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# Title: Nicolai Mercatoris Holsati, è Soc. Reg. Institutionum Astronomicarum Libri Duo, De Motu Astrorum Communi & Proprio, Secundum Hypotheses Veterum & Recentiorum præcipuas; Deqve Hypotheseon ex observatis constructione (shelfmark Leibn. Marg. 63)
# Folio 147, page id 820424455:0169
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Sect. 2..
ASTRONOMLL
perrIT, PTOUT _E AX TuNE PArEeS TRCCEHECTIMX PeXAGCHMX
TOTIUS ATCX P P XIP. Ouidni enim liceat torum tempus
Periodicum, vel eoram aream ellipleos dividere, itidem yt
Deripheriam, in parres 360, quas deinde gracus appelli-
lemus, inque parres minuriores subdiricamus? Ouidui li-
Ceac etiam nomen Anomalix tribuere vel tempori, vel arca,
eque ac arcubus vel angulis : quandoquidem nomina impo-
nuncur rebus pro arbirrio Inventorum. Carerum ne diffi-
eile videarur cuiquam invenire quancirarem arex P AC, Lan-
quam portionis ellipscos; invenir Keplerus huic rei reme-
dium, dum pro ellipseos porcione Pa C substimie porcio-
hem circuli P AK, exrensa videlicet per PlaneraM C Per-
Dendiculari ad lineam apsidum C. L (quam ordinatam vo-
CanC) ee concinuara ad peripheriam usque circuli circum-
eripei in R; dust aque A R. DiCO, Partem circuli P A K
ad corum circulum, habere candem rationem, quam parS
ellipleos P A C habec ad eoram elliplin. Dirisa enim parre
circuli P A K in duas porriones PL. I, _ RL A; icem-
que parte ellipseos P A C. in duas portiones P L. C _ C L A;
PrIIEIM arCA P R L ad arcaM P C L eandem habec racionem,
quam R L ad C I, vel quam D B ad F B eandemque adeo
quam ordinara lingulae circuli, ad ordinatas singulas ellip-
leos; Siquidem area tam circuli, quam ellipleos constar
quali ex innumeris ordinatis vrraque luis, quas eandem om-
nestras ad illas rationem obrinere diximus. Unde non modo
lemicirculus P D X ad semiellip(in P P Z eandem habet rg-
tionem, quam DB ad F B; sed _ torus circulus ad roram
elliplin, _ porrio circuli P K L. ad porcionem ellip seosP C L
Candem vero _ Triangula RL A _ C L A rarionem h2-
ben, quam ipsorum alcicudines R L _ C L; ergo _ com-
DOLITA L A R area ad compolIcAI P A C, eandem habeF FA-
tionem, quam R L ad CL., vel quam inceger circulus ad
incegram ellixlin; porestque pro superticie P AC substicui
uperticies P AR, dummodo eadem opera pro inceera el-
ipa substimmatur inceger circulus, qui nunc incellisatur re-
terre anomaliam mediam, dividendus similicer in 360 gra-
lus, uc ancea dividebatur ellip(Is.