. The first three sections of Newton's Principia; with an appendix, and the ninth and eleventh sections. Edited by John H. Evans . 3. the difference of either series and the area AKa may be madeless tlian any assignable quantity, and therefore, by Lemma i,the hmit of either series is the curvilinear area AKa. Lemma III. If the two series of parallelograms be described in thesame manner as in the last Lemma, except that their bases {.are not all equal, the limit of each series, when their basesare diminished indefinitely, is in this case also the curvi-linear area AKa. For take AF equal to the
. The first three sections of Newton's Principia; with an appendix, and the ninth and eleventh sections. Edited by John H. Evans . 3. the difference of either series and the area AKa may be madeless tlian any assignable quantity, and therefore, by Lemma i,the hmit of either series is the curvilinear area AKa. Lemma III. If the two series of parallelograms be described in thesame manner as in the last Lemma, except that their bases {.are not all equal, the limit of each series, when their basesare diminished indefinitely, is in this case also the curvi-linear area AKa. For take AF equal to the great-est base, and complete the parallel-ogram Fa ; then this parallelogram,?which is evidently greater than thedifference between the two series ofparallelograms, may, by diminishingthe base, be made less than anyassignable quantity. Hence the dif-ference between the two series, and therefore a fortiori, thedifference between each series and the area AKa may be madeless than any assignable quantity; and they tend continuallyto equality, therefore, by Lemma i, the limit of each seriesis the curvilinear area AKa. CoK. 1. If t3edfirstthreesec00newtuoft
Size: 1859px × 1344px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthornewtonisaacsir16421727, bookcentury1800, bookdecade184
