Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſaltem ſecat portionem ABC ſupra baſim AD, ſi rectum cadat inter M, & </
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<
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echoid-s2004
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<
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G, quale eſt CO nam iuncta regula IO, & </
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<
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xml:id
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echoid-s2005
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xml:space
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">producta omnino ſecat
<
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a
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position
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xlink:label
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xlink:href
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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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GL ſupra eandem AD. </
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<
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echoid-s2006
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xml:space
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">Quare Hyperbolæ portio ANCD eſt _MAXIMA_ in-
<
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ſcripta quæſita cum dato tranſuerſo CI. </
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<
s
xml:id
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echoid-s2007
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xml:space
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">Quod erat primò, &</
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<
s
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echoid-s2008
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xml:space
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">c.</
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<
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echoid-s2009
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</
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<
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<
s
xml:id
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echoid-s2010
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xml:space
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">Iam eidem Ellipticæ portioni ABCD inſcribenda ſit _MAXIMA_ Hyperbo-
<
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læ portio cum dato recto CM, quod tamen ſit minus latitudine EL, ſemiap-
<
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plicatæ AE (ſi enim ei æquale, vel maius eſſet, iuncta regula LM nunquam
<
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cum diametro EC conueniret) Supra C.</
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<
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echoid-s2011
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</
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<
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echoid-s2012
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">Iungatur I.</
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<
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">M, quę ideo producta occur-
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<
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number
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<
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file
="
0082-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0082-01
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ret diametro in I, & </
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<
s
xml:id
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echoid-s2014
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xml:space
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">cum tranſuerſo IC,
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datoq; </
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>
<
s
xml:id
="
echoid-s2015
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xml:space
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preserve
">recto CM adſcribatur per C
<
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symbol
="
b
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position
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left
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xlink:label
="
note-0082-02
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xlink:href
="
note-0082-02a
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xml:space
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">6. huius.</
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perbolæ portio ANCD, quæ datæ portio-
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ni ABC occurret in A, & </
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<
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echoid-s2016
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">D, & </
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<
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echoid-s2017
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xml:space
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"> erit
<
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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-0082-03
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xlink:href
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">1. Co-
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roll. 19. h.</
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pta; </
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>
<
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xml:id
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echoid-s2018
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xml:space
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">quàm dico eſſe _MAXIMAM_: </
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<
s
xml:id
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echoid-s2019
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xml:space
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">nam quę
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adſcribitur cum eodem recto CM, ſed cum
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tranſuerſo, quod excedat CI minor
<
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symbol
="
d
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position
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xlink:label
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xlink:href
="
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xml:space
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">4. Co-
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roll. 19. h.</
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ipſa ANC; </
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<
s
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echoid-s2020
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xml:space
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">quæ verò cum tranſuerſo, quod
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ſit minus CI, quale eſt CP, eſt
<
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e
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position
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xlink:label
="
note-0082-05
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xml:space
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">ibidem.</
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maior ipſa ANC, ſed omnino ſecat datam
<
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portionem ABC, ſupra baſim AD
<
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symbol
="
f
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position
="
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xlink:label
="
note-0082-06
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="
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xml:space
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">1. Co-
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roll. 19. h.</
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iuncta regula PM, & </
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<
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="
echoid-s2021
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">producta, omnino
<
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ſecet regulam GL ſupra eandem AD. </
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>
<
s
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echoid-s2022
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xml:space
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">Qua-
<
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re huiuſmodi Hyperbolæ portio ANCD,
<
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eſt _MAXIMA_ inſcripta cũ dato recto CM.
<
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</
s
>
<
s
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echoid-s2023
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xml:space
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">Quod ſecundò, &</
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>
<
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echoid-s2024
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xml:space
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">c.</
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<
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echoid-s2025
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</
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<
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<
s
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="
echoid-s2026
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xml:space
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">Ampliùs ſit data Hyperbolę portio AN
<
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CD, cuius tranſuerſum CI, rectum CM, regula IM, diameter CE, baſis
<
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AD: </
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<
s
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echoid-s2027
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xml:space
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">oportet per verticem C _MINIMAM_ Ellipſis portionem circumſcribere
<
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cum dato tranſuerſo CF, quod tamen excedat diametrum CE.</
s
>
<
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echoid-s2028
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</
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<
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<
s
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echoid-s2029
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">Producatur item AE occurrens regulæ IM in L, & </
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<
s
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echoid-s2030
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">iungatur FL, quæ pro-
<
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ducta conueniat cum contingente CM in G, & </
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>
<
s
xml:id
="
echoid-s2031
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xml:space
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">cum dato tranſuerſo CF, ac
<
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recto CG adſcribatur per C Ellipſis portio ABCD, quæ datæ
<
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symbol
="
g
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position
="
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xlink:label
="
note-0082-07
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xlink:href
="
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xml:space
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">7. huius.</
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occurret in A, D, eritque circumſcripta, & </
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>
<
s
xml:id
="
echoid-s2032
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xml:space
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">erit _MINIMA_: </
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>
<
s
xml:id
="
echoid-s2033
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xml:space
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">Nam quæ adſcri-
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bitur cum eodem tranſuerſo CF, ſed cum recto, quod excedat CG eſt
<
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symbol
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h
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position
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xlink:label
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xlink:href
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xml:space
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">1. Co-
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roll. 19. h.</
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ior ipſa ABC, quæ verò cum recto, quod minus ſit CG; </
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>
<
s
xml:id
="
echoid-s2034
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xml:space
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">vel tota cadit intra
<
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ANCD, tùm cum rectum æquet ipſum CM, & </
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<
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xml:space
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"> eò magis ſi ipſo ſit minus;</
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<
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<
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symbol
="
i
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position
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xlink:label
="
note-0082-09
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xlink:href
="
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xml:space
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">1. Co-
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rol. 19. h.</
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vel ſaltem ſecat portionem ANC ſupra baſim AD, quando nempe rectum cadat inter CM, & </
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>
<
s
xml:id
="
echoid-s2037
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xml:space
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">CG, quale eſt CO, nam iuncta regula FO, omnino ſecat
<
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<
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symbol
="
l
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position
="
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xlink:label
="
note-0082-10
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xlink:href
="
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xml:space
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">20. h.</
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Hyperbolæ regulam ML ſupra eandem AD. </
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<
s
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echoid-s2038
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xml:space
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">Quapropter Ellipſis portio
<
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ABCD, erit _MINIMA_ circumſcripta cũ dato tranſuerſo CI. </
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>
<
s
xml:id
="
echoid-s2039
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xml:space
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">Quod tertiò, &</
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<
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xml:id
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echoid-s2040
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xml:space
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">c.</
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<
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</
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<
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<
s
xml:id
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echoid-s2042
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xml:space
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">Poſtremò, datis ijſdem, ſit circumſcribenda _MINIMA_ Ellipſis portio, cum
<
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dato recto CG, quod tamen excedat latitudinem EL (ad hoc vt iuncta re-
<
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gula GL cum diametro CE poſſit conuenire infra E) & </
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>
<
s
xml:id
="
echoid-s2043
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xml:space
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">ipſa GL occurrat CE
<
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in F, & </
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>
<
s
xml:id
="
echoid-s2044
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xml:space
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">cum dato recto CG, ac tranſuerſo CF adſcribatur per C
<
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symbol
="
m
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position
="
left
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xlink:label
="
note-0082-11
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xlink:href
="
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xml:space
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">7. h.</
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>
portio ABCD, quæ item datæ portioni occurret in A, & </
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>
<
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xml:id
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echoid-s2045
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">D, eritq; </
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<
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="
echoid-s2046
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<
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symbol
="
n
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position
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xlink:label
="
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xlink:href
="
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xml:space
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">1. Co-
<
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roll. 19. h.</
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>
ſcripta; </
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>
<
s
xml:id
="
echoid-s2047
"
xml:space
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">quàm dico eſſe _MINIMAM_: </
s
>
<
s
xml:id
="
echoid-s2048
"
xml:space
="
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">quæ enim adſcribitur cum codem recto
<
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<
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symbol
="
o
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position
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xlink:label
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xml:space
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">4. Co-
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roll. prop.
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19. huius.</
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>
CG, ſed cum tranſuerſo, quod ſit maius CF, eſt etiam maior ipſa ABC;</
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