Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GREGORII à S. VINCENTIO.
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ex æquo erit cylindrus parabolicus A V C E D B ad ungu-
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lam A B C D ut 40 ad 16, hoc eſt, ut 5 ad 2; </
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<
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xml:space
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demonſtrandum.</
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</
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<
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<
s
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xml:space
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">Quæ hîc dixi à Cl. </
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<
s
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xml:space
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">Viro oſtenſa fuiſſe, veriſſima ſunt,
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ac proinde non eſt quod de veritate hujus Theorematis du-
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bitemus: </
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<
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xml:space
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<
s
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xml:space
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">adferre poſſem, lon-
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ge ab iſta diverſam, niſi ad ſequentia properarem.</
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<
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</
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<
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<
s
xml:id
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echoid-s762
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xml:space
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preserve
">Repetitâ igitur parte ultimâ ſchematis, quod ſuprà de-
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<
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right
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xlink:label
="
note-0043-01
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xlink:href
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xml:space
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">TAB. XXXVII.
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Fig. 2.</
note
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ſcripſimus, ſit oſtendendum, quod ſolidum Μ Ξ, id eſt,
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quod oritur ex ductu plani E Ξ S in planum E M Λ S ad
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ſolidum Λ Σ, id eſt, quod oritur ex ductu plani S Ξ Σ P
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in planum S Λ Π P, eam habet rationem quam 53 ad 203.
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</
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<
s
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xml:space
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">Deſcribatur ſuper E F parabola E Π F, axem habens P Π,
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quam conſtat eſſe quartam partem ipſius E F ſive M E. </
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<
s
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xml:space
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igitur parabola E Π F eadem quam V. </
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<
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<
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<
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">& </
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42. </
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42. </
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xml:space
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">& </
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<
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xml:space
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">veriſſimum eſt, ſolidum quod producitur ex ductu
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plani E Σ L F in planum F Π M E æquari ſolido quod fit
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ex parabola E Π F ducta in ſe ipſam: </
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quod ſubjungit in Coroll. </
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<
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">nimirum quod ſolidum ex pla-
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no S Ξ Σ P in planum S Λ Π P, æquatur ſolido ex ductu
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plani S Φ Π P in ſe ipſum; </
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<
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xml:space
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">unde ſimiliter ſolidum ex pla-
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no E Ξ S in planum E M Λ S æquabitur ſolido ex plano
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E Φ S in ſe ipſum ducto.</
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<
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xml:space
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">Oportet itaque oſtendere ſolidum ortum ex plano E Φ S
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ad ſolidum ex plano S Φ Π P, utroque in ſe ipſum ducto,
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eſſe ut 53 ad 203.</
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<
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<
s
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xml:space
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">Eſto ungula parabolica A E F Π, cujus baſis parabola
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<
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xlink:label
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">TAB. XXXVII.
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Fig. 4.</
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E Π F repetita ſit ex figura præcedenti, eodemque modo
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ut iſtic diviſa lineis Π P, Φ S. </
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A Π dupla diametri baſis Π P. </
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quam intelligit in prop. </
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<
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</
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rum conſideratione uſus quæ eſt in Scholio propoſ. </
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9. </
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minas ungulas produci, ſingulas altitudine æquales </
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