Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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<
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FED. COMMANDINI
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triangulum m k φ triangulo n k φ. </
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<
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xml:id
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xml:space
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">ergo anguli l z k, o z k,
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m φ k, n φ k æquales ſunt, ac recti. </
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<
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xml:id
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xml:space
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">quòd cum etiam recti
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ſint, qui ad k; </
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<
s
xml:id
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xml:space
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">æquidiſtabunt lineæ l o, m n axi b d. </
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<
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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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note
>
demonſtrabuntur l m, o n ipſi a c æquidiſtare. </
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<
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xml:space
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">Rurſus ſi
<
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iungantur a l, l b, b m, m c, c n, n d, d o, o a: </
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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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">bifariam di
<
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uidantur: </
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<
s
xml:id
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xml:space
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">à centro autem k ad diuiſiones ductæ lineæ pro-
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trahantur uſque ad ſectionem in puncta p q r s t u x y: </
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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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<
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ſtremo p y, q x, r u, s t, q r, p s, y t, x u coniungantur. </
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<
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xml:space
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ter oſtendemus lineas
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p y, q x, r u, s t axi b d æ-
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quidiſtantes eſſe: </
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<
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xml:space
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<
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">q r,
<
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p s, y t, x u æquidiſtan-
<
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tesipſi a c. </
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<
s
xml:id
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xml:space
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">Itaque dico
<
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harum figurarum in el-
<
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lipſi deſcriptarum cen-
<
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trum grauitatis eſſe pũ-
<
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ctum k, idem quod & </
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<
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lipſis centrum. </
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<
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xml:space
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<
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lateri enim a b c d cen-
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trum eſt k, ex decima e-
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iuſdem libri Archime-
<
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dis, quippe cũ in eo om
<
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nes diametri cõueniãt.
<
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</
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<
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xlink:label
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xlink:href
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xml:space
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">13. Archi
<
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medis.</
note
>
d o, quoniam trianguli
<
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alb centrum grauitatis
<
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<
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position
="
left
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xlink:label
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xlink:href
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xml:space
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">Vltima.</
note
>
eſt in linea l e: </
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<
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">trapezijq́; </
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>
<
s
xml:id
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xml:space
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">a b m o centrum in linea e k: </
s
>
<
s
xml:id
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xml:space
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">trape
<
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zij o m c d in k g: </
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<
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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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">trianguli c n d in ipſa g n: </
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<
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xml:id
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xml:space
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">erit magnitu
<
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dinis ex his omnibus conſtantis, uidelicet totius figuræ cen
<
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trum grauitatis in linea l n: </
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<
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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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">o b eandem cauſſam in linea
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o m. </
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<
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<
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xml:id
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xml:space
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">trapezij
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a l n d in h k: </
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<
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xml:space
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">trapezij l b c n in k f: </
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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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">trianguli b m c in fm.
<
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</
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<
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xml:id
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xml:space
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">cum ergo figuræ a l b m c n d o centrum grauitatis ſit in li-
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nea l n, & </
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>
<
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">in linea o m; </
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<
s
xml:id
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">erit centrum ipſius punctum k, </
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