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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 75, page id 1066518432:0103
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DE VTREBOSET MOTTDOS CORPOROM. L IB. I. 75
circa arem DA deseripta intellisatur curra quaecunque algebraica
L. FTh: descriptoque luper ordinata ejus AL. quadrante L. MO cir.
culi, ex quolibet hujus circumterentixe puncto M agatur quaedam
MHI parallela axi AD, currae L. HI alicubi occurrens in El subter
ordinatam AL, per currae L. HI punctum II tansens Ha ducta in-
celligatur axi occurrens in s, e ordinata FIF. axi AD perpendicu.
laris, in qua, ordinata HIF ad alteram axis partem procracta, lumatur
ubique P.a = Tubtangenti Bo, adco ut puncta a fucura sint in qua.
dam curra A=, cujus subtangens sit in ejus puncto a linea Ro, du-
cta Scilicet tangente 15. Ouibus poltis, si in altera Agura (37.) an-
sulus AON ubique fuerit ad angulum MAL, uc unitas ad quemlI-
bec numerum policirum ex rationalem n, atque in Aisura 37. Jongi
cudo DN semper aequalis fuerie abscisae DE. in Agura 38. manite.
um, singula puncta AY locatum iri in curra algebraica AUn; quan
doquidem omnia haec puncta algebraice detiniri polsune, cum sectio
anguli in ratione numeri ad numerum omnino geometrice heri pol.
Cic. Jam, sicur ex alia acque alia curra L. H alia atque alia AN ori-
tur, ita quaelibet curra AN aliquam generatricem, L. II admictet,
adeo uc hac curra considerata duntaxar in genere, absquemlla atten-
tione ad particularem aliquam speciem, etiam suppeditare poNIE
omnes pomibiles curras AAn. Ldcirco, cum canon generalis quaeri-
cur, quo lex graritatis rariabilis in omnibus curris alsebraicis deter-
minetur, res co deducetur, ut inveniatur formula Tolicitationum
centralium C Pro hac curra generali ANV, quatenus ea ex curra iti-
dem generali ex alsebraica LII resultat. In hac rero disquisitione
ita porro eMt procedendum.
TI. ANumto Scilicet in curra L FLejus elemento FTh, Per punctum
B aGANEuT Bn X hm rectis AHI _ HIM aequidistantibus, ac ductis
per puncta M, m Secantibus AS, AS; centro A dt radio AX =DP
in Agura 37, delcriptus sic arculus Xa, quo het ut, quoniam (se-
cundum hypothesin) ang. ADNV: ans. MAL = L: n, eriam ODO:
NAm vel XAX, hoc est arculus 90 sc ad arculum Xa SicuF F ad n.
Duibus positis (C arguo.
TII. Prianoula similia l  plabe De (MM): 69(tli)
=FA: AC (FTI), ex triangula similia AMC et Mmu, dant (18
(Ma): NIm =GM: AL (AM) _ MIm: Z∞ = AL (AM): AX (DP)
ac denique, num. L. hujus Xa: O0 =n: F, ergO Cx se quo ec Per com-
positionem rationum, het FC: O0 = n. FA. GM: AC. DP (vel quia
ob triangulorum AOM ec ALS similicudinem CML: AC = L S: AL.)