Full text: Volumen secundum. Opera geometrica. Opera astronomica. Varia de optica. (2)

107. PROP. XXXV. PROBLEMA.
Rectâ per datum punctum in diametro ductâ,
ſemicirculum in ratione data dividere.

Sit ſemicirculus A D G, cujus diameter A G, centrum E,
punctum in diametro datum B. ſupponatur factum quod
jubetur; ſitque recta B D ſemicirculum dividens in ratione
data: quoniam datur ſemicirculi menſura & ratio in qua
dividitur, igitur datur ejus portio nempe D B G. Sit recta
B D, z: ex datis rectis B D, B E, E D, innoteſcunt tri-
angula D E B, D E F, D E G: deinde ſit ut D E F una cum
D E G ad D E G ità duplum D E G ad trapezium circum-
ſcriptum D E G H: & poſitis primis terminis convergenti-
bus D E G, D E G H continuetur ſeries convergens poly-
gonorum complicatorum, ſecundum circuli proprietates ſæ-
pius repetitas, donec conveniens fuerit approximationem ad-
hibere ita ut exhibeatur ſector D E G, qui una cum trian-
gulo D B E æquatur portioni D B G cognitæ, cujus æquatio-
nis reſolutio manifeſtat ignotam quantitatem z ſeu rectam
B D: reliqua patent.

107.1.

TAB. XLIV.
fig. 2.

Idem problema eodem omnino modo reſolvitur in ellipſe,
hyperbola vel earum ſectore dato.

108. SCHOLIUM.

Si quis prædictorum problematum mechanicam deſideret
praxim; non difficile erit calculum, approximationem,
& æquationis reſolutionem ſecundum vulgatas Geome-
triæ practicæ regulas quodammodo imitari, multa talia
problemata poſſem hic reſolvere ope analyſios & noſtræ ſe-
ricrum convergentium doctrinæ, quæ antea impoſſibilia æſti-
mabantur: ſed dicet fortè aliquis has reſolutiones non eſſe geo-
metricas; reſpondeo, ſi per geometricum intelligatur praxis

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