Vitruvius
,
De architectura libri decem
,
1567
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514.01.307
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NONVS.
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Quoniamlinea A D, diameter eſt ſemicirculi A B D, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">diameter etiaim est ſemicirculi erecti ſupra
<
lb
/>
A B D, ideo dum mouetur ſemicirculus erectus à D, uerſus B, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">à B. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">uerſus A. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">immobili perma-
<
lb
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nente ſigno A, tanquam cardini, ſecumſeret ſuam diamertron, & </
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>
<
s
xml:id
="
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xml:space
="
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">ita ex duabus diametris, quæ prius in unam
<
lb
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lineam conueniebant, altera non diſcedet a loco ſuo, nimirum A D. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſemicirculi plani, altera loci permuta-
<
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/>
tione à D uerſus E, & </
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<
s
xml:id
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xml:space
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">àB. </
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<
s
xml:id
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xml:space
="
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">uerſus A, unà cum ſemicirculo erecto diuerſas partes hemic ylindrij ſeca-
<
lb
/>
bit, donec fiet A C. </
s
>
<
s
xml:id
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xml:space
="
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">extra ſuperficiem hemicylindrij, & </
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>
<
s
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xml:space
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">recte cadet ſuper ſignum A. </
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>
<
s
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xml:space
="
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">quod est extremum
<
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diametri A D. </
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>
<
s
xml:id
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xml:space
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">cum in integra illa uerſatione ſigno D, deſcripſerit circuli tetrantem. </
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<
s
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">quoniam diame-
<
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tros A D, translata à D uerſus B. </
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>
<
s
xml:id
="
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"
xml:space
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">& </
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<
s
xml:id
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xml:space
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">à B. </
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<
s
xml:id
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"
xml:space
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">uerſus A. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ubicunque ſiſtitur ſecat lineam ſemicirculi
<
lb
/>
A B D, ſecetigitur eam in ſignis E F G H I K L M N O P Q R S T. </
s
>
<
s
xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
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xml:space
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">ab A. </
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>
<
s
xml:id
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xml:space
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">ad ſingula
<
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<
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note-514.01.307-01
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xlink:href
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note-514.01.307-01a
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xml:space
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note
>
ea ſigna, ducantur ſaltem imaginatione rectæ A F. </
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<
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xml:space
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<
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xml:space
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">A H. </
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<
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xml:space
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">A I. </
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<
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xml:id
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xml:space
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">A K. </
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<
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xml:space
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">A L, A M. </
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>
<
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xml:space
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">A N.
<
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</
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>
<
s
xml:id
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xml:space
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">A O. </
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>
<
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xml:id
="
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xml:space
="
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">A P. </
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>
<
s
xml:id
="
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"
xml:space
="
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">A Q. </
s
>
<
s
xml:id
="
echoid-s20751
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xml:space
="
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">A R. </
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>
<
s
xml:id
="
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xml:space
="
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">A S. </
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>
<
s
xml:id
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xml:space
="
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">A T. </
s
>
<
s
xml:id
="
echoid-s20754
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">producantur ad tetrantis circumſerentiam in ſigna. </
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>
<
s
xml:id
="
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xml:space
="
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">
<
lb
/>
e. </
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>
<
s
xml:id
="
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xml:space
="
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">f. </
s
>
<
s
xml:id
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xml:space
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">g. </
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<
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xml:space
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">h. </
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<
s
xml:id
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xml:space
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">i. </
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<
s
xml:id
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xml:space
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">k. </
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<
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xml:space
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">φ. </
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<
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xml:space
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<
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xml:space
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">n. </
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<
s
xml:id
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xml:space
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">o. </
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>
<
s
xml:id
="
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xml:space
="
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">p. </
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<
s
xml:id
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xml:space
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">q. </
s
>
<
s
xml:id
="
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xml:space
="
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">r. </
s
>
<
s
xml:id
="
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xml:space
="
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">s. </
s
>
<
s
xml:id
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xml:space
="
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">t. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Singulæ ex his lineæ referent diametrum ſemicirculi
<
lb
/>
translatam circa cylindri ſuperficiem. </
s
>
<
s
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xml:space
="
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">Diuidatur media diametros A D, in X, & </
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>
<
s
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xml:space
="
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">centro A, inter-
<
lb
/>
uallo A X, tetrans circuli deſcribatur x y, linea circinationis tetrantis x y ſingulas diametros me-
<
lb
/>
dias ſecabit, & </
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<
s
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xml:space
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">occaſionem dabit terminandi ſingulas illas lineas, quæ a ſigno D. </
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>
<
s
xml:id
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xml:space
="
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">omnium communi termi-
<
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no proficiſcentes ſe ſe conſequentes alio eorum extremo ad circinationis lineam, quæ ſupra diametrum de-
<
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/>
ſcriberetur, peruenirent. </
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>
<
s
xml:id
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xml:space
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">ſupra diametrum dico, quam quæ libet earum ſecat in circinatione A B D. </
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<
s
xml:id
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xml:space
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">ima-
<
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ginemur itaque ſemicirculos ſupra ſingulas diametros a e. </
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<
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<
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<
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<
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xml:id
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xml:space
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<
s
xml:id
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xml:space
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">reliquas quæ ab A. </
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<
s
xml:id
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xml:space
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<
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gredientes ad circinationis tetrantis B C. </
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<
s
xml:id
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xml:space
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>
<
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xml:id
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<
s
xml:id
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xml:space
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">a ſigno D, per ſingula puncta, in quibus Linea
<
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<
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note-514.01.307-02
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note-514.01.307-02a
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>
circinationis A B D, ſecat ſingulas diametros mobiles, & </
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<
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xml:space
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>
<
s
xml:id
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xml:space
="
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">erigantur
<
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/>
lineæ, quæ ad circinationes ſemicirculorum,quos imaginati ſumus, perueniant adſigna α. </
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<
s
xml:id
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xml:space
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">β. </
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<
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xml:id
="
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<
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<
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xml:id
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<
s
xml:id
="
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xml:space
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<
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</
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<
s
xml:id
="
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"
xml:space
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">{σθ} ι κ. </
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<
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xml:id
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xml:space
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">λ μ. </
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<
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xml:id
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xml:space
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<
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<
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<
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xml:space
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">π. </
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<
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xml:space
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">Aio ſingulas lineas E α. </
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<
s
xml:id
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xml:space
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">F β. </
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<
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xml:id
="
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xml:space
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">G γ. </
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<
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xml:id
="
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xml:space
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">H δ I. </
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<
s
xml:id
="
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xml:space
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">ε. </
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<
s
xml:id
="
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xml:space
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">K ζ. </
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<
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xml:id
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xml:space
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">L η. </
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<
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xml:id
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xml:space
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">M ξ N ι. </
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<
s
xml:id
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xml:space
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<
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O κ. </
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<
s
xml:id
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xml:space
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">P λ. </
s
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<
s
xml:id
="
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xml:space
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">q. </
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<
s
xml:id
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xml:space
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">μ. </
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<
s
xml:id
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xml:space
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">R ν. </
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<
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xml:id
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xml:space
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">S ξ T ο. </
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<
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xml:space
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">V π. </
s
>
<
s
xml:id
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xml:space
="
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">eſſe medias comparabiles inter eas diametri partes, quas in illa
<
lb
/>
ſecant in aliquo dictorum ſignorum. </
s
>
<
s
xml:id
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xml:space
="
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">Deſcribatur ſupra diametrum A φ ſemicirculus A η φ. </
s
>
<
s
xml:id
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xml:space
="
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">aio lineam
<
lb
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n L. </
s
>
<
s
xml:id
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xml:space
="
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">eſſe mediã inter partes diametri A L. </
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>
<
s
xml:id
="
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xml:space
="
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">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">L φ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quam diametron ipſa ſecat in ſigno L. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s20824
"
xml:space
="
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">quoniam an-
<
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/>
guli A. </
s
>
<
s
xml:id
="
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xml:space
="
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">L D. </
s
>
<
s
xml:id
="
echoid-s20826
"
xml:space
="
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">η λ φ.</
s
>
<
s
xml:id
="
echoid-s20827
"
xml:space
="
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">oppoſiti ſunt,ideo æ quales ſunt, ex decima quinta primi elementorum. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Sed angulus A L
<
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/>
D, quia eſt in ſemicirculo,rectus eſt ex trigeſima prima tertij: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Angulus ergo η L φ rectus erit. </
s
>
<
s
xml:id
="
echoid-s20830
"
xml:space
="
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">Ex ſigno L. </
s
>
<
s
xml:id
="
echoid-s20831
"
xml:space
="
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">
<
lb
/>
erecta est diametro A φ ad angulos rectos linearcta L.</
s
>
<
s
xml:id
="
echoid-s20832
"
xml:space
="
preserve
">x. </
s
>
<
s
xml:id
="
echoid-s20833
"
xml:space
="
preserve
">quæ peruenit ad circinationem circumferen-
<
lb
/>
tia A η ο ergo recta η L erit media proportione reſpondens inter lineas A L. </
s
>
<
s
xml:id
="
echoid-s20834
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20835
"
xml:space
="
preserve
">L φ extertia de-
<
lb
/>
cima ſexti. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Aio præ terea lineam n L, ſupra planum ſemicirculi A B D. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">in ſigno L. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ad rectos angulos
<
lb
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<
note
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="
left
"
xlink:label
="
note-514.01.307-03
"
xlink:href
="
note-514.01.307-03a
"
xml:space
="
preserve
">30</
note
>
stare. </
s
>
<
s
xml:id
="
echoid-s20839
"
xml:space
="
preserve
">Quoniam ſemicirculus A η φ rectus eſt ad planum ſemicirculi A B D
<
lb
/>
D. </
s
>
<
s
xml:id
="
echoid-s20840
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20841
"
xml:space
="
preserve
">ab uno circinationis ſi- gno A η φ ſcilicet η.</
s
>
<
s
xml:id
="
echoid-s20842
"
xml:space
="
preserve
">ducta eſt recta η L, quæ peruenit ad planum ſemicirculi A B D. </
s
>
<
s
xml:id
="
echoid-s20843
"
xml:space
="
preserve
">ergo x L re-
<
lb
/>
cte ſtabit ad planum ſemicirculi A B D. </
s
>
<
s
xml:id
="
echoid-s20844
"
xml:space
="
preserve
">Sed n L quoniam comparabiles estinter A L. </
s
>
<
s
xml:id
="
echoid-s20845
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20846
"
xml:space
="
preserve
">L. </
s
>
<
s
xml:id
="
echoid-s20847
"
xml:space
="
preserve
">φ. </
s
>
<
s
xml:id
="
echoid-s20848
"
xml:space
="
preserve
">ad
<
lb
/>
rectos angulos cadit in L, commume rectarum A
<
unsure
/>
& </
s
>
<
s
xml:id
="
echoid-s20849
"
xml:space
="
preserve
">D L ſegmentum; </
s
>
<
s
xml:id
="
echoid-s20850
"
xml:space
="
preserve
">ideo n L a rctos stabit an-
<
lb
/>
gulos ſupra ſemicirculi A B D. </
s
>
<
s
xml:id
="
echoid-s20851
"
xml:space
="
preserve
">planum, in ſigno L. </
s
>
<
s
xml:id
="
echoid-s20852
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20853
"
xml:space
="
preserve
">quoniam ad id planum ſemicriculi, A B D, re-
<
lb
/>
ctum & </
s
>
<
s
xml:id
="
echoid-s20854
"
xml:space
="
preserve
">hemcylindrium, ita quod eius baſis diametros, diametro ſemicir culi quadrat, & </
s
>
<
s
xml:id
="
echoid-s20855
"
xml:space
="
preserve
">circinationis linea
<
lb
/>
unius conuenit lineæ circinationis alterius. </
s
>
<
s
xml:id
="
echoid-s20856
"
xml:space
="
preserve
">n L. </
s
>
<
s
xml:id
="
echoid-s20857
"
xml:space
="
preserve
">pariter rectè cadet ſupra lmeam circinationis baſis bemicy
<
lb
/>
lindrij in ſigno L. </
s
>
<
s
xml:id
="
echoid-s20858
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20859
"
xml:space
="
preserve
">bac ratione recta η L in ſi perficie hemicylindrij reperietur.</
s
>
<
s
xml:id
="
echoid-s20860
"
xml:space
="
preserve
">atque etiam in plano ſe-
<
lb
/>
micirculi. </
s
>
<
s
xml:id
="
echoid-s20861
"
xml:space
="
preserve
">A η φ. </
s
>
<
s
xml:id
="
echoid-s20862
"
xml:space
="
preserve
">ita ut pariter in utroque plano ſtare contingct. </
s
>
<
s
xml:id
="
echoid-s20863
"
xml:space
="
preserve
">Semicirculus ergo A η φ. </
s
>
<
s
xml:id
="
echoid-s20864
"
xml:space
="
preserve
">tanget he-
<
lb
/>
micylindrium in ſigno H. </
s
>
<
s
xml:id
="
echoid-s20865
"
xml:space
="
preserve
">Similiratione ac uia demonſtrabitur ſingulas rectarum linearum. </
s
>
<
s
xml:id
="
echoid-s20866
"
xml:space
="
preserve
">E α. </
s
>
<
s
xml:id
="
echoid-s20867
"
xml:space
="
preserve
">F β.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s20868
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-514.01.307-04
"
xlink:href
="
note-514.01.307-04a
"
xml:space
="
preserve
">40</
note
>
G γ & </
s
>
<
s
xml:id
="
echoid-s20869
"
xml:space
="
preserve
">reliquas eſſe medias comparabiles inter diametri partes, & </
s
>
<
s
xml:id
="
echoid-s20870
"
xml:space
="
preserve
">rectas cadere conſequenter u-
<
lb
/>
nam poſt aliam ſuper lineam baſis hemicylindrij. </
s
>
<
s
xml:id
="
echoid-s20871
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20872
"
xml:space
="
preserve
">quod quæ libet erit in utroque plano, quam pri-
<
lb
/>
mum peruenerit ad hemicylindrij ſuperſiciem, ad ſuam quæ q; </
s
>
<
s
xml:id
="
echoid-s20873
"
xml:space
="
preserve
">altitudinem in ſignis ſcilicet.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s20874
"
xml:space
="
preserve
">θ. </
s
>
<
s
xml:id
="
echoid-s20875
"
xml:space
="
preserve
">ι. </
s
>
<
s
xml:id
="
echoid-s20876
"
xml:space
="
preserve
">κ. </
s
>
<
s
xml:id
="
echoid-s20877
"
xml:space
="
preserve
">λ. </
s
>
<
s
xml:id
="
echoid-s20878
"
xml:space
="
preserve
">μ. </
s
>
<
s
xml:id
="
echoid-s20879
"
xml:space
="
preserve
">ν. </
s
>
<
s
xml:id
="
echoid-s20880
"
xml:space
="
preserve
">ξ. </
s
>
<
s
xml:id
="
echoid-s20881
"
xml:space
="
preserve
">ο. </
s
>
<
s
xml:id
="
echoid-s20882
"
xml:space
="
preserve
">π. </
s
>
<
s
xml:id
="
echoid-s20883
"
xml:space
="
preserve
">in quibus ſignis ſemicirculus mobilis tranſlatus, ( ut dictum eſt) neceſſario he-
<
lb
/>
micylindrij ſuperficiem tanget, & </
s
>
<
s
xml:id
="
echoid-s20884
"
xml:space
="
preserve
">quæſitam lineam illi circumſcribet. </
s
>
<
s
xml:id
="
echoid-s20885
"
xml:space
="
preserve
">V nde ſi ducatur linea, quæ per ſingula
<
lb
/>
illa ſigna tranſeat, & </
s
>
<
s
xml:id
="
echoid-s20886
"
xml:space
="
preserve
">eam hemicylindrij partem ſecet, quæ illi ſubiacet, abſque ullo impedimento circumagi
<
lb
/>
poterit dictus ſemucirculus circa ſuperficiem hemicylindrij, & </
s
>
<
s
xml:id
="
echoid-s20887
"
xml:space
="
preserve
">ſemper ſua circinatione per ſingula ſigna tan-
<
lb
/>
get lineam nuper deſcriptam in hemicylindri ſuperficie. </
s
>
<
s
xml:id
="
echoid-s20888
"
xml:space
="
preserve
">A ſingulis autem ſignis E. </
s
>
<
s
xml:id
="
echoid-s20889
"
xml:space
="
preserve
">F. </
s
>
<
s
xml:id
="
echoid-s20890
"
xml:space
="
preserve
">G. </
s
>
<
s
xml:id
="
echoid-s20891
"
xml:space
="
preserve
">H. </
s
>
<
s
xml:id
="
echoid-s20892
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s20893
"
xml:space
="
preserve
">K. </
s
>
<
s
xml:id
="
echoid-s20894
"
xml:space
="
preserve
">L. </
s
>
<
s
xml:id
="
echoid-s20895
"
xml:space
="
preserve
">
<
lb
/>
M. </
s
>
<
s
xml:id
="
echoid-s20896
"
xml:space
="
preserve
">N. </
s
>
<
s
xml:id
="
echoid-s20897
"
xml:space
="
preserve
">O. </
s
>
<
s
xml:id
="
echoid-s20898
"
xml:space
="
preserve
">P. </
s
>
<
s
xml:id
="
echoid-s20899
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s20900
"
xml:space
="
preserve
">R. </
s
>
<
s
xml:id
="
echoid-s20901
"
xml:space
="
preserve
">S. </
s
>
<
s
xml:id
="
echoid-s20902
"
xml:space
="
preserve
">T. </
s
>
<
s
xml:id
="
echoid-s20903
"
xml:space
="
preserve
">inſuper planum A B D, ſecundum ſuperficiem hemicylindrij erigantur
<
lb
/>
ſub ſequentis rectæ lineæ æ quales ſingulæ ſingulis ijs, quæ ab eodem ſigno ductæ ſunt, in plana eorum circulo-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-514.01.307-05
"
xlink:href
="
note-514.01.307-05a
"
xml:space
="
preserve
">50</
note
>
rum, quos imaginat ione ſinximus, & </
s
>
<
s
xml:id
="
echoid-s20904
"
xml:space
="
preserve
">quȩ oſtenſæ ſunt mediæ comparabiles inter ſuarum diametrorum par-
<
lb
/>
tes.</
s
>
<
s
xml:id
="
echoid-s20905
"
xml:space
="
preserve
">Poſt hæc deſcribātur lineæ, quæ per omnia extrema earum ſigna tranſeant, quæ ſuperius terminum habent
<
lb
/>
circa hemicylindrij ſuperſiciem,& </
s
>
<
s
xml:id
="
echoid-s20906
"
xml:space
="
preserve
">ita perfectum erit, quod quærebatur. </
s
>
<
s
xml:id
="
echoid-s20907
"
xml:space
="
preserve
">poterimus quoque ſupra diametrum
<
lb
/>
A B. </
s
>
<
s
xml:id
="
echoid-s20908
"
xml:space
="
preserve
">æquare parallelogrammum A D σ ν quod referet hemicylindrium, & </
s
>
<
s
xml:id
="
echoid-s20909
"
xml:space
="
preserve
">a ſingulis prædictis iam ſi-
<
lb
/>
gnis circinationis A B D. </
s
>
<
s
xml:id
="
echoid-s20910
"
xml:space
="
preserve
">parallelas ducere lateribus A σ D ν quæ ſuper latus σ ν cadant, at-
<
lb
/>
que incipiendo a ſignis E F G H. </
s
>
<
s
xml:id
="
echoid-s20911
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20912
"
xml:space
="
preserve
">reliquis deſcendendo ad baſim σ ν excipere lineas ſingulis præ-
<
lb
/>
dictarum medias comparabiles, & </
s
>
<
s
xml:id
="
echoid-s20913
"
xml:space
="
preserve
">inde lineam deſcribere, quæ per ſingula extrema ſigna tranſeat, quæ ſigna
<
lb
/>
termini ſunt dictarum linearum ad baſim σ ν. </
s
>
<
s
xml:id
="
echoid-s20914
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s20915
"
xml:space
="
preserve
">habebitur hoc modo lineatio cylindricæ linæ a nobis quæ-
<
lb
/>
ſitæ, quemadmodum in diagrammate cerni potest.</
s
>
<
s
xml:id
="
echoid-s20916
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">60</
note
>
</
div
>
</
div
>
</
text
>
</
echo
>