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Some Considerations

of Mr. Nic. Mercator, concerning the Geometrick and direct Method of Signior Cassini for finding the Apogees, Excentricities, and Anomalies of the Planets; as that was printed in the Journal des Scavans of Septemb. 2. 1669: which Considerations are here delivered in the Latine Tongue, wherein they were written by the Author, as chiefly regarding the Learn'd in Astronomy, viz.

Clarissimi Cassini Methodus

Investigandi Apogéa, Excentricitates & Anomalias Planetarum, breviter Exposita & Demonstrata.

SUpponit Cl. Cassinus, ad Planetam in Ellipsi moventem extendi ab utroque foco duas rectas, quarum altera sit medii, altera autem veri motûs linea. Constructio porro talis est;

Fig. II. Left Centrum Concentrici A B C D E.

B L D est Diameter.

B A, B C, B P, sunt intervalla apparentia.

D E, D F, D Q, sunt intervalla mediorum motuum.

B E, B F, B Q; item D A, D C, D P, sunt lineæ rectæ.

B E secat D A in H; B F secat D C in G; B Q secat D P in R.

R H G est linea recta.

B I est perpendicularis ad R H G.

I est Centrum Ellipseos.

L I est Excentricitas.

I O = L I.

O est focus, circa quem ordinatur medius motus; L, circa quem verus.

I M = I N = L B.

M est Apogéon; N, Perigeon; BLM Anomalia vera.

Demonstratio.

I. Illustrissimus ac Reverendiss, Sethus Wardus, quondam in Celeberr. Acad. Oxon. Professor Astronomiæ Savilianus, nunc Episcopus Sarisburiensis, in Examine Astronomiæ Philolaicæ, edito Oxon. A. 1653. c. 6. docuit Methodum, ex data Anomalia media Planetarum, investigandi veram; quæ est hujusmodi:

Fig. III. C, est Centrum Ellipseos AEP: F, focus, circa quem ordinatur medius motus. S, focus, circa quem ordinatur verus motus. A, Apogéon. P, Perigeon, E, Erro sive Planeta. APE, Anomalia media. ASE, Anomalia vera. PET, linea recta, E T = S E. S T est linea recta.

In △ ○ S F T dantur, 1. S F distantia socorum: 2. F T = F E + E S = A P. 3. A F T, angulus externus, sive Anomalia media, æqualis summæ angulorum FST & T. Ergo inveniri potest FSE, sive Anomalia vera, æqualis differentiæ Angulorum FST & T. Nimirum