Bošković, Ruđer Josip
,
Theoria philosophiae naturalis redacta ad unicam legem virium in natura existentium
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SUPPLEMENTA. §. III.
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<
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<
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ditiones rema-
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nere inde
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r-
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minationem
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parem cuicun-
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que acceſſui ad
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quaſvis cur-
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vas in punctis
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datis quibuſ-
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vis.</
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nibus, ſatisfieri primis quinque conditionibus curvæ . </
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<
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ro poteſt valor Q variari inſinitis modis ita, ut adhuc im-
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pleat ſemper conditiones, cum quibus aſſumptus eſt. </
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<
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inde arcus curvæ intercepti interſectionibus poterunt inſinitis
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modis variari ita, ut primæ quinque ipſius curvæ conditiones
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impleantur; </
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<
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conditionem impleant.</
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<
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<
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<
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tur, ut trans-
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eat per quævis
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earum puncta.</
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rumcunque curvarum, modo ſint ejuſmodi, ut ab aſymptoto
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A B perpetuo recedant, adeoque nulla recta ipſi aſymptoto pa-
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rallela eos arcus ſecet in pluribus, quam in unico puncto, & </
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in iis aſſumantur puncta quotcunque, utcunque inter ſe proxi-
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ma; </
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<
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">poterit admodum facile aſſumi valor P ita, ut curva per
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omnia ejuſmodi puncta tranſeat, & </
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<
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dis variari ita, ut adhuc ſemper curva tranſeat per eadem illa
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puncta.</
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<
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<
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præſtandum.</
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=r, & </
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<
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">a ſingulis ejuſmodi punctis demittantur rectæ pa-
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rallelæ A B uſque ad axem C' A C, quæ debent eſſe ordina-
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tæ curvæ quæ ſitæ, & </
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<
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di ordinatas dicantur M1, M2, M3 &</
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<
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ordinatæ N'1, N'2, N'3 &</
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<
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<
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quantitas Az
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+ Bz
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+ Cz
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.</
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<
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</
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<
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">Tum alia aſſumatur quantitas T ejuſmodi , ut evaneſcente
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z evaneſcat quivis ejus terminus, & </
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<
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munis valoris P, & </
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<
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">valoris R + T, quod facile fiet, cum in-
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noteſcant omnes diviſores quantitatis P . </
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<
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= R + T, & </
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<
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">jam æquatio ad curvam erit P - Ry - Ty
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= o. </
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<
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">Ponantur in hac æquatione ſucceſſive M1, M2, M3 &</
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pro x, & </
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<
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<
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<
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tiones numero r, quæ ſingulæ continebunt valores A , B,
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C, . </
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<
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<
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<
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<
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">G, unius tantum dimenſionis ſingulos, numero pa-
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riter r, & </
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<
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">præterea datos valores M1, M2, M3 &</
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<
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N2, N3 &</
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<
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cientes ipſius z.</
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<
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<
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terior.</
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minabuntur illi valores A, B, C . </
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<
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">G, qui ſunt pari-
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ter numero r, aſſumendo in prima æquatione, juxta metho-
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dos notiſſimas, & </
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<
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do in æquationibus omnibus ſequentibus, quo pacto habebun-
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tur æquationes r - 1. </
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<
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">Hæ autem ejecto valore B reducentur
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ad r - 2, & </
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<
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">ita porro, donec ad unicam ventum fuerit, in
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qua determinato valore Q, per ipſum ordine retrogrado de-
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terminabuntur valores omnes præcedentes, ſinguli in ſingulis
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æquationibus.</
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<
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<
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<
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