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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 265, page id 826603459:0311
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C AP. 30.
De Rarionum Compositione.
id Sdreer  ac EEns Ert rncor, Eco5 av v aranogia deZn. C MM
ires maenitudines (Concinue) proporrionales fuerint, Prima ad terriam,
duplicatam rationem habere dicitur ejus quam habet ad secundam: A1
cum quaruor magnitudines CConcinue) proporrionales fuerint; prima ad
quariam, triplicatam rationem habere dicitur ejus quam habet ad secun
dam: e semper deincep s, uno amplius, quamdiu proporrio exriterit. V exbi
fracia, E quancitas prima A, Ec Pemissis sccundae B, _ HXC Fer-
cix C, acq. haec quarca D, de sic deinceps, (ubiq: scilicer inra-
tione subdupla;) Erie B = 2, C = 2B =- 4 A, I = 2
4B = 8 A, _C. Idcogi ratio A ad B est Z, Ccum enim B
ZR, CTTEA. B3: F, 2.) RacIO A adC (duplicata) 2 = ZX Z, (ma
PrOPter C = 4 A, erit A. C: : T. 4.) Racio A ad D (cri
Plicaca) 3 = 2X EXZ, (namIPrOpTer A = BD, CrIE A . D: 3
1. 8,) EC Hc deinccps.
Acq; hic non incommodum erie notaro; quod Fuclides non
SimNer, relxnur, _C. vel SixnaSioV, rexnastor, _C. dicit, (qui
bus rocibus alibi id innuere Coler quod Lacini rocibus duplum,
triplum, _c. vel etiam duplex, triplex, _c.) Ced sernaciora, rec
naoioran _C. (quod _ perpecuo hoc senlu oblerrac,) quem
aliquacenus imicari conantur incerpreces, dum non tam racio-
nem duplam, triptam, Scc. vel etiam duplicem, triplicem, ec. hoc
Tenu; led pocius, mucara Forma, duplicaram, triplicaram, eC. di
CunC: cum uc direrlcarem Formarum Sonasi O, et SWdnaoicor
apud Puclidem, aliquatenus reteranes cum ut scoroula aliqua-
FenuS CareaTuE.
Verum ee hujusmodi rationes (pura duplicaca, criplicaca, Ratio Sub-
Subduplicaca, ecc.) invicem concinuari possune, unde rario ex duplicalae-
Eslis compolica emersac. Pura rarionis A
2c
B sratio criplicara eR C.
DC hujus aurem Subduplicata cAY BC: erxo racie
ratio Triplicacae. Subduplicata, erie N BC Sic racionis 
ratio TriplicaraeSubduplicaca, erit N Zc. Eodem modo,
cum racionis Z racio duplicoca sic
4-
XX 3
cciplicata R 974 9X X 4 =  n Z n V Y V X
A3 acq; hajuS
racionis Z expolicae, racio duplicacae criplicata, (Hre criplica-
1X
Triphealao.