Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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centrum eſt perpendicularis ad
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eg
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parallelum ipſi
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bd,
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erunt an
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guli
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ace. acg
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inter ſe æquales. </
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<
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ica. lcn
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ex conſtructione ſimilia; & angulus
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ica
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æqualis angulo
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lcn:
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quibus ablatis ex
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ace. acg
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anguli reliqui
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ecf. mcn,
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incidentiæ
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& reflexionis inter ſe ſunt æquales. </
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THEOREMA IX.
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Motus Trianguli Iſogoni ſi ne〈que〉 ad planum, ne〈que〉 ad baſim ſit per
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pendicularis, ad angulos inæquales reflectit.
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<
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>In 3 figurâ triangulum
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abc
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occurrat plano habens latus
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ac
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eidem parallelum:
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ſitq;
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Iinea hypomochlij
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cd,
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& linea ad eam
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perpendicularis
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ef:
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eritq;
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grauitas mouens centri Quadratum
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ef:
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plaga autem huius complementum quadratum
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go.
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quod
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quidem habetur, ſi lineâ
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gf
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ſectâ bifarium in
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p,
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eo centro de
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ſcribatur ſemicirculus
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gof,
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ſumaturq;
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chorda
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fo
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æqualis
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fe:
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nam
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chorda reliqua
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og
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dabit illud quadratum. propterea quòd gra
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uitas tota ſit quadratum
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fg.
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fiat
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ut
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fo
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ad
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og,
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ita
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fi
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ad
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fb;
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erit motus reflexus in lineâ
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fh
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diametro parallelogrammi
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fb hi:
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angulus autem reflexionis
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ifh:
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quem dico angulo
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acd
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eſſe in
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æqualem. </
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<
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>Quia angulus
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age
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externus cſt maior angulo in
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terno
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ecg,
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æqualis autem angulo
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ofg;
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propterea quòd
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uterq;
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aſſumpto angulo communi
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ogf
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facit rectum: eſt verò huic
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angulo æqualis angulus reflexionis
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hfi;
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quòd ſimilia ſint trian
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gula
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gef: hfi:
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erit ergo æqualis
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quoq;
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angulo externo
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age:
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ac
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proinde maior interno
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acd
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angulo incidentiæ. </
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<
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figurâ centrum
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e
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cadat intra lineam hypomochlij. cùm igitur
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centrum gravitatis contineatur in hypomochlio, erit plaga per
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fecta:
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huius lineæ
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ea. ef. ec:
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ac proinde per 1 theor: hu
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ius motus reflexus in lineâ
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eb.
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Quia ergo angulus reflexionis </
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