Full text: Volumen primum. Opera mechanica (1)

Producto axe à parte verticis, ſumatur B E æqualis B D,
& jungatur E A, quæ parabolam A B C in A continget. Porro ſecetur A D in G, ut ſit A G ad G D ſicut E A ad
A D. Et utrisque ſimul A E, D G æqualis ſtatuatur recta
H. Item trienti baſis A C æqualis ſit recta L, & inter H
& L media proportionalis inveniatur K. qua tanquam radio
circulus deſcribatur. Is æqualis erit ſuperficiei curvæ conoi-
dis A B C. Hinc ſequitur, ſi fuerit A E dupla A D, ſu-
perficiem conoidis curvam ad circulum baſeos fore ut 14 ad
9. Si A E tripla A D, ut 13 ad 6. ſi A E quadrupla A D,
ut 14 ad 5. Atque ita ſemper fore ut numerus ad numerum,
ſi A E ad A D ejusmodi rationem habuerit.

65.1.

De linea
RUM CUR-
VARUM
EVOLUTIO-
NE .

66. Sphæroidis oblongi ſuperſiciei circulum æqualem
invenire.

ESto ſphæroides oblongum cujus axis A B, centrum C,
ſectio per axem ellipſis A D B E, cujus minor diame-
ter D E.

66.1.

TAB. XIII.
Fig. 4.

Ponatur D F æqualis C B, ſeu ponatur F alter focorum
ellipſeos A D B E, rectæque F D parallela ducatur B G,
occurrens productæ E D in G. centroque G, radio G B,
deſcribatur ſuper axe A B arcus circumferentiæ B H A. In-
terque ſemidiametrum C D & rectam utrisque æqualem, ar-
cui A H B & diametro D E, media proportionalis ſit recta
K. Erit hæc radius circuli qui ſuperficiei ſphæroidis A D B E
æqualis ſit.

67. Sphæroidis lati ſive compreſſi ſuperficiei circulum
æqualem invenire.

SIt ſphæroides latum cujus axis A B, centrum C, ſectio
per axem ellipſis A D B E.

67.1.

TAB. XIII .
Fig. 5.

Sit rurſus focorum alteruter F, diviſâque bifariam F C
in G, intelligatur parabola A G B quæ baſin habeat axem
A B, verticem vero punctum G. Sitque inter dimatrum D E,
& rectam curvæ parabolicæ A G B æqualem, media pro-

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