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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 43, page id 1066518432:0071
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DE VFRTBOS ETNOTIBOS CORPORUM. I. IB. I. 43
tem A, Sicut sinus curritatis in currae puncto, cui pocentia appli-
cata est ad radium; ex permutando erit potentia applicata BD ad
sinum curritatis in B sicut A ad radium, id cst, in ratione data.
Elegans haec proprictas ab Acutistimo Ceometra Joh. Bernoulli
primum animadrersa est; sedeam, quantum ex C ommentariis ACadl.
Keg. Scient. Paril. 1706. ad diem 12. Maji apparet, ex alio funda-
mento deduxic.
C OR OL E A R Y U M V.
98. Tisdem acthuc positis, quae in duobus proxime antecedenti-
bus Corollariis, quia (5. 93.) HIF: hF BF: bF = T: Bb (rel 5. 96.)
=A: Bb, erit sFHI: SFh =sBF: sBF =A: Bb, si singula currxe ele
menta aequalia astumta Fuerine. Atqui (8. 87.) PhE, seu omnes ht
vel An, Posita Bn ==bM, respectu currae porrionis ABB aequantur
excessui maximae ordinatarum differentis ac (posto arculo CurrX
Aa = BD = BB == ZZ) supra minimam bMI, id est, ac - bM (vel
etiam, quia de ac a A aequales tunt cum axis C A currae perpendieus
laris est in A) Aa - bMI =Bb -bM; et sbF =sMm =BM - AC (vet
quia Ac hoc casu cranescit prae Aa vel BB) = BM. ErgO SVHI:
Bb -bM =sBF: BM = A: BC. Ubi omnes FFI Ccu sFHL, etsBF
Pertinent ad arcum currae AB1.
Sin verO sFH et sBF pertinuerint ad arcum currae BZ ee tan.
sens hujus arcus in Z axi AC parallela Fuerit, erit ZY = 0, POsITa
ut Cupra Z2 = Bb = BB eC. atque adco 2Y = Z Z =BB; unde shF
vel sNn erit hoc casu (5. 87.) BN =ZY. = BN, e sbF-sMm
YZ = AB = Z y -AIB = BB =AB, atque adeo stHL: BN = sBF: BB-
AB = A: BB.
C OR OL L A R L U M VI
99. diporenla catra abbileala B2. blcac. adc A agalai.
stantes sunt, coincident BFI, BF, ex bh ac bf cranescentibus HIF.
hf; atque adeo omnia ordinatarum elementa BMI, BN ecc. hoc Ca
su requalia sumenda sunt; ac proinde omnes potencia secundum di-
rectiones ordinatarum ex tenacitate elementorum cuirx deriratxe in
ilta hypothesi aequales existent. Propterea, rocando unamquam que
harum aequalium potentiarum B, Het nunc (5. 95.) BF: bF vel
NIm = B: DMI, adeoque cum B ex bM constantes sint hoc casu, erit
sBE: SMm = B: bMI, vel quia (5. 98.) sNm =- BMI -= AO= BM
eranescente AC Dra Aa; fiet sBC: BM =B: bM ec permucando
st