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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 427, page id 1040780814:0445
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ib. 1
exo Cd
TrianB
InuTII
ItaP
1ria1B
nrel
1
1d
ritL
disten
XVI
etd P
sit;
11
Orted
Pat
OI.
qud
l
teM
rtet
L. Ib. V.
_E GTEOMETRLCE PLEMENTA.
4.27
clinet potius rersus B quam a, propter rationem supra allatam;
nempe quod error minor exit si c distat ab r rersus e, quam si inde
distat versus A.
CiOROLLARTUM 2.
Si sermenti rertex rnon multum distet à Parabola vertice prin-
cipali X, nec punctum c ab V, recta
Sc ex ipso Parabola foco s educta, di-
videt chordam aB in y fere in ratione
Temporum quibus Cometa arcus AC
e cvdescribit. Ouod si sradmodum
Fuerit magna respectu ipsius M V, exit
Mo ipsius ertripla: Nam in ilto casu
rCCta SeC, SVV sunt pro parallelis
habendae; adeoque (per Prop. II. FI.
VI.) Me cA ad erlicut mCad aV; hOC
Cst, ex constructione, ut 3 ad T.
CiOROLL ARTUM 3.
Iisdem manentibus, erit OF aequalis 3e5 F 3MV. LTat p C
Structionem SE = 2SC, ad eOque EF. = 3SC, hOC CA, 6F. = 35 F3,
si ero ab utrague parte auferatur OC, erit OF = 35a + 20c: Sed
ob ec, rr ParallelaS, eC eA ad rV sieut m c ad M V, hoc CAt, sicut
3 ad 2; Quare 22C = 37V: C r. V aequalis mr, cum ansuli rMr
MVV sint aequales, quia recta sr ei mr aequales ansulos Faciunt
cum recta tansente Parabolam in V, qua (per ProP. XLVI. Lib. 1.
Conic.) est chorda a B Parallela, ideoque 3M r = 20C; _ isitur OF.
305 + 3M V. Si politio rectae a B paululum mutetur, erunt pra
cedentia omnia etiamnum proxime rera.
PROPOSITTO ZIZ. LLMMA.
T in ParabOla BAP, Cujus focus S ducta chorda AB abscindatur
Seementum aV B, cujus vertea V, diameter vu chordae occur-
rens in puncto medio M, e ex M ad AB excitetur normalis MF
rectae Z. V ad aB parallelae occurrens in L, e compleatur paralleto
grammum YIMK; coeuntibus punctis re M, sive nascente se
mento aV B, diazonalis rX producta in S incidit.
Nam (per PrOP. XVI. Lib. Y. Flem. Conic.) recta L. F Parabolam in
rcontinsit, unde angulus svL. aqualis est
anguloM VI: Sed quia parallelosrammum
MEYI eA rectangulum, anguluS XIY eAt
aqualis angulo MVT; C isitur angulus
XEr aqualis ansulo SVE, idcoque (PeL
PrOP. XXVIIL. FV. 1.) TK Parallela CA ad YS,
atque hoc semper: cocuntibus isitur punctis +ecV, hoc eAt, coeun.
tibus punctis M e V, recta EX productâ per focum S transit. O. F. D.
CiOROLLARTUM.
Hinc sequitur, quod si ab aliquo Parabolae puncto c, sesmenti
AnH 2