Musschenbroek, Petrus van
,
Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae
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DE MAGNITUDINE TERRÆ.
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<
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<
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style
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">Datis quadrilateri L R V Q lateribus & diagonio R V, abſque
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Triangulorum canonibus invenire reliquam diagonium Q L.</
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Tab. XVI. fig. 16. Per Problema XIX datur R L di- \\ ſtantia inter Dordracum & Bommeliam # 10755. 3.
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Per Problema XXII datur RV, diſtantia inter Dor- \\ dracum & Bredam # 7000. 0.
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Per Problema XXVII datur R Q diſtantia inter Dor- \\ dracum & Bergam ad-Somum # 11735. 6.
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Per Problema XXVI datur V Q diſtantia inter Bre- \\ dam & Bergam-ad-Somum # 9414. 7.
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Per Problema XXII datur V L diſtantia inter Bre- \\ dam & Bommeliam # 10887. 2.
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<
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<
s
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echoid-s9184
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xml:space
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">Quibus datis diagonius Q L diſtantia inter Bommeliam & </
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<
s
xml:id
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echoid-s9185
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xml:space
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">Ber-
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gam-ad Somum eruetur hoc modo. </
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<
s
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xml:space
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">In triangulo R L V demitta-
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tur à vertice L perpendicularis L V, in datam diagonium V R.
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</
s
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<
s
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echoid-s9187
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xml:space
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">Et à Q itidem perpendicularis in eandem ſit Q M. </
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>
<
s
xml:id
="
echoid-s9188
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xml:space
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">Cum itaque
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in triangulo R L V tria dentur latera, dabuntur quoque ſegmenta
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R V N V ab angulis ad perpendicularem L N. </
s
>
<
s
xml:id
="
echoid-s9189
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xml:space
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">Atque inde de-
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mum cum in triangulo rectangulo R N L detur baſis recti R L & </
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<
s
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xml:space
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crus alterum R N, dabitur quoque perpendicularis L N. </
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<
s
xml:id
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xml:space
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preserve
">Per ea-
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dem præcepta invenientur ſegmenta M V & </
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<
s
xml:id
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xml:space
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">V R, & </
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<
s
xml:id
="
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xml:space
="
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">perpendicu-
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laris Q M in triangulo R Q V. </
s
>
<
s
xml:id
="
echoid-s9194
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xml:space
="
preserve
">Verum differentia ſegmentorum
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R M & </
s
>
<
s
xml:id
="
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xml:space
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">R N eſt ipſa M N inter ſegmentum inter ipſas perpendicu-
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laris interceptum. </
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>
<
s
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xml:space
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">Continuetur porro perpendicularis Q M uſque
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in H æqualiter ipſi L M, & </
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xml:space
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">connectatur L H. </
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<
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xml:space
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">Erit itaque L H
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parallela & </
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<
s
xml:id
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xml:space
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">æqualis perpendiculari L M, & </
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">angulus H rectus: </
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dantur autem Q M & </
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<
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xml:space
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">M H, datur itaque tota Q H. </
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<
s
xml:id
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echoid-s9203
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xml:space
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">Datur ve-
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ro etiam ipſa M N; </
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>
<
s
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xml:space
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">hoc eſt L H ei parallela & </
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<
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">æqualis. </
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<
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xml:space
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">Quam-
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obrem in triangulo rectangulo L H Q, datis cruribus Q H & </
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<
s
xml:id
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xml:space
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H L, dabitur quoque baſis Q L diſtantia inter Bommeliam & </
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Bredam quæſita. </
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<
s
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xml:space
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">Hujus problematis explicatio in numeris ita
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habet.</
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Si quadratum ab R L # 11720227600.
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