Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

auctum, ad ſextam partem vltimæ proportionalis propor-
tionis dicti radij ad radium baſis coni, continuatæ in tot
terminos vt numerus eorum excedat numerum conoidis
ternario.

SEd ſupponamus A B C, eſſe conoides paraboli-
cum, & D G H, maximum conum illi inſcri-
ptum, & c. & ratio A D, ad G F, continuetur in tot
terminos vt numerus excedat numerum conoidis ter-
nario, ſitque vltimus terminus A Q. Dico conoides
ad conum eſſe vt pars A D, quæ sè habeat ad dictam
A D, vt vnitas ad numerum conoidis binario au-
ctum, ad ſextam partem A Q. V. g. in primo conoi-
de, nempe in cono, vt tertia pars A D, ad ſextam
partem A Q, quartæ proportionalis. In ſecundo,
vt quarta pars A D, ad ſextam partem A Q, quin-
tæ proportionalis. In cubico, vt quinta pars
A D, ad ſextam partem A Q, ſextæ. Et ſic in in-
finitum.

In cono, patet. Quia ſi A B C, eſt conus, B F,
eſt dupla F D. Cumque pateat ex propoſ. 52, A B C,
eſſe ad G D H, vt cubus D B, ad factum ſub qua-
drato B F, in F D, nempe in medietatem B F; nempe ad medietatem cubi B F; & cum ſit vt cubus
D B, ad medietatem cubi B F, ſic cubus A D, ad
medietatem cubi G F; nempe tertia pars cubi A D,
ad ſextam partem cubi G F: & pariter cum ſit vt cu-
bus A D, ad cubum G F, ſic A D, ad A Q, & vt
tertia pars cubi A D, ad ſextam partem cubi G F,

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer