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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 295, page id 826603459:0341
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C. BP. 33.
De Proeressione Ceometrica.
28 In quancieatum continue proportionalium quorcunque
prosrestione; Ouod tic ex duccu cermini primi in ulcimum, 2-
quacur Facto ex muruo ductu duorum quorumvis terminorum
ab extremis aequalicer uorinq; remocorum. Vel, Rectangulum
termediis ab excremis verinqi xequalicer dictancibus. CIncelliee
quorum unustoc praecile gradibus ab uno excremo, quoc resi.
quus a reliquo, dictat.) Cum enim sic cerminorum alcer ARd
perpr. 2. alcer Rd) V, per pr. 5. Sieque distancia D urrobique
eadem; eric rectansulum Rd) V X ARd = VA = H - a0-
BB = c7 = d st _C. Acque hac Cunc illa rectangula quorum
omnium asxregatum Symbolo Z designacum volumus; Pu
quae simpliciter Rechaneutorum aecrepatum deinceps appellabin
InUS.
20 Sin terminus omnium medius ab VETOQ; CXETCIO XqUA-
licer distet, (quod cum continget quum cerminorum numerus
estimpar;) Ouadiatum medii aeguatur extremorum rectan-
EulO. Nam PEOPECE Rd) V =N ==ARd, (_ distanriam D
utrobiq; aqualem,) erit Rd; V X ARd = M XN - H9
20 Similicer, In quacuor cerminis ucur disconcinue propor.
rionalibus, Rectangulum excremorum aequatur rectangulo me.
diorum. PACA A. M: : N. V. Cum enim Cpropcer aequalem
utrobigue rationem) lIC AR =M, _NR = V, adeoque R)
V = N; CFIENXM = K) VXAR = VA. AIque hinc segNICUE
Rexula quae dicitur aurea, sire Recula Trium. Nempe
3r Ouacuor erso provorcionali.
am, dacis cribus quibuslibec, datur d Datis. DaTUIE.
religuus. Cum enim HC, Der PERCCd. A) M XN CV
A = V = MXNY, criC (XQUaLIEEF vETIM- V, MXN, (A
MN MN N A XV CN
que dividendo) V = a a
1
N
a
N) A = VC
N = M aEAq; haec Rexula intinici peneutlis Per
eoram Machelin, ideoque merico Aurea dicta
22 Excribus autem concinue proportionalibus, Rectangu-
dum extremorum a quatur quadraco medii. PaTA A. NI. V 
Nam, propcer aequalem urrobigie rationem, est A R  M,. de
1L