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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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M A Y E R L A R Y N.
P A RS S E X T A
Varias proportionalitatum proprietates complectitur.
atiseribus continuis, ratio prima ad secundam, ducta in rationem secundae ad
tertiam, idem producit quodratio tertiae ad secundam, ducta in rationem se-
cundae ad primam.
Pas. 932. pr. 127.
Proprietates amcenae serierum quae ab eadem incipiunt. 932. pr. 128. 129. pas. 934.
pr. 132. 133.
Proprietates duarum serierum septem proportionalium quarum quarta sunt aequales.
933. pr. 130. 131.
Propriecates serierum crium continue proportionalium quae ab eadem incipiunt. 935.
pr. 135. 136.
Vira proprietas quatuor serierum continue proporcionalium, quarum binae ab eadem
incipiunt, es rursus ad duas alternatim terminantur.
Tresrationes continué proportionales determinantur.
Inter duas datas rationes media proporeionalis invenitur.
Datis duabus rationibus media proportionalis inuenitur.
936. pr. 137.
936. Pr. 138. 139. 140.
937. pr. 141.
938. pr. 142. 143.
Datis tribus rationibus quarta proportionalis invenitur. 939. pr. 144. Pas 940. pr. 145.
Ostenditur differentia incerrationes continue proportionales es quantitates quae eam-
demrationem continuant.
939. in Schol.
Sitres quantitates sint continie proportionales, rationes primae ad secundam, es secun-
dae ad certiam minima sunt omnium rationum, quae rationem primae ad terciam com-
ponunt.
940. pr. 146.
Determinantur rationes quae duplicatam es quadruplicatam rationem habeant alte-
rus rationis determinata. 940. pr. 147. 2 sque 157. pas. 947. pr. 159. 160. pas. 950.
pr. 165. pac. 952. pr. 169. 170. 171.
Determnanturrationes quae triplicata haheant ratione. 946. pr. 158. pac. 950. pr. 166.
Imo ex series continue proporrionalium datur, in quarationes ad se invicem triplicata,
quadruplicata, quintuplicata ex sic in infinitu ratione habeat. 947. pr. 161. v59 164.
Ostendieur duversitas inter rationes simplices es rationum proporriones. 949 in Schol.
Danturrationes quae quadruplicatam habeant rationem ejus, cujus alia determinata
ratio est criplicata; imo ex quae sit sextuplicata, cuius alia est quintuplicata. 951.
pr. 167, 168.
rlimus terminus exhibetur procressionis rationum quae ad se inuicem semper sunt in
L IB F R N O N V S.
953 pr. 162.
Decylindro, cono. hara, spharoide, (9 vtroque conoidepara
bolico o hyperbolico.
P A R S P R I M A
Vneulaseylindricas, etusque partes, planis ad cylinari a
barallelis, rescissas adcubum reducit.
duplicataratione.
Efinitiones.
957. pr. 12.
Segmeto circuli inscribitur paralleloerammum marus dimidio seementi. 95d pr. 3.
d Xe Hc X 4
Trian-
DRismata diuisa in certa ratione.