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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 262, page id 1066518432:0290
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262 DE V TREBAS ET MIOTEBUS COREORUM. LIB. HI.
punctorum B et 2B positio, atque adeo abscissarum AFL, A2FI, 8
ordinatarum BFI ec 2B2FI magnitudo pendet a positione rectie AI,
seu ab angulo quaesito TAW. Ouomodo vero procalibus hisce cal.
culus debeat subduci, ex sequenti elucelcet corollario.
C OR OE Z A R E V M TV.
458. Sint sindY: nn = AF: 2; vel A2: 2; vel A3: a procurris AC,
A2B e CB, item (dy: nn = BE: aa vel B2: 22; aut B3: aa, respe.
Etu carundem CurVarum AC, A2B, _ CB. sndX: AN = CT: 9 vel
C12: 2, vel C3: 2; respectu carundem currarum, et denique sdx:
An = DF: 2a, vel D2: 2a vel D3: aa. Vbi numeris literis A, B, C13
D postpositi non lunt porestatum indices, sed tantum indicant quam-
Nam Cx CurriS AC, A2B _ BC hoc ordine, quorocensentur, relpi-
ciant in Fgura T25. Unde, quia in A8. 213, OR vel RL. ant III =
e; + 2bem: nn; + eff: nn = e; + 2bem: nM; + (bb = aa). e: nn; quia ff
=bb = aa UE SuPEa (5. 4 5 4.) invenimus. Ilinc area AdIR = e. CD;
+ 2be. AT: a; + (bb = aa). eBF: aa, respeCtU CUEVA AC H8. TI5. AFCA
2A2d2L 2K = c. 2B2FI; = 2bC. A2: a; + (bb -a4). eB2: aa, respectu
CUITVA A2B. ArCA FKL = C. RF; = 2bC. A3: a; + (bb =a4). eB3: aa,
respectu currae CB. Area Aa Yd = e. AD; + 2bC. CF: A; + (bb = aa).
eDF: aa FCSPCCtUCUEVA AC. ArCa 2 A242 Y2I = e. A2II; =2be. C2: a;
+ (bb = aa). eD2: aa; FE(pECtU CUEVX A2B, ec ArCa dYI = C. DHI;
=2bc. C3: 2; + (bb - 44). eD 3: aa; respectu currae BC. ErSO AdLR
+ 2A282L 2I FLK =e. F2K; + 2bC. (AT - A2 = A3): a; + bb -aa.
(BT F B2 =B3) c: aa _ A~Yd + YaI = 242a2 l2 l = e. Il2IL; +
2bc. (C 1 + C. 2 - C3): a; + bb = aa. (DF = D2 = D3) e: aa. Atqui
(5. 453) CA AWV: WVS =ADLR + 2A2DEIER -FLK: AaYd + YaI
2A242 Y2I, ergo criam AW: WS = C. F2R; + 2bc. (AF = A2 +
A3): a; + bb - aa. (BF + B2 =B3) c: a4, 2d e. TI2II; + 2bc. (CF +
C2 -C3): a; + bb - aa. (DF - D2 + D3) e: aa. Vnde, CUM TWV SIE
ad AWV =a: b; habebitur ex xquo analogia, quae suppeditabit aequa-
tionem quaesitam anguli TAV tangentem manifestaturam; sed quia
ip(a A2HI, 2FT2B, FTI, TIB ac per consequens ip(x quoque FID
e 2FID pendent a quantitatibus a e b, quarum haec adhiuc incogni-
ta est, ideo ctiam ip(X A2, A3, B2, B3, C2, C3_ D2 _ D3
ab iisdem pendent; quod calculum perplexum reddit; praelertim
si currx ACL. et A2BP. Fuerinc dissimiles seu dirersx.
433. L6
Fb. L15.