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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 241, page id 1040780814:0259
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MP
Lib. TII.
EE GTEOMETRLCE FLKMENTA.
Dat.) etiam data es: Sed datur F. F, ut supra ostentum; et 56 Del L
Dat. dabitur TY magnitudine. Ac politio ejus datur per 28. Dat,
quippe per datum punctum z. medium data positione d magnitu
dine rectae FF, ad datam positione rectam N e Parallela: isitur dan-
tur, tam positione quam magnitudine, recta P. F, TY, diametri
nempe conjusatae Fllipseos per data quinque puncta N, M, L, K, H
transcuntis.
Cas. Il. Sed non sint parallela recta linca MHI, NK, negHC alia
quaeris dua: hX erGO MH, NK (producta Caltem) se mutuo seca
bunt, puta in P Duncto, quod per 25. Dat. dabitur. DuCatuT PeT L
recta P r ipsim _I Parallela, recta NX occurrens in e, quod (per 28.
e 25. Dat.) itidem datum erit: Pritque ratio rectansuli Nox ad
rectangulum L er data; eadem nempe (per Prop
XVIT. Lib. MII. Flem. Conic.) qua est dati rectanguli
N LK ad datU MTFI. Sed rectangulum No x datum
CA cum ejus latera red o dentur, e isitur rect
ansulum Lar etiam est datum: Inde, cum dati
sIt P. O, Per 57. Dat. recta er magnitudine data
eA; sed _ etiam positione, quipue per datum
punctum o data positione recta u parallela;
erso ipsum r punctum, per 27. Dat; cum detur recta or magni
tudo e politio ee altera extremitas e. Ouare derenimus ad calum
priorem; dantur nempe quinque puncta N, M, C, V, H, VeLM, T, K, V.
II, per qua L.lliplis cranseat, talia tamen ut recta duae L. V, V H sint
Parallela. Ex praedictis erso inveniantur istius EIlipseos diametri
conjusata. G. F. V.
Sint duae rectae inter se parallelae AP, MK, in quas incidat
recta linea XCDE,  a quibustibet ejus punctis Xe L. ducan-
tur utcunque rectae L. M C, XP K parallelis Occurrentes In M, C, P
X: dico rectanculum XDL esse adt HDK Ut XCL. adt CCP
rectanculum.
Rectanguli XDL ad rectangulum MDK ratio (per PrOP. XXIII.
Elem. VI.) componitur ex ratione XD ad DK
ee ratione LD ad DM; e ratio rectansuli
XCr ad rectansulum ccp ex rationibus XC
ad cD e L C ad cc. Sed propter parallelas
NDK, GCD CA XD. DK:: XC. CP; ItCM L. D.
DM:: L. C. CC. Cum isitur rationes compo-
ventes aquales sint erunt et composita aequa-
les; hoc CAt, XDL. ad MDK Sicut XCL ad CCP.
Si detur utrumque rectanculum E AF, PBF, eg data sint A e
B puncta; dantur etiam F.  F puncta, posita E ABF recta.
Rectangulo enim P. a F aequale ponatur rectansulum Ba c, dc rect.
ansulo E BF rectansulum ABD: Adeoque, cum (ex Hy P.) P. A F _ B A
dentur, datur (Per 57. Dat.) a C. Similiter ob data L BF CE AB da-
Bitur AD. Propter priorem aequalitatem erit (per XVI. Llem. VI.)
eA. AB:: AC. AP, e per convertionem ratIONIS PA. BF: : 1C. C~.
RursuS.
A