Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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[113] Pag. 542.Fig. 1.♃
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[120] Pag. 550.TAB. XLV III.Fig. 1.* a * b 27. Mart. 1655.
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155428VERA CIRCULI ſequentes Vqab, {aa. /Vqab} ſumma terminorum convergentium a + b
multiplicata in terminum convergentem primum a efficit
aa + ab: & ſumma terminorum convergentium immediate ſe-
quentium nempe Vqab + {aa/Vqab} multiplicata in primum terminum
convergentem Vqab efficit etiam aa + ab; ex his invenienda ſit ſe-
riei propoſitæ terminatio. manifeſtum eſt quantitatem aa + ab
eodem modo fieri à terminis convergentibus a, b, quo à termi-
nis convergentibus immediatè ſequentibus Vqab, {aa/Vqab: } & quo-
niam quantitates a, b, indefinitæ ponuntur pro quibuslibet to-
tius ſeriei terminis convergentibus, evidens eſt ſummam quo-
rumcunque terminorum convergentium propoſitæ ſeriei mul-
tiplicatam in primum terminum convergentem efficere quan-
titatem æqualem illi, quæ fit à ſumma terminorum conver-
gentium immediatè ſequentium multiplicata etiam in primum
ſuum terminum convergentem; cumque duo termini conver-
gentes duos terminos convergentes ſemper immediatè ſe-
quuntur, manifeſtum eſt ſummam duorum quorumlibet ter-
minorum convergentium multiplicatam in primum ſemper
efficere eandem quantitatem nempe aa + ab, atque ultimi ter-
mini convergentes ſunt æquales, & proinde ſit ultimus ille
terminus ſeu ſeriei terminatio z, quæ ſibi addita & in ſum-
mam multiplicata efficit 2 zz, quæ quantitas debet eſſe æqua-
lis quantitati aa + ab, & æquatione reſoluta dabitur z ſeu ſeriei
terminatio {Vq aa + ab,/2} quam invenire oportuit.
Et proinde ad inveniendam cujuscunque ſeriei convergen-
tis terminationem; opus eſt ſolummodo invenire quantitatem
eodem modo compoſitam ex terminis convergentibus primis,
quo componitur eadem quantitas ex terminis convergentibus
ſecundis.
CONSECTARIUM.
Quoniam non refert in problemate ſive termini conver-
gentes a, b, ſint primi, ſecundi, vel tertii & c; manifeſtum

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