Ceva, Giovanni
,
Geometria motus
,
1692
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lius motus deſcribentis curuam parabolicam, cuius baſis
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ad axem eius habet eandem rationem, quam duplus axis
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propoſitæ hyperbolæ ad ductam illam
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inter
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eiuſdem hyperbolæ aſſymptotos interiectam. </
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Tab.
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5.
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fig.
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2.</
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">Hyperbolæ IRS ſit centrum H, ſemiaxis HI, aſſymptoti
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HT, NH, et SN parallela HI; tùm ducta HM ſecunda dia
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metro hyperbolæ, intelligatur deſcriptio parabolæ AFD;
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itaut duplus axis hyperbolæ, hoc eſt quadruplum ipſius
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HI ad NT eandem habeat rationem, quam DB baſis pa
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rabolæ ad BA axim eiuſdem. </
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">Dico quadrilineum HISM
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eſſe imaginem velocitatum, iuxta quam motu compoſito
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deſcribitur parabola AFD; & cum ſit homogenea imagi
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nibus HILM, HTM, eſſe quoque rectangulum HDLM ad
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imaginem ipſam HISM vt recta CA ad curuam AFD.
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">Fiat rectangulum ACDB, et HM ſit tempus, quo curritur
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vtrunque latus AB, AC, nempe axis AB motu grauium
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iuxta imaginem triangulum HTM, alterum verò latus AC
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æquabili motu iuxta imaginem rectangulum HILM, quod
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quidem erit HILM; etenim AB ad ſpatium AC eſt vt ima
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go triangulum HMT ad imaginem rectangulum HILM,
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ſcilicet eſt vt MT ad duplam HI, vel vt NT ad quadru
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plam HI, quemadmodum poſuimus. </
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lineam, quæ curritur iuxta illas imagines motu compoſito
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parabolam eſſe, cuius diameter AB, & baſis BD; & pro
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pterea erit ipſa AFD (nam vnica tantum parabola ex
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datis AB, BD poſitione, ac magnitudine, axi ſcilicet, ac
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baſi dari poteſt) Ducatur nunc à quolibet puncto F dictæ
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parabolæ rectæ FE, FG parallelogrammum conſtituentes
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AEFG; & P ſit momentum, quo mobile punctum inueni
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tur in F. </
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">Habebit inibi ipſo temporis momento P veloci
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tatem PQ iuxta directionem GF, ſunt verò iſtæ directiones
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ſibi ipſis perpendiculares; ergo recta, quæ diameter eſſet
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rectanguli AEFG, & ob id potentiâ æqualis duabus PK,
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PQ erit gradus velocitatis, quem mobile habet momen-</
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