Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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<
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<
s
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echoid-s1929
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xml:space
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">Datæ portioni circuli, vel Ellipſis, per eius verticem MAXI-
<
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MAM Parabolæ portionem inſcribere; </
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>
<
s
xml:id
="
echoid-s1930
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xml:space
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">& </
s
>
<
s
xml:id
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echoid-s1931
"
xml:space
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">è contra.</
s
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<
s
xml:id
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echoid-s1932
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xml:space
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"/>
</
p
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<
p
>
<
s
xml:id
="
echoid-s1933
"
xml:space
="
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">Datæ portioni Parabolæ per eius verticem, cum dato recto,
<
lb
/>
quod excedat rectum datæ Parabolæ, vel cum dato tranſuerſo,
<
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/>
quod maius ſit diametro datæ portionis MINIMAM Ellipſis por-
<
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/>
tionem circumſcribere.</
s
>
<
s
xml:id
="
echoid-s1934
"
xml:space
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preserve
"/>
</
p
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<
p
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<
s
xml:id
="
echoid-s1935
"
xml:space
="
preserve
">SIt data circuli, aut Ellipſis portio ABC, cuius diameter ſit BE, baſis AC.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1936
"
xml:space
="
preserve
">Oporter per eius verticem B, _MAXIMAM_ Parabolæ portionem inſcri-
<
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bere.</
s
>
<
s
xml:id
="
echoid-s1937
"
xml:space
="
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"/>
</
p
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<
p
>
<
s
xml:id
="
echoid-s1938
"
xml:space
="
preserve
">Sit BF tranſuerſum latus dati circuli, vel
<
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fig-0080-01
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fig-0080-01a
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number
="
50
">
<
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file
="
0080-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0080-01
"/>
</
figure
>
Ellipſis, BG rectum, & </
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<
s
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="
echoid-s1939
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">FG regula, cui pro-
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ducta AE occurrat in H, & </
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>
<
s
xml:id
="
echoid-s1940
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xml:space
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">per H agatur LHI
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ipſi BF ęquidiſtans, & </
s
>
<
s
xml:id
="
echoid-s1941
"
xml:space
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">cum recto BI, per ver-
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ticem B adſcribatur portioni ADBC
<
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a
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xlink:label
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note-0080-01
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xlink:href
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note-0080-01a
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xml:space
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">5. huius.</
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bole AMBC, quæ per extrema A, C
<
note
symbol
="
b
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position
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left
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xlink:label
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note-0080-02
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xlink:href
="
note-0080-02a
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xml:space
="
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">1. Co-
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roll. 19. h.</
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ſibit, ac datæ portioni ſupra baſim AC erit
<
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inſcripta, & </
s
>
<
s
xml:id
="
echoid-s1942
"
xml:space
="
preserve
">erit _MAXIMA_: </
s
>
<
s
xml:id
="
echoid-s1943
"
xml:space
="
preserve
">quoniam, quæ
<
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/>
adſcribitur cum recto, quod minus ſit BI mi-
<
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/>
nor eſt ipſa AMBC, quæ verò cum
<
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symbol
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c
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position
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xlink:label
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note-0080-03
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xlink:href
="
note-0080-03a
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xml:space
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">2. Co-
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roll. prop.
<
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/>
19. huius.</
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>
quod excedat BI, veltota cadit extra Ellipſis
<
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/>
portionem ADB, ſinempe eius rectum
<
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symbol
="
d
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position
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xlink:label
="
note-0080-04
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xlink:href
="
note-0080-04a
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xml:space
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">20. h.</
note
>
idem cum recto BG, & </
s
>
<
s
xml:id
="
echoid-s1944
"
xml:space
="
preserve
">eo magis ſi ipſum ex-
<
lb
/>
cedat; </
s
>
<
s
xml:id
="
echoid-s1945
"
xml:space
="
preserve
">vel ad minus ſecat datam portionem ſupra baſim AC, ſi Parabolę re-
<
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/>
ctum cadat inter I, & </
s
>
<
s
xml:id
="
echoid-s1946
"
xml:space
="
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">G, vt in N. </
s
>
<
s
xml:id
="
echoid-s1947
"
xml:space
="
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">Nam eius regula ex N ducta
<
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e
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position
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xlink:label
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note-0080-05
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xlink:href
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note-0080-05a
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xml:space
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">1. Co-
<
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roll. 19. h.</
note
>
ter ipſi IH omninò ſecat Ellipſis regulam HG ſupra baſim AC. </
s
>
<
s
xml:id
="
echoid-s1948
"
xml:space
="
preserve
">Quare Pa-
<
lb
/>
rabolæ portio AMBC eſt _MAXIMA_ inſcripta quæſita. </
s
>
<
s
xml:id
="
echoid-s1949
"
xml:space
="
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">Quod primò, &</
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>
<
s
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echoid-s1950
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xml:space
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">c.</
s
>
<
s
xml:id
="
echoid-s1951
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xml:space
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s1952
"
xml:space
="
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">Iam ſit data Parabolæ portio AMBC, cuius rectum BI, regula IL, diame-
<
lb
/>
ter BE, baſis AC, & </
s
>
<
s
xml:id
="
echoid-s1953
"
xml:space
="
preserve
">per eius verticem B oporteat _MINIMAM_ Ellipſis por-
<
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/>
tionem ei circumſcribere cum dato recto BG, quod excedat rectum datæ
<
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/>
portionis.</
s
>
<
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xml:id
="
echoid-s1954
"
xml:space
="
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s1955
"
xml:space
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">Conueniat applicata AE cum regula IL in H, iunctaq; </
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>
<
s
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="
echoid-s1956
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xml:space
="
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">GH, & </
s
>
<
s
xml:id
="
echoid-s1957
"
xml:space
="
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">producta,
<
lb
/>
occurrat portionis diametro in F (ſecans enim vnam parallelarum IH, ſecat
<
lb
/>
alteram BE:) </
s
>
<
s
xml:id
="
echoid-s1958
"
xml:space
="
preserve
">cum tranſuerſo autem BF, ac dato recto BG adſcribatur
<
note
symbol
="
f
"
position
="
left
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xlink:label
="
note-0080-06
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xlink:href
="
note-0080-06a
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xml:space
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">7. huius.</
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>
B Ellipſis ADBC, quæ datę Parabolæ AMB occurret in A, & </
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>
<
s
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="
echoid-s1959
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">C, & </
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>
<
s
xml:id
="
echoid-s1960
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xml:space
="
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">
<
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symbol
="
g
"
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xlink:label
="
note-0080-07
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xml:space
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">1. Co-
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roll. prop.
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19. huius.</
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>
circumſcripta, quàm dico eſſe _MINIMAM_. </
s
>
<
s
xml:id
="
echoid-s1961
"
xml:space
="
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">Nam Ellipſis quæ adſcribitur
<
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per B, cum eodem recto BG, ſed cum tranſuerſo, quod excedat BF, maior
<
lb
/>
eſt ipſa ADB; </
s
>
<
s
xml:id
="
echoid-s1962
"
xml:space
="
preserve
">quæ verò adſcribitur cum tranſuerſo, quod minus ſit
<
note
symbol
="
h
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position
="
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xlink:label
="
note-0080-08
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xlink:href
="
note-0080-08a
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xml:space
="
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">4. Co-
<
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roll. prop.
<
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19. huius.</
note
>
BF, eſt quidem minor eadem ADB, ſed omnino ſecat Parabolen
<
note
symbol
="
i
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position
="
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xlink:label
="
note-0080-09
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xlink:href
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note-0080-09a
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xml:space
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">ibidem.</
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>
ſupra baſim AC, cum & </
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>
<
s
xml:id
="
echoid-s1963
"
xml:space
="
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">ipſarum regulę ſe mutuò ſecent ſupra eandem AC.</
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>
<
s
xml:id
="
echoid-s1964
"
xml:space
="
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">
<
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symbol
="
l
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xlink:label
="
note-0080-10
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xlink:href
="
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xml:space
="
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">1. Corol.
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19. huius.</
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>
Quare Ellipſis portio ADBC eſt _MINIMA_ circumſcripta quæſita cum dato
<
lb
/>
recto BG. </
s
>
<
s
xml:id
="
echoid-s1965
"
xml:space
="
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">Quod ſecundò, &</
s
>
<
s
xml:id
="
echoid-s1966
"
xml:space
="
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">c.</
s
>
<
s
xml:id
="
echoid-s1967
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1968
"
xml:space
="
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">Sit tandem circumſcribenda datæ portioni Parabolicæ AMB </
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