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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 88, page id 1066518432:0116
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88 DE V ERTBOS ET MIOTTBDS CORDOROM. LIB. I.
rem AS. Verum quia ductis per puncta A ex S tansentibus AY et
ST occurrentibus in T, lxe tansentes crunt aequales, etiam uS X
quabitur Ss, atque adco perpendicularis Sm bifariam diridet basim
su crianguli iloscelis sSu, adco ut su sII = 25m, at que adeo Pe = su;
idcirco quadrilaterum Fesu, in quo latera oppolita FW et es TunE X
quidistantia et reliqua oppolita latera Le, us sequalia, crit paralle.
losrammum, atque adco lS = es = u5 = S5, hinc (5. 87.) omnes dit.
Ferentiae PS = es seu excessus maximx FS supra minimam, quae in
vertice A nulla est, hoc est Cola ES aequatur omnibus Ss Peu arcui
circuli AS e Sc ubique, propterea TlOchrOna quaeSITa BE A est Cy.
clois ordinaria, cujus lemibasis BC aequatur peripheria lemicirculi
ASC. Duod erat inreniendum.
C O R O L L A X Y U M.
280. Tempus descensus per crcloidis arcum BF, erit ad tem-
Dus per axis partem aequealtam CFI, sicut arcus CS circuli gene-
ratoris interceptus inter parallelas BC e FHI, ad subtenlam CS
ejusdem arCuS. Nam propter parabolam AKD e circulum ASC,
eACI(OD): OP(HIK) =OA: AS, atque adeo anguliICP et C AS
vel CSTI aequales Tunt, adeo ut SC e CI in directum jaccant.
Tam guia (5. 272. R. TT.) EBF = NV. ang. TCD erit ceiam FBR = N.
ang. SAC, atqui (5. 229.) anguluS SAC = 2 ArC. SC: : CA = aFC.
CS: CA, ergO FBF = N. arC. CS: CA, rel quia N = Y (OA: A2),
exit FBF = arC. CS. VOA: C AV Aa, aut quia O A = 2C A, ACF FBF =
2. aFC. CS: V (2C A. A2) = 2arC. CS: OD, propter parabolam ARD;
_ FOHI (5. 15T.) =V (2CTT: A2) nulla habita ratione mastae cOrpO.
ris, cum hoc loco mobile non conferatur cum aliis; sed unum idem-
que corpus tantum in linea curra BF A vel in axc CA moveri in
telligatur, adeo ut loco ipsius M, qua Formulam articuli citati L5T.
inoreditur, poni pOsit unitaS. Sed tCFI =V (ZCFI: Aa) reducitur
ad FCTI = Y (4 AC. CTI: 2C A. A2) =2CS: CD; ergO EBE: FOTI,
Ut Fractio Zacc. Cs Elubc. C5
cD a
co; atque adeo tempus per BF est ad cempus
Per CFI sicut arcUS CS ad ejus subtenlam C5.
Propterea tempus per totam semiercloidem BF. A ad tempus
delcentus mobilis per axem ejus C. A se habet, ut semicircumterentia
CSA ad diametrum C A. prout primum ab Flusenio, dein a mul.
tis aliis demonstratum est; sed ex fundamentis ab hisce nostris muI.
cum direelIs.