Exhibeat sphærois oblonga ADC_d_ (_Fig._ 7.) terram fluidam, cujus centrum T, AC axis transversus jungens centra terræ et solis vel lunæ, D_d_ axis minor, EO diameter æquatoris, et XZ axis motûs diurni. Centro T et radio TD describatur circulus BD_d_ secans axem transversum AC in B, et agatur BK perpendicularis in TE: tum ex quovis circuli puncto P ductâ PM ad axem XZ normali quæ secet TA in H, sit P_pr_ circumferentia circuli quam punctum P rotatione suâ diurnâ describit, ad cujus quodvis punctum _p_ ducatur T_p_ et producatur donec occurrat superficiei sphæroidis in _q_; deinde demissâ _p_G perpendiculari in PM, et GF perpendiculari in TA, si per puncta A_q_C transire intelligatur ellipsis ellipsi ADC similis et æqualis, erit ex naturâ curvæ, quia sphærois nostra parùm admodùm differt à sphærâ, _pq_ = AB × ((TF)² ⁄ (TP)²) quamproximé. Jam designet U velocitatem particulæ in terræ æquatore revolventis motu diurno circum axem XZ ad distantiam semidiametri TP, eritque ((U × PM) ⁄ TP) velocitas particulæ P circulum P_pr_ describentis, et cum sit TF =(((GM - HM) × TK) ⁄ TP) + TH, erit motus totius lineolæ _pq_ æqualis _pq_ × ((U × PM) ⁄ TP) = ((U × AB × PM) ⁄ (TP)³) × (((GM - HM) × (TK)²) ⁄ TP) + TH, adeoque summa horum motuum in circuitu circuli P_pr_, hoc est, motus superficiei inter circulum P_pr_ et sphæroidem in directione T_p_ contentæ, æquabitur circumferentiæ hujus circuli ductæ in ((U × AB × PM) ⁄ (TP)³) × (((TK)² × (PM)²) ⁄ 2(TP)²) + ((TK)² × (HM)²) ⁄ (TP)²) - ((2TK × HM × TH) ⁄ TP) + (TH)²) sive quia est HM. TM ∷ TK. BK, et TH. HM∷ TP. TK, scribendo D pro circumferentiâ circuli BD_d_, æquabitur ille motus quantitati ((U × AB × D) ⁄ 2(TP)⁶) × ((TK)² × (PM)⁴ + 2(BK)² × (TM)² × (PM)²). Deinde horum motuum summa in toto circuitu globi collecta, hoc est, motus totius materiæ globo BD_d_ incumbentis prodibit æqualis ((U × AB × DD) ⁄ 32) x ((3(TP)² - (BK)²) ⁄ (TP)²). Ubi planeta in plano æquatoris consistit, fit BK = 0, et motus prædictus æqualis ((U × 3AB × DD) ⁄ 32). Motus autem globi QPR circa eumdem axem est (uti facilé demonstratur) ((U × TP × DD) ⁄ 16), adeoque motus terræ totius fit ((U × TP × DD) ⁄ 16) + ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²), qui cum idem semper manere debeat, denotet V velocitatem in superficie æquatoris terrestris ubi planeta versatur in plano æquatoris, eritque ((U × TP × DD) ⁄ 16) + ((U × 3AB × DD) ⁄ 32) = ((U × TP × DD) ⁄ 16) + ((U × AB × DD) ⁄ 32) × ((3(TP)² - (BK)²) ⁄ (TP)²); unde scribendo 1 pro TP quatenùs est radius ad sinum BK anguli BTK, habetur V. U∷ TP + (3AB ⁄ 2) - ((AB × (BK)²) ⁄ 2). TP + (3AB ⁄ 2), indeque, quia minima est altitudo AB respectu semidiametri TP, U - V. V∷ AB × (BK)². 2TP, et U - V = V × ((AB × (BK)²) ⁄ 2TP): pro V autem patet scribi posse velocitatem angularem terræ mediocrem quia ab eâ differt quam minimé et ducitur in quantitatem perexiguam ((AB × (BK)²) ⁄ 2TP), et quia tempora revolutionum terræ circa centrum suum sint reciprocé ut