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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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HII.
SE CTEOMETRFCA E LEMENTA.
PROPOSITIO LIX.
Onae Maenitudinem definire.
Ouoniam Lunx Distantia angulusque sub quo appatet ex Pla
cedentibus cognita habentur, hoc est (reterente aBC Lunam, cu.
jus centrum L, ∞0 oculum) recta or. e ansulus AOB, husuque
proinde semissis AOL; in triansulo r a0 rectansulo ad a inre
tur La Luna Semidiameter: vel brevius
Sic: Diameter Lunx eAt ad Diametrum Ter
ra ut Semidiameter L UMa aPPaFCNSCOS.
nita ad notam Luna Parallaxin horizon
talem, uti patet. Luna autem ipta est ad Ferram (Der PrOP. XVIII.
EI. XH.) in triplicata ratione sux Diametri ad Diametrum Perra,
ac proinde detinitur. O. H. V.
Sacellitum Torialium ee Saturniorum Magnicudo similiter dofi-
nietur ex cognitis Distantia ec ansulo quem quisque subtendit.
PROPOSTTTO LX.
Vancitatem materiae in Luna definire respectu duantitatis
materice in Terra.
Delionet s Solem; aBc Orbem magnum, in cuslls circumteren.
tia commune centrum graritatis Telluris r e L una L. circumfer-
tur, Sicut L ib. I. explicatum eAt. Sit a
centrum iltud noto Tempore Nori.
lunii cujusdam; B idem illud centrum
Prove notum TempUS OuadraLEX eN.
er. insequentis: AEque ex datis duo.
bus hisce Temporibus dabuntur (ver
PFOD. AVTIT. L Ib. TIT.) Solis LOCa Cx
punctis a ex B rila: commune enim il.
Jud Terra et Luna graritatis centrum
(PeF PFOD. LXHT. L ib. T.) ita Orbem
masnum peragrat, ut area per radios
ad Solem ductos abscilta tine temporibus proportionales. ObTer.
ventur Loca Solis et Luna c Tellure in + vila. Noti erso sunt an-
Suli B+S, ASF: Sed prius innotuit ASB; ergo non latebit BSF. In
triansulo isitur BSt datis angulis BFS, BSF e latere SB (Oebis
magni lined ex Sole dueta e positione datd, in Terra Diameeris ex
Solis Theoria _ Parallaxi cognita) innotescet e sD latus in iildem
notis menturis: Sed ex Luna Theoria nota cA +V Distantia L una
a Terra; nOta ersO CA (per F. Dat.) ratio inter YV _ FB, ad eoque 
inter BF, BI. POTIO, ex Mechanicis notistimum est candem esse
rationem graricatis Luna versus longinquum Solem ad gravitatem
Terra vertus cundem, hoc est (per CorOL. PrOP. XL. VIT. L ib. T)
Ouantitatis materia in Luna ad Ouancitatem materia in Terra, at
que rectae B+ ad BV rectam; definita ergo est ratio Ouantitatis ma-
cerix in Luna ad Ouancitatem materia in Terra. O. R. F.
BbD2
Tem.
LatD. L1.