Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

CHRIST. HUGENII meratoris partis alterius e carentes, omitti poſſe, cum quan-
titates inde ortæ eædem utrinque eſſent futuræ ideoque de-
lendæ. Quare in terminis poſterioribus ii tantum ab ini-
tio ſcribendi erant in quibus unum e, omiſſis omnibus reli-
quis, ut æquatio hîc futura ſit iſta
{bx 3 - ccxx - 2bccx/bcc + x 3 } = {3bexx - 2ccex - 2bcce/3exx}

Hîc jam multiplicationes alternæ per denominatores in-
ſtituendæ eſſent ad tollendas fractiones. Verum examinan-
do diligentius quænam futura ſint harum multiplicationum
producta, aliud adhuc compendium inveniemus, & nec
ſcribendos quidem omnino eſſe terminos poſteriores: quia
enim deſcribuntur ex prioribus mutato x in e, præpoſito-
que numero dimenſionum ipſius x, non difficile eſt col-
ligere ex ſolis terminis prioribus quænam futura ſint iſta
omnia producta.

Ita quoniam propter - ccxx in prioribus, habetur -
2ccex in poſterioribus; & propter x 3 in denominatore prio-
rum, in poſteriorum denominatore eſt 3exx; facile per-
ſpicitur utraque producta ex - ccxx in 3exx & ex -
2ccex in x 3 , quæ ſunt - 3ccex 4 & - 2ccex 4 , eaſdem
literas habitura, ſed diverſos numeros præpoſitos 3 & 2,
idque inde fieri quòd in termino ccxx unam dimenſio-
nem minus habeat x quam in termino x 3 . Itaque & au-
ferendo poſtea ex utraque parte æquationis, - 2ccex 4 , ap-
paret ſuperfuturum - ccex 4 à parte terminorum priorum. Quare ab initio hoc ſciri poteſt, multiplicando tantum in
terminis prioribus - ccxx numeratoris in x 3 denomina-
toris, unumque x in e mutando, ac productum ſimplex ſcri-
bendo; quia differentia dimenſionum x in iſtis duobus ter-
minis eſt unitas.

Eadem ratione producta ex - 2bccx in 3exx, & ex -
2bcce in x 3 , quæ eaſdem literas habent, ſunt enim -
6bccex 3 & - 2bccex 3 , habebunt numeros præpoſitos di-

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