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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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6
ASTRONOMLE PHXSTCA
L. ib. L.
Y Cst ad F Sicut orea SBP ad aream SB p; sire ut illius duplum
SP BD ad hujus duplum S p = B d. Positâ erso, locorationis F ejus
BRLSPGXbaq
SegrBDq et v BreSe quBDQ ire V ad v SicutBR ~ SP9.
B ag ad Br = SP9Y BD9; id cA, (applicando ad BR X Br,) sicut
Spg 2 bd4 44 SPGLBDG
r
SPg L BDg
BR. Vis isitur in e ad stendens eA reciproce ut
ep Solidum (C. nascens rel eranesCenS. Ouod erat demon-
Atrandum.
GOROLLARTOM.
Onde, sidetur figura quaevis, (ut Axp.) ee in ea punctum s, ad quod
Vis centripeta dirisitur; inreniri potest Lex Vis centripeta, qua
corpus a cursu rectilineo perpetuo retractum in fisura illius peri-
metro detinebitur, eamque revolvendo describet; modo Vis haec
componatur cum idonea Vi secundum Agura tangentem impresta.
Ouippe L ex quaesita est (per PrOP. hanC ZXXVII.) ut Vis sit reci.
proce ut nascens Solidum 3Pqr BD
tandum. Fsujus rei dabimus exemplum illustrius ab ipla rerum na-
tura pecitum.
PROPOSTTTO XXXVII LEMMA.
TFlipsin a eT, cujus foci s e F, tangat recta L P X in puncto
 quovis e, e huic per centrum c ducatur par allela diameter LX
rectae Se, focorum alterutrum (ut 5) eo contactus punctum juncentis
portio F. e inter dictas paraltelas interjecta, aequalis est Fllipsis
semiaxi majori c A.
Per focum alterum i’aucatur L.H ad PR parallela, ipsi se occur.
rens in H. Ouoniam (Per PrOP. XIVITI. Lib. 3. FI. Conic. Mpollo-
nii) anguli FPZ, HPR sunt aequales, _ hisce alterni P FH, PH F
aequantur; unde P _ aqualiS P F.
RursuS (per II. Hl. 6.) Crit SF aqua
lis F H, quia S c aequalis cF; cumque
Se Sc disterentia rectarum PS, PH
erit eadem e difterentia iplarum PS.
PF; _ P. H semi difterentia carundem.
Ft isituE P P (consata nempe ex mi
nore e semi ditterentia) aequalis eAt se
misumma ipTaTUM PS, PF. Sed (DeT
Prop. LTI. Lib. 3. Fl. Conic.) recta
SP, PF simul sumpex aequantur axi majori: Ouare de semitumma
iplarum hoc est, ipsa PP) semiaxi majori c a aequalis cst. Ouod
exat demonstrandum.
PRO