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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)
# Folio 536, page id 851387705:0556
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DE C Y CL OID F.
serentia iplarum DN, DN (anceccdentis et CoMIS:) IpIa VerO DM
cum sint magnieudines in intinitum decrescentes ditteremtarum lummam aequalem
habenC maXIMA DMI; ETGO LUMMA MMIIITCM LM MaS M e (ejuldem Cubien(a,)
subcensarum in intinuum accrelcentum, xquatur maxima A(Ic ae1.)
Frgo duplum summae ipsarum DM (hoc est duplum diametri) minus summa L a-
cerum DN, aequalis cM. Ergo omnium polysoni Iulerri Lacera deticiunt
a duplo aaHCs ACICCMSM.
BC. Sed AB aequalis ell p aC, eb C iph CD. Ergo omnia Polysoni circun.
dati lacera superant duplum Brametri execllu DC.
centas in MI et C ubique. Ononiam ergo subten (X AD disponuntur in data ra.
tiOnC AD ad AM; elZ AHI, (anceccleis suea) asualis est (consequen.
EI) AD; erso samec asae Co) C
ubique: ergo disterentia iplarum DNI, M N(ejuidem subtenla) aequalis cst dit.
aeguaCuT maxima D ML. Sec quoniam D N minus M N, aequalis est duplo DM
minus DNI, _ Sic ubique; ec quoniam summa omnium DM, cum linc ditterentix
Curlus quoniam AM, AD, A C. Tunc in continua proportione; er3O C. D (an-
recedentis Tubrentae) aequalls cpB C (conlequentis) ee lic ubique. L18O
(eodem modo quo lupia) demoeratus, quod duplum lumma iplarum BC (BoC
est duplum subcensa A B) minus lumma lacerum BD, aequalis sic maximae B Ci
erxo omnia Polysoni circunaa lalela t a Miplo subtena AB, defectu
Addatur demum detectus, et excestus quibus, hinc inde polysona ditferunt d
duplo diametri; erso CN est urrisque disterencia; et aequalis quidem ponitur
iph X. Ergo semicirculo A D D polysonum serratum insercum ctt, et Cimile cAt cir-
cundatum, hoc majus, illud minus duplo diametri, ucriusque aurem ditterenua a
qualis eAt datae magnicudini X. Ouod erat Faciendum. 1
Sehosium.  a
Dato circuli sexmento quovis A s D, eodem prortus modo polysonum serraculle
inseritur et circundacur; et demonstracur lacera inserri deticere d duplo balis leg.
menti AD, delectu DM; Lacera rero circundati excedere duplum ejuldem, ex
cettu D C; uriusque rero disterentiam esse CM; qua cum minor lc, quam
CM, minos est quam X.
11t1
 eit
mne ed t  a Lemma.