Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . B 2 and 20 A COMMENT ok tl& and £=:{/; therefore the area SPp zz ^al% —24. # 5*tf£-i*SJ, and the fluent BSP = ± - njL & zaa 4 4a X area EHQT — n— •, and corre&ed, BSP zz 6ad a±+™!x area RTQ-^Ifl. But RTQ = iz 4 40 6<2# i- ixs. Whence BSP = »«& + — X !^~|^ #*&* 20* + nrij nnls w tf# , nss A ,/2 —?. x — + Ana 6## 8# <?# 8 ,. .j. 8««j , ax , nss __ ^ dividing, z — —_ x — +
Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . B 2 and 20 A COMMENT ok tl& and £=:{/; therefore the area SPp zz ^al% —24. # 5*tf£-i*SJ, and the fluent BSP = ± - njL & zaa 4 4a X area EHQT — n— •, and corre&ed, BSP zz 6ad a±+™!x area RTQ-^Ifl. But RTQ = iz 4 40 6<2# i- ixs. Whence BSP = »«& + — X !^~|^ #*&* 20* + nrij nnls w tf# , nss A ,/2 —?. x — + Ana 6## 8# <?# 8 ,. .j. 8««j , ax , nss __ ^ dividing, z — —_ x — + -T- — T3 2<?? 4- ann 8 6 the mean anomaly. Whence z zz T H- 4^^ + 2»» 4»J + XL-— x \ becaufe T is near- 6a* -j- 3^»^ ly z= 2, and 2W zz But fince n is very fmall by fuppofition, 2 = T+~x 4- — X 4** 3«J \ Where the quantities JUL X , and -— X » are fmall arches to be added to ;*3 Now D zz c — £L zz -L x ^ — f; and D xa a AO + OD zz_Lxaa~cc=— = ?;« nearly, becaufe c zz ^ very. near. Therefore : rad (1): : nn : qaa, and or Y ^in fmall arches) zz 11 j alfo V : Y : : S T : rad (0, and V zz Y x P/tncufia .20. B. I. the PRINCIPIA. %i = — X , which is our firft term, orFig-\aa ^ 24. his firft equation. Again, : rad (1) : : 4^D or l?f x « — ^: 3AOa or 3^, and = l^f x^ — c. But^+ir 3a X~a — c — aa — cc zz nn, and a — c zz. 2_ a + c ± ™ nearly, therefore z= 15 x n— = H!f2# 3^5 2tf 30+ zz H3, nearly. Alfo X : Z : : STP: rad (1). And3^3 X = Zx S?fJ = — X S?f5, which is the fecond 3aiterm, or his fecond equation. And when T is a- bove 90°, then , and V will be negative, and<CBHP — T-f-X+V. He calls, Y or -^- the greateft firft equation, becaufe it is greateft when s 1, and TZZ450. And Z or JL the greateft fecond equation, becaufe 3^ the greateft it can be is when * z 1, orT zz 900. SECT. VII. [Pr. 33, to AB the prin
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