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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 273, page id 1066518432:0301
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DE VIETDDS EX MOTTBOS CORPORVU. L IB. II. 273
C OR OE L A R F u M I.
472. Ouia in hyperbola equilatera L. N EreS AZ, AL de AG
Tunt continue proportionales propter tansentem hyperbolae A, _
ex natura hyverbolae etiam trCS AZ, AL _ rs, adeo ut Ng e. r5
aquentur, crunt, ducta A5, triangula ABM e Asr similia; nam
AX = MN (COnSEF.) = BMI CA ad AL vel AB, SICAE AL vel A5
ad Ag velrs, atque adeo triangula ABM e rsa similia Punt, ac
Per consequens AS ipsi BMI seu etiam tangenti relariae in C Paral-
Tela est, angulusque nas aequabitur illis quem tansens relarix mo-
do nominata, et quantum opus est producta, cum axc AW consti-
tuit, cujus semistis est angulus rsu; unde cum PO sIE lo9-US ratiO-
nIS PA ad LA, PCU PA ad AW, hoc cR, rationis rs ad ru; lequi
tur PO esse log. mum rationis, quam radius habet ad tansentem an-
Sulirsu vel dimidii anguli uAs, in logarithimica, cujus subtansens
par CA radio AI; ec in omni alia logarithimica, sI TUmatUE GUaFEA
provortionalis ad log.micae subtansentem AL, ec ad lOg- Um PEX-
dicta rationis radii ad tansentem semissis anguli uas, manifestabit
ea ordinatam relaria CI in puneto C, E Scilicet anguluS uA5 ~qVIa-
lis fuerit angulo, quem tansens relariae in C producta Cum aXC AW.
Continet.
C O R OL Z A R Y U M TI.
473. Circulus centro B radioque BA descriptus rectam BM pro-
ductam secet in , critque propter tansentem circuli AM dt lCCan-
FeM NISD, MIB: MIA =MA: Mo, PCu 2AB F MO: AMI = AM: MC,
adeoque 2AB + Ma: MI0 = AM: M∞2, e diridendo 2AB: M0 =
2. AB. Mo: NIC= AM: = M∞: Mo, aEquCadco 2AB. M∞ = AN. -
Wo. Innotelcit ergo ex datis AM vel AC ex Ma rel AI parame.
ter velarise AB seu AU.
Porro quia (5. 472.) Ar: rS = AM: AB = 2AMI. Mo: 2AB. M0 =
2AMI. HIO: AM =Mo, CFIE ASVCI AN: Ar = AM + Ma: ZAMI. Mo,
de diridendo AV =Ar vel ru ad Ar = (AM = N∞): 2AM. Mo,
d Ar: rS = ZAM. MO: ANP =M∞, ergO CX XqUO rU: rS = (AM -
Mo): AMI = Ma =AM = MO: AM F Ma = curra AC abscicta ejuIS
AL, ad AC + AT. Vnde, Cum SIE PA: TA =rS: YH = AC + AI:
AC = AI, ex PO 109- us rationis PA ad LA; erit etiam P.O lOg- US
rationis AC + AI ad AC - AI, cujus rationis termini, scilicet 18-
et m
SIC.