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

CHRIST. HUGENII ſiones quantitatis incognitæ in termino numeratoris diffe-
runt à dimenſionibus ejuſdem incognitæ quantitatis in ter-
mino denominatoris. Signa autem affectionis productis
ſingulis præponenda qualia lex multiplicationis exigit, quo-
ties dimenſiones quantitatis incognitæ plures ſunt in termi-
no numeratoris quam in termino denominatoris: at quo-
ties contra evenit, contraria quoque ſigna productis præ-
ponenda; quæ denique omnia æquanda nihilo. Sint, exempli gratiâ, inventi termini priores, quos maxi-
mum deſignare velimus, iſti {bx 3 - ccxx - 2bccx/bcc + x 3 }, ubi nul-
la eſt quantitas cognita. Hîc ergo, ſecundum regulam, multi-
plico terminos omnes numeratoris primum per bcc, prioris-
que producti ex bx 3 in bcc, ſcribo triplum, quia bx 3 ha-
bet tres dimenſiones quantitatis incognitæ x, bcc verò
nullam. Secundi producti ex - ccxx in bcc ſcribo duplum,
propterea quod in - ccxx duæ ſunt dimenſiones x, & in
bcc nulla. Tertium verò productum ex - 2bccx in bcc ſcri-
bo ſimplex, quia in - 2bccx & bcc differentia dimenſionum
x eſt unitas. Tribus autem hiſce productis vera ſigna af-
fectionis adſcribo, quoniam dimenſiones x in terminis nu-
meratoris excedunt eas quæ in termino bcc, quippe quæ
nullæ ſunt, ita ut tria hæc producta ſint
3bbccx 3 - 2bc 4 xx - 2bbc 4 x.

Jam porrò terminos omnes eoſdem numeratoris duco in x 3 ,
terminum alterum denominatoris, primumque productum ex
bx 3 in x 3 ſcribere omitto, ſive per 0 multiplico, quoniam
eædem dimenſiones utrobique ſunt ipſius x, ideoque diffe-
rentia nulla. Secundum autem productum ex - ccxx in
x 3 ſcribo ſimplex, quia in his terminis differentia dimenſio-
num x eſt unitas. At tertium productum ex - 2bccx in
x 3 ſcribo duplum, quia differentia dimenſionum x in his eſt
2. Signa verò affectionis productis hiſce duobus adſcribo
contraria iis quæ requireret lex multiplicationis, eo quod di-

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