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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 110, page id 1041163592:0144
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HIGVHIII
1.0
DTITLOSOPMLME NATVRALIS
PROPOSITIO XXXVI PROBLEMA XXV.
Corporis de loco dato a cadentis determinare Tem-
pora descensus.
Super diametro A5 (dictantia corporis a cen
ero sub initio) describe Semicirculum  D S, UE 8
huic aequalem Semicirculum OR HI circa centrum
S. De corporis loco quoris C’erige ordinatim ap-
plicatam CD. Punge SD, e arcae ASD aequa-
lem constitue sectorem OS K. PatCE PEF PFOP.
XXXV, quod corpus cadendo delcribet spacium AC
eodem Tempore quo corpus aliud uniformiter cir-
ca centrum S orrando, describere potest arcum
OR. d. F. F:
PROPOSITIOXZZMI. PROBLEMA XEVI
Corporis de loco dato sursum vel deorsum projecti definire Tempora
ascensus vel descensus.
Exeat corpus de loco dato  lecundum
lincam ASC cum velocitate quacunque.
In duplicata ratione hujus relocitatis ad
unitormem in C irculo velocitatem, qua cor-
pusad interrallum datum Se circa centrum
S revolri Postet, cape GA ad = AS.
Si ratio illa est numeri binarii ad unita-
cem punctum  infinice distat, quo ca-
Tu Parabola vertice S, axc SC, latere quo-
vis recto describenda cAt. Patet hoc per
PFOP. XZZEV. Sin racio illa minor vel ma-
Jor est quam 2 ad 1, priore casu Circulus,
Dolteriore Llyperbola rectangula super di-
ametro S A describi debet. PAtCE PeF
PFOP. XRXITT. Tum centro s, intervallo
aequante dimidium lateris recti, describatur
Circulus TTKk, ec 2d corporis alcenden-
tis vel descendentis loca duo quaevis Cr, C,
erigantur perpendicula CFY, CD Occurren-
tia Conica Sectioni vel Circulo in lac D.
Den
DE MOrD
CORDOROM