Philosophiae naturalis principia mathematica . amp;^et rec-tangulum KLXKN ut ATxKCxKN, hoc eft, ob datum rec-rangulum ^CXi^iV, ut AT. Atqui areas Hyperbolicae KNOLad reftangulam KLxKNratio ultima , ubi coeunt punda K&Lyeft sequalitatis. Ergo area illa Hyperbolica evanefcens elt ut AT.Compbnitur igitur area tota Hyperbolica ABOL ex particulisKNOL velocitati AT femper proportionalibus , & proptereaIpatio velocitate ifta defcripto proportionalis eft, Dividatur jamarea illa in partes aequales ABMIy IMNK, KNOL, &c. & vi- ¥fz res za8 PHILOSOPHIiE NATURALIS DxMoTu res abfolutae AC, IC, KC, LC, &c. er
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Philosophiae naturalis principia mathematica . amp;^et rec-tangulum KLXKN ut ATxKCxKN, hoc eft, ob datum rec-rangulum ^CXi^iV, ut AT. Atqui areas Hyperbolicae KNOLad reftangulam KLxKNratio ultima , ubi coeunt punda K&Lyeft sequalitatis. Ergo area illa Hyperbolica evanefcens elt ut AT.Compbnitur igitur area tota Hyperbolica ABOL ex particulisKNOL velocitati AT femper proportionalibus , & proptereaIpatio velocitate ifta defcripto proportionalis eft, Dividatur jamarea illa in partes aequales ABMIy IMNK, KNOL, &c. & vi- ¥fz res za8 PHILOSOPHIiE NATURALIS DxMoTu res abfolutae AC, IC, KC, LC, &c. erunt in progrefficme Geo-Co&poRUM, nietrica. ^E.T). Et fimili argumento, in afcenfu corporis, fu-mendo , ad contrariam partem punfti A, aequales areas ABmi, imnky knol, &c. conftabit quod vires abfolutae AC, iC, kC, lC, &c. funt continue proportionales. Ideoque fi fpatia omnia in afcen-fu & defcenfu capiantur aequalia; omnes vires abfolutae /C, kC, iC, AC) ICy KC, LC, &c. erunt coniinue proportionales. ^E.D.. Corol. I. Hinc fi fpatium defcriptum exponatur per aream Hy-perbolicam ABNK; exponi poflunt vis gravitatis, velocitas cor-poris & refillentia Medii per lineas AC, AT 8c ^^refpeftive ;& vice verfa. Corol. z. Et velocifatismaxims, quam corpus in infinitum def-cendendo poteft unquam acquirere, exponens eft linea AC. Corol. 3. Igitur ft in data aliqua velocitate cognofcatur refiften-tia Medii, invenietur velocitas maxima, fumendo ipfam ad veloci- latem PRINCIPIA MATHEMATICA. zic> .tatem iilam datam iti fubduplicata ratiohe, quam habet vis Gravi-tatis ad Medii refiftentiam illam cognitam. .;. j;:^;/;/ • pROPOsiTio IX. theoremAvil Poftthjam demonftrath , dico qmdfi Tangentes angulorumfeB:oris Ctrcularh ^ feBorh H^yperbolki fumantur velo^cttattbus proportionales , exiftente radio jufta magnitudinis : erit tempus omne afcenfus futuri ut feBor Circuli, ^ tempus omne defcenftds prneteriti ut feBor Hyperbola. Reftae AC, qua vis gravitatis exponitur , perpendicularis & ge-qualis d