Facta operacione, pro-
dic quaelicus ( = -3. C qui prius tuerac rerminus primus,
jam auem quartus,) parec operacionem recte peractam esse.
Sed aliis hujulmodi muleis modis insticui potcst hoc examen:
Nec tamen canri est uc: plures recenseam.
Aeque hactenus de Aurea Regula quae dicitur Directa, dietum
eAto. De Reeula inversa dicetur C’ apite leguente.
BAP. 37.
AD. XZ a =L1.
Se Aurea Repula reciproca. Luidem a Directa, discrimen. Praxis. e
Demonstratio. Quaestiones per hanc reculam solvendae. De operationum
compendiis eprobationibus. Reductio hujus adreeulam Dire
Et am.
Recula an
 Vrea quae dlcitue sccenta inverta, live Reciproca, et ubi: rea Tnversa-
LLexposiris tribus quantitaribus quaerituriguaria reciproce proporiio-
nalis.
Gnomode a
Distert aucem a Regula Directa, quam Prxccdence capile eetus
L X
poluimnssert.